Publications of the Astronomical Institute i i \ i i s - m f - - i 1 359

of the Czechoslovak Academy of Sciences

Publication No. 67

10
EUROPEAN REGIONAL
•™ ASTRONOMY MEETING OF THE IA U
Praha, Czechoslovakia August 24-29, 1987

INTERPLANETARY
MATTER

Edited by

ZDENEK CEPLECHA, PETR PECINA

Proceedings, Vol. 2

1 987
INTERPLANETARY
MATTER
A selection of 6 images of the nucleus of Comet Halley. The resolution Improves
from 600 to 90 m per pixel, (c) Max-Planck-Institut fuer Aeronomie. Courtesy H.U.
Keller.

This image of the nucleus of Comet Halley is composed of 7 images taken from Giotto
on 13 March 1986. Several features such as a mountain, a chain of hills, a crater
or jets can be seen in the originals. (c) Max-Planck-Institut fuer Aeronomie.
Courtesy H.U. Keller.
 Publications of the Astronomical Institute
of the Czechoslovak Academy of Sciences
Publication No. 67

10
EUROPEAN REGIONAL
ASTRONOMY MEETING OF THE IA U
Praha, Czechoslovakia August 24-29, 1987

INTERPLANETARY
MATTER

Edited by

ZDENGK CEPLECHA, PETR PECINA

Proceedings, Vol. 2

1987
CHIEF EDITOR OF THE PROCEEDINGS:
LUBOS PEREK

Astronomical Institute
of the Czechoslovak Academy of Sciences
251 65 Ondfejov, Czechoslovakia
 T A B L E OF C O N T E N T S

Preface J-Q

a.Rahe: Review of Results on Halley's Comet (invited) 1u

B. Valnicek: The Phobos Mission (invited) 7:

C o m e t s

W.M. Napier: The Origii and Evolution or the Oort Cloud (Invited) 13*
A. Carusi, G.B, Valsecchi: Dynamical Evolution of Short-Period Comets (invited) 21 ""
A. Carusi, t. Kresak, E. Perozzi, G.B. Valsecchi: Long-Term Resonances and Orbital Evolutions 29 -
of Halley-Type Comets
V. Padevet: Planetary Origin of Fireballs and Comets 33 *"
H. Ricknan: Physical Evolution of Comets (invited) 37 •-
M. Sole, E.K. Jessberger, P. Hsiung, 3. Kissel: Halley Dust Composition 47 "
S. Ibadov: On the Phenomenon of Anomalous Distribution of Metal Atom Emission in Cometary Heads 51 ^
Kh.I. Ibadinov, A.A. Rahmonov, S.A. Aliyev: Laboratory Investigation of Thermal Conductivity 55 '
of Dust Crust Models on the Ice Comet Nuclei Surfaces
3.F. Crifo: Are Cometary Dust Mass Loss Rates Deduced from Optical Emissions Reliable? 59*•
D. Mohlmann: Image Processing of VEGA-TV Observations 67 ~
O.M. Mamadov: Spectral Observations of Comet Halley (1982 i) in Dushanbe 71 <-
3. Svoren: Pre-Perihelion Photometry of Comet Halley at the Skalnate Pleso Observatory 75 u
R. Falciani, M. Festou, L.A. Smaldone, G.P. Tozzi: Spatial Distribution of Neutral and Ionized Gas 79 *-
in the Halley Comet Coma After the Perihelion
F. Esin-Yilmaz, F. Limboz, G.A. Tammann: The Tail Length of Comet Halley from Historical Data 83'
3. Zvolankova, D. Kubacek, E.M. Pittich: The Plasma Tail of Comet Bennett 1970 II 87l
B. Stecklum, W. Pfau: Production Rates of Gases and Solids in Cornet P/Halley During the 1986 Apparation 91
D.A. Andrienko, V.N.Vashchenko, I.I Mishchishina, I.D. Zosimovich: Solar Corpuscular Radiation 95 <•
and Outbursts of Cometary Brightness

A s t e r o i d s

P. Paolicchi, V.Zappala: Collisional Evolution of Asteroids and Asteroid Families (invited) 101
Z. Knezevic', B. 3ovanovic': Asteroid Short-Periodic Perturbations: Critical Eccentricity and 107 L
Inclination for Analytically Derived Mean Semimajor Axes t
P. Farinella: Physical Properties of Asteroids (invited) 111^
A. Cellino, V. Zappala, M.Di Martino: Effects of Non-Triaxial Shape ori the Determination of the 121
Asteroid Spin Axis Direction Via the Amplitude-Magnitude Method
D. Olsson-Steel: Meteoroid Streams Associated with Apollo Asteroids: Evidence from the Adelaide 125'
Radar Orbit Surveys
L.K. Kristensen: Present Status of Photometric Parameters of Asteroids 131 -
K. Ziolkowski: Unusual Motion of Amor 133 (.

M e t e o r s
Prof. Dr. 3. Hoppe Distinguished Meteor Physicist Died f?9
P.B. Babadzhanov, Yu.V. Obrubov: Evolution of Meteoroid Streams (invited) ' 141
C. Froeschle, H. Scholl: Resonance Intermittance Causes the Gravitational Splitting of Meteor Streams 151
D. Olsson-Steel: The Dispersal of Meteoroid Streams by Radiative Effects 157
3. Stohl, V. Porubcan: On Applicability of Meteor Stream Membership Criteria 163
V. Porubcan, 3. Stohl: The Meteor Complex of P/Encke 167
M. Hajdukova: Particle Density Variations Along the Orbit of the Halley Meteor Stream 173
A. Hajduk: Dust Production of Comet Halley with Account of Large Particles Contribution 177
G. Cevolani, A. Hajduk: Activity of the Meteoric Complex of Comet Halley 179
P. Pecina: Meteor Physics (survey paper instead of invited paper of O.W. Hughes) 183
P.B. Babadzhanov, N.A. Konovalova: On the Light Pulsation of Bright Geminids According to 189
Photographic Data
D. Olsson-Steel, W.G. Elford: The True Height Distribution and Flux of Radar Meteors 193
M. Simek: Mass Distribution of Underdense Meteor Echoes: Selection of Basic Data 199
B.A. Lindblad: The IAU Meteor Data Center in Lund 201
P. Pecina: Meteoroid Deceleration and the Fresnel Characteristics 205
Z. Ceplecha: Numbers and Masses of Different Populations of Sporadic Meteoroids From Photographic 211
and Television Records
3. Rajchl: On the Interaction Meteor Complex 217
V.S. Getman: Separation of the Particles During Meteor Flares 221
P.B. Babadzhanov, Z. Ceplecha: Photographic Data of Extreme Precision Evaluated by Exact 223
Single-Body Solution of Meteor Physics
P. Spurny: Some New Aspects in the Positional Reduction of the Photographs Taken by Fish-Eye 225
Objectives

u
I n t e r p l a n e t a r y Dust .

R.H. Giese, B.Kneissel: Distribution of Interplanetary Dust (invited) 231

lB.Knei.sseJ, R.H. Giese: The Dynamics of the Zodiacal Bust Cloud On Account of Optical and 241
Infrared Observations
R. Wallenwein, Ch. Antz, E.K. Jessberger, K. Traxel: Proton Microprobe Analysis of Interplanetary 2*5
Dust Particles
Ch. Antz, M. Bavdaz, E.K. Jessberger, A. Knb'chel, R. Wallenwein: Chemical Analysis of 249
Interplanetary Dust Particles with Synchrotron Radiation
H. Fechtig: On the Source and Structure of Interplanetary Dust Particles 253
E. Criin: Dynamics of Interplanetary Dust (invited) 257
C. Kresak, M. Kresakova: The Contribution of Periodic Comets to the Zodiacal Cloud 265
M. Banaszkiewicz, I. Kapisinsky: Evolution Equations for Interplanetary Dust ,273
3. Svestka, E. Grun, S. Pinter, S. Schumacher: Laboratory Charging of Dust by Electrons and Ions C2^3
R. Dumont, A.C. Levasseur-Regourd: The Symmetry Plane of the Zodiacal Cloud Retrieved from 281
IRAS Data

O t h e r B o d i e s

3. Xanthakis, C. Banos, B. Petropoulos: Probable Periodicities of the 3ovian Atmospheric Activity 287
B. Petropoulos, A.A. Georgakila-: A Reference Model for the Atmosphere of Titan 291

Index of Authors 295

II
 PREFACE

• One of the main topics of the 10th European Regional Meeting of the International Astronomical Union,
held in Prague during 23 - 29 August 1987, was THE COMPLEX OF INTERPLANETARY BODIES.

As the title indicates, the problems in fore-ground were the interrelations, interactions, and evolu-
tionary processes working in different types antf systems of interplanetary objects. The interplanetary
population covers an immense mass range of 40 orders of magnitude and, as a whole, is only detectable
by completely diverse observing techniques, in different environments: comets and asteroids in the inter-
planetary space, from the whole earth; meteoroids in the upper atmosphere, from limited areas on the
earth; and the finest dust in spacecraft-borne detectors. The gaps between the relevant mass ranges are
diminishing with the development of observing techniques, but are still there and attract special atten-
tion. As to the evolutionary scale, the interplanetary population icludes both the most pristine matter
preserved since the formation of the solar system, and the most recent products of intricate disinte-
gration processes. The physical and dynamical history of each minute dust particle goes far back to its
original, much larger parent body.

The spacecraft encounters with comet Halley have supplied us with a wealth of information, and
many new exciting results. However, at the same time they have posed many new problems, awaiting a correct
explanation. With this in view, it became obvious that our meeting should concentrate on more general
problems, rather than on the properties of individual objects (such as their orbits, lightcurves, spectra
etc.), which provide just the fundamentals for further studies.

Owing to the rapidly increasing interest in this research area, stimulated by the first cometary
missions and current advances in measuring and computing techniques, our topical sessions attracted over
100 participants from 20 different countries. From among the plenary meetings, with still higher atten-
dance, two were devoted to problems closely related to our area. Their proceedings are included at the
beginning of this volume. The invited discourse by 0. Rahe summarizes the main results of the worldwide
cooperative efforts connected with the recent apparition of COMET HALLEY. It covers both the unique
ensemble of space missions and the ground-based International Halley Watch. The review of the PHOBOS
MISSION, presented by B. Valnicek, describes another unique space project to be realized in the near
future, in broad international cooperation.

The main part of this volume consists of the papers presented at six half-day sessions on the COMPLEX
OF INTERPLANETARY BODIES. One of them was held jointly with the topical session on the RESONANCES; for
the papers given there, the reader is referred to the volume of TS-3 of this series. Altogether , 11
invited reviews, 29 contributed papers and 17 posters were presented. Since there was a great interest
in having these proceedings published as quickly as possible, we had to put a strict deadline for the
receipt of the camera-ready typescripts. Papers which did not meet this requirement had to be left out,
to our regret.

For the same reason, there was no refereeing of the manuscripts, and only a few papers were retyped
by the editors. At the end of each paper, and abbreviated discussion record is appended, as prepared
from the question and answer forms. We believe that, in spite of its conciseness, this record may give
the reader a complementary insight into the so far unresolved problems and controversial implications.
However, it is clearly insufficient to let him feel the beautiful cooperative atmosphere of the meeting,
created by all its participants and guests.

The other topics of the 10th European Regional Meeting of the IAU were published in four other vol-
umes. The survey of all papers presented and published in all five volumes are contained in "Program
of the Meeting and Directory of the Proceedings", Publication of the Astronomical Institute of the Czecho-
slovak Academy of Sciences, No. 65.

It is a most pleasant duty to thank all the colleagues who have contributed to the success of the
meeting. The members of the organizing panel P.B. Babadzhanov, Z. Ceplecha, P. Pecina, P. Farinella,
H. Fechtig, and H. Rickman have significantly contributed to the outline of the program, and alternated
in chairing the individual sessions. The authors of the invited reviews, as identified in the Table of
Contents, have outstandingly summarized our present state of knowledge in the individual research areas,
and the authors of the contributed papers have presented many important new results and ideas. The local
organizers Z. Ceplecha and P. Pecina have excellently managed all the organizational and editorial work;
in preparing this book they were assisted by P. Spumy, D. Pivova, L. Surkovicova, H. Ceplechova and
C. Zavrel.

The kind sponsorship of the International Astronomical Union, the European Physical Society, and
the Czechoslovak Academy of Sciences, and their-generous travel grants to a number of participants, are
also acknowledged with thanks.

C. Kresak

III
 REVIEW OF RESULTS ON HALLEY'S COMET
Jurgen Rahe
Solar System Exploration Division
NASA Headquarters
Washington, D.C., U.S.A.

ABSTRACT
Since U s recovery 1n 1982, Comet Halley has been the focus of an unparalleled
global scientific effort of exploration. Remote and 1n-s1tu measurements were
conducted from the ground, from Earth orbit, from Venus orbit, from inter-
planetary space, and from the comet itself. Many discoveries, such as the
presence of an unexpectedly large and dark nucleus or the abundance of organic
m a t e r i a l , have led to major .changes 1n our ideas about the general nature of
comets. In this report, results of various studies are summarized.

INTRODUCTION p a r t i c l e s w i t h i n about 20 min b e f o r e

c l o s e s t a p p r o a c h , r e o r i e n t i n g the
During i t s 30th h i s t o r i c a l l y recorded s p a c e c r a f t s p i n a x i s by n e a r l y one
and f o u r t h p r e d i c t e d a p p a r i t i o n 1n d e g r e e , b u t c a u s i n g no damage t o
1986, Comet H a l l e y was observed from e i t h e r s p a c e c r a f t or I t s scientific
the ground by m o r e t h a n 1,000 instruments. For t h e Vega s p a c e c r a f t ,
p r o f e s s i o n a l a s t r o n o m e r s i n over 50 a s e v e r e d u s t p a r t i c l e bombardment
different countries. In a d d i t i o n , t h e damaged 4 5 * o f t h e s o l a r c e l l s f o r
comet was v i s i t e d by s i x s p a c e c r a f t Vega 1 and 8 0 * f o r Vega 2 w e r e , but
f r o m f o u r space a g e n c i e s , c a r r y i n g a most experiments c o n t i n u e d t o operate
t o t a l of f i f t y s c i e n t i f i c after the encounters. Giotto
instruments. a p p r o a c h e d the nucleus t o w i t h i n 600
km, but dust impacts caused a n e a r l y 1
In s p i t e of t h i s tremendous e f f o r t , i t degree n u t a t i o n of the s p i n a x i s
i s e v e n now - 1 8 m o n t h s a f t e r the s h o r t l y b e f o r e the e n c o u n t e r . Several
comet's p e r i h e l i o n passage- i m p o s s i b l e e x p e r i m e n t s c o n t i n u e d t o work a f t e r
t o present a coherent p i c t u r e of Comet t h e f l y b y but were shut down when t h e
H a l l e y ; i n s t e a d , t h e r e are more pieces p o s t e n c o u n t e r d a t a g a t h e r i n g phase
o f a s t e a d i l y g r o w i n g puzzle and I t was c o m p l e t e d .
w i l l t a k e many more m o n t h s , i f n o t
y e a r s , b e f o r e a comprehensive p i c t u r e The s p a c e c r a f t encountered t h e comet
i s avai T a b l e . a t d i f f e r e n t t i m e s and a t d i f f e r e n t
d i s t a n c e s , r a n g i n g f r o m about 600
Results of the Comet Halley ( G i o t t o } t o about 30 m i l l i o n . (ICE) km.
measurements from the ground and from The t i m e o f the i n - s i t u measurements
space have r e c e n t l y r e p e a t e d l y been i n the cometary environment t y p i c a l l y
reviewed. For more detailed l a s t e d a few h o u r s f o r each s p a c e -
r e f e r e n c e s , the reader i s r e f e r r e d t o craft. The c o m e t ' s heliocentric
t h e P r o c e e d i n g s of the H e i d e l b e r g d i s t a n c e r a n g e d f o r t h e time of the
Symposium " E x p l o r a t i o n o f H a l l e y ' s e n c o u n t e r s from 0.8 t o 0.9 AU. More
Comet" (ESA SP-250, 3 volumes; 1987) t h a n 100 s c i e n t i f i c i n s t i t u t e s and
and the s p e c i a l issues of Nature (May over 500 s c i e n t i s t s from a l l over the
1986) and Astronomy and A s t r o p h y s i c s , w o r l d were i n v o l v e d i n these m i s s i o n s .
1987. Since at the present
conference s p e c i a l emphasis was g i v e n A l l s p a c e c r a f t were t a r g e t e d t o the
to the r e s u l t s of ground-based nucleus on t h e sunward s i d e , the s i d e
m e a s u r e m e n t s , i t was d e c i d e d t o where a l l a c t i v i t y o r i g i n a t e s . The
d i s c u s s i n t h i s paper e s p e c i a l l y w i t h cameras onboard the two Vega and the
the i n s i t u measurements. G i o t t o missions obtained f o r the f i r s t
time d i r e c t images of a c o m e t ' s
IN SITU MEASUREMENTS nucleus. I t a p p e a r e d as a s i n g l e
s o l i d body of i r r e g u l a r elongated
H a l l e y ' s Comet moves i n a r e t r o g r a d e shape -comparable t o a g i a n t peanut or
o r b i t around t h e Sun which i s I n c l i n e d p o t a t o , both l a r g e r (about 16x8x8 km)
at 162 degrees t o the e c l i p t i c p l a n e . and darker (albedo lower than 4%) than
A l l s p a c e c r a f t f l y b y s occurred around p r e v i o u s l y t h o u g h t , making i t one of
.the t i m e the comet c r o s s e d the the d a r k e s t o b j e c t s in the solar
ecliptic plane on M a r c h 1986 system. Only a few o u t e r solar
( d e s c e n d i n g node) w i t h v e l o c i t i e s of s y s t e m o b j e c t s , such as J u p i t e r ' s
a t l e a s t 68 km/sec r e l a t i v e t o t h e s a t e l l i t e Almethea, the dark side of
comet. At such speeds, even f o r t h e S a t u r n ' s s a t e l l i t e I a p e t u s , and the
d u a l bumper s h i e l d e q u i p p e d G i o t t o r i n g p a r t i c l e s of Uranus are as b l a c k .
s p a c e c r a f t , an i m p a c t w i t h a 0 . 0 0 1 Gas and dust emanate from o n l y a few
gram p a r t i c l e could cause c o n s i d e r a b l e r e g i o n s f r o m t h e s u n l i t side of the
damage t o t h e i n s t r u m e n t s or change nucleus.
the o r i e n t a t i o n of the s p a c e c r a f t s p i n
axis. The Japanese s p a c e c r a f t S u i s e i An i m p o r t a n t new r e s u l t is the
was h i t by t w o mi 1 1 i g r a m - s 1 z e d d e t e c t i o n of i n f r a r e d r a d i a t i o n from
 t h e n u c l e u s r e g i o n by t h e infrared The 1 8 0 / 1 6 0 r a t i o o f 0 . 0 0 2 3 agrees
spectrometer o n b o a r d Vega 1 . The w i t h the t e r r e s t r i a l v a l u e , but t h e r e
c o r r e s p o n d i n g t e m p e r a t u r e was f o u n d t o a p p e a r s t o be a l a r g e uncertainty
be a b o u t 3 0 0 K, i.e. a b o u t 100 K a b o u t t h e 12C/13C v a l u e .
higher than the s u b l i m a t i o n
t e m p e r a t u r e of water i c e , indicating Another surprise was the high
t h a t t h e n u c l e u s s u r f a c e i s c o v e r e d by abundance of very small particles.
a insulating l a y e r of d a r k , porous Ground-based o p t i c a l and infrared
r e f r a c t o r y substance which is o b s e r v a t i o n s had p r o v i d e d practically
consistent with the observed low no i n f o r m a t i o n a b o u t p a r t i c l e s s m a l l e r
albedo. The t h i c k n e s s o f t h e d u s t t h a n 0 . 1 m i c r o n and t h e i r number was
l a y e r i s unknown and c o u l d r a n g e f r o m e x p e c t e d t o be v e r y s m a l l . The d u s t
l e s s t h a n a cm t o s e v e r a l t e n m e t e r s ; detectors onboard the spacecraft
i t might in f a c t vary considerably f o u n d , h o w e v e r , t h a t t h e i r abundance
f r o m one a r e a t o t h e o t h e r . increased c o n s i d e r a b l y towards smaller
s i z e s , and G i o t t o measured s p e c k s o f
Before the in s i t u measurements, m a t t e r o f 1 0 e x p ( - 1 7 ) gram w h i c h were
cometary dust was t h o u g h t to be perhaps only a millionth of a
composed of c e r t a i n carbonaceous c e n t i m e t e r - i . e . , a b o u t 100 a t o m s - i n
c h o n d r i t e s , i . e . rare stony diameter
m e t e o r i t e s w h i c h c o n t a i n s m a l l amounts
of c a r b o n . A d e t a i l e d a n a l y s i s of the ^ W h i l e m o s t a s t r o n o m e r s were p r o b a b l y
d u s t p a r t i c l e s r e v e a l e d t h a t t h e mean c o n v i n c e d t h a t t h e comet n u c l e u s must
elemental abundances of several be mainly water ice and dust
t h o u s a n d g r a i n s are very similar to p a r t i c l e s , H a l l e y was t h e f i r s t comet
abundances o f C l - c h o n d r i t e s , w i t h t h e in which water was d e f i n i t e l y
e x c e p t i o n of those p a r t i c l e s which are identified. Measurements f r o m NASA's
l a r g e l y made up o f C, H, 0 , and N- Kuiper Airborne Observatory (KAO)
l i g h t e l e m e n t s w i t h a t o m i c masses o f c l e a r l y r e v e a l e d the presence of water
less than 20. The H e i d e l b e r g t e a m and showed w a t e r v a p o r s t r e a m i n g f r o m
i n v e n t e d t h e acronym "CHON" f o r t h e s e t h e n u c l e u s a t v e l o c i t i e s between 0.8
dust p a r t i c l e s . Their density is 0.1 and 1.4 k m / s e c . At t h e t i m e o f t h e
t o 4 g r a m / c c m , and t h e y c o n t r i b u t e up Vega 2 e n c o u n t e r , a b o u t 1.6 t o n s o f
t o a b o u t 1/3 i n w e i g h t t o t h e t o t a l w a t e r were e m i t t e d from the n u c l e u s ;
dust mass. T h e y may f o r m tar-like when Vega 1 passed t h e n u c l e u s , t w i c e
s u b s t a n c e s w h i c h c o u l d be a r e a s o n f o r t h i s a m o u n t was p r o d u c e d , i n d i c a t i n g
the dark n u c l e u s . The CHON p a r t i c l e s t h a t 80-90% o f t h e n u c l e u s c o n s i s t s o f
have c o s m i c abundance i n w h i c h c a r b o n w a t e r i c e and d u s t .
i s a b o u t e i g h t t i m e s more a b u n d a n t
than in carbonaceous c h o n d r i t e s . This
Giotto and t h e t w o Vegas detected
r e s u l t may a l s o s o l v e an o l d p u z z l e :
c a r b o n d i o x i d e , b u t i t had o n l y 2-3%
B e f o r e t h e i n s i t u m e a s u r e m e n t s were
of the water abundance. Measurements
made, o b s e r v a t i o n s indicated that
f r o m IUE and f r o m s o u n d i n g r o c k e t s , on
c a r b o n ( r e l a t i v e t o o x y g e n ) was a b o u t
the other hand, found considerably
4 times l e s s abundant than in the
m o r e CO, a b o u t 10% t h e abundance o f
cosmic abundance. Now i t a p p e a r s t h a t
water. C a r b o n m o n o x i d e and d i o x i d e
t h e m i s s i n g carbon i s " l o c k e d up" i n
v a p o r i z e a t much l o w e r temperatures
t h e CHON p a r t i c l e s .
than water i c e . T h e i r presence c o j l d
e x p l a i n why comets d e v e l o p comas w h i l e
Most of the CHON p a r t i c l e s are still f a r away f r o m t h e s u n . It is
p r o b a b l y composed o f o r g a n i c m a t t e r . i n t e r e s t i n g t o n o t e t h a t most o f t h e
M. Greenberg has shown in the c a r b o n m o n o x i d e does n o t l e a v e the
l a b o r a t o r y t h a t o r g a n i c m a t e r i a l can n u c l e u s i n gaseous f o r m ; i t appears
be f o r m e d o u t o f c o m e t a r y m a t t e r . He to escape instead from the f i n e dust
postulates that submicroscopic particles w h i c h a r e h e a t e d by t h e
s i l i c a t e c o r e s a r e c o v e r e d by o r g a n i c s o l a r r a d i a t i o n in a r e g i o n of about
c o a t e s and i c e . These b u i l d i n g b l o c k s 1 0 , 0 0 0 km. The e x p a n s i o n v e l o c i t y o f
form loosely connected larger t h e gas was d e t e r m i n e d t o 800 m/sec a t
p a r t i c l e s which is in agreement w i t h 2 , 5 0 0 km d i s t a n c e f r o m t h e n u c l e u s ; i t
t h e l o w d e n s i t y f o u n d by t h e dust i n c r e a s e d s t e a d i l y t o 1,000 m/sec a t
experiments. 2 0 , 0 0 0 km d i s t a n c e . I n March 1 9 8 6 , a
coma b r i g h t n e s s o u t b u r s t was f o l l o w e d
The i n s i t u m e a s u r e m e n t s o f t h e d u s t b y a l a r g e f l a r e - u p i n C0+, C02+ and
p a r t i c l e d e n s i t y of about 0.1 to 4 d u s t ; t h e w a t e r p r o d u c t i o n , however,
gram/ccm agree also well with the remained essential constant during
average p a r t i c l e d e n s i t y of 0.25 that time. This observation indicates
gram/sec measured in the meteor t h a t CO and C02 were i n v o l v e d i n t h i s
s t r e a m s o f t h e O r i o n i d e s and A q u a r i d e s o u t b u r s t and t h a t p o c k e t s o f these
w h i c h are b o t h p r o d u c e d by Hal l e y . and s i m i l a r volatile are perhaps
present in the cometary nucleus.
O t h e r m e a s u r e m e n t s f r o m t h e g r o u n d and
The d e u t e r i u m - t o - h y d r o g e n r a t i o is
f r o m IUE c o n f i r m e d t h e s e c o n s i d e r a b l e
estimated t o be b e t w e e n 0 . 6 and
brightness f l u c t u a t i o n s which
<3.8xl0exp(-4), a value which is higher
o c c u r r e d on a v e r y s h o r t t i m e s c a l e .
t h a n t h e one i n t h e interstellar
medium and in the g i a n t planets
J u p i t e r and S a t u r n , b u t w h i c h i s i n Another r a d i c a l , CN, was f o u n d in
g o o d a g r e e m e n t w i t h t h e one f o u n d i n s t r a n g e j e t s w h i c h r e m a i n e d n a r r o w and
t h e a t m o s p h e r e s of T i t a n and U r a n u s . w e l l - d e f i n e d f o r up t o 6 0 , 0 0 0 km b u t
 w h i c h d i d not c o i n c i d e w i t h tha j e t s b r i g h t n e s s v a r i a t i o n w i t h a p e r i o d of
made o f v i s i b l e o u s t . The CN r a d i c a l s 2 . 2 days w h i c h was i n t e r p r e t e d as t h e
apparently d i d n o t come f r o m the r o t a t i o n p e r i o d o f an i n h o m o g e n e o u s l y
n u c l e u s d i r e c t l y but f r o m streams of active nucleus. Measurements from
extremely t i n y (and v i s u a l l y Vega and a l s o f r o m t h e g r o u n d gave t h e
u n o b s e r v a b 1 e ) p a r t i c l e s w h i c h may same r e s u l t and p o i n t e d i o a r o t a t i o n
c o n s i s t o f CHON m a t e r i a l . a x i s not f a r from the o r b i t a l pole
axis. Measurements of other
Combining the results from the b r i g h t n e s s v a r i a t i o n s , on t h e o t h e r
d i f f e r e n t m e a s u r e m e n t s , one f i n d s for h a n d , i n d i c a t e d a r o t a t i o n p e r i o d of
Comet H a l l e y the f o l l o w i n g 7.4 d a y s . The s i t u a t i o n i s p r e s e n t l y
d i s t r i b u t i o n of t h e m a j o r m o l e c u l e s : not completely r e s o l v e d , but it
80? w a t e r , 10 % carbon m o n o x i d e , 32 appears feasible that Halley turns
c a r b o n d i o x i d e , 2.5% m e t h a n e , 1.5% l i k e an e l o n g a t e d p o t a t o e v e r y 2 . 2 .
a m m o n i a c , 0.13. c y a n i d e . days about i t s short axis which is
more o r l e s s a l i g n e d w i t h t h e p o l e o f
B e f o r e the e n c o u n t e r s , t h e d e n s i t y of the e c l i p t i c . The motion is
t h e n u c l e u s m a t e r i a l was e s t i m a t e d t o r e t r o g r a d e , i n t h e same sense as t h e
be a b o u t 1.2 g r a m / c c m . Now i t t u r n e d orbital motion. However, it is
out t h a t the l a r g e r dust p a r t i c l e s are f e a s i b l e that t h i s is only the comet's
aggregates of submicron sized precessional motion and t h a t the
particles. The n u c l e u s must be a b o u t actual rotation period is 7.4 days
h a l f "empty" space, perhaps s i m i l a r t o w i t h t h e . s p i n a x i s s h o w i n g a 77 d e g r e e
f r e s h l y f a l l e n s n o w , and i n s t e a d o f inclination.
calling i t a " d i r t y s n o w b a l l " , F.L.
Whipple c a l l e d i t r e c e n t l y a " d i r t y The i n t e r a c t i o n b e t w e e n t h e s o l a r w i n d
snowdrift" t h a t h a s somehow b e c o m e p l a s m a and t h e c o m e t a r y i o n o s p h e r e can
compressed over time. The low be c h a r a c t e r i z e d by t w o distinct
p a c k i n g d e n s i t y r e s u l t s i n a v e r y low b o u n d a r i e s , t h e bow s h o c k and t h e
heat c o n d u c t i v i t y between the outer c o n t a c t s u r f a c e or i o n o p a u s e . Outside
d u s t l a y e r and t h e i c e - d u s t mixture t h e bow s h o c k , t h e s u p e r s o n i c solar
underneath. wind is undisturbed; inside the
c o n t a c t s u r f a c e , o n l y cometary ions
M a t e r i a l w h i c h i s more v o l a t i l e than are present. Within these two
water is s t i l l present in Halley's r e g i o n s , one f i n d s c o m e t a r y as w e l l as
Comet an.i c a u s e s p r o n o u n c e d a c t i v i t y subsonic s o l a r wind i o n s . Neutral
a t d i s t a n c e s f r o m t h e sun ( 3 - 5 All) p a r t i c l e s can t r a v e l l a r g e d i s t a n c e s
where w a t e r ices are not affected. from the nucleus before they are
One c a n p e r h a p s c o n c l u d e t h a t the i o n i z e d and p i c k e d up b y t h e solar
n u c l e u s has n o t been h e a t e d d u r i n g and wind ( " p i c k - u p i o n s " ) . High f r e q u e n c y
following its formation. S i n c e some A l f v e n waves w h i c h a r e due t o p l a s m a
o f t h e e l e m e n t s and compounds o b s e r v e d instabilities associated with these
i n H a l l e y can have s o l i d i f i e d only p i c k - u p i o n s , were o b s e r v e d o u t t o 10
n e a r a b s o l u t e z e r o , t h e n u c l e u s must m i l l i o n km b y the plasma wave
h a v e f o r m e d i n an a r e a r e a c h i n g f r o m e x p e r i m e n t s o n b o a r d S a K i g a k e and o u t
near t h e o u t e r p l a n e t s t o t h o u s a n d s o f t o 30 m i l l i o n km by I C E .
AU away f r o m t h e m .
At a d i s t a n c e o f 8 m i l l i o n km f r o m t h e
A l t h o u g h m e t h a n e i s a low t e m p e r a t u r e nucleus, the Giotto ion mass
condensate, is was f o u n d to be s p e c t r o m e t e r measured besides solar
abundant in the o u t e r s u r f a c e l a y e r s , wind protons a l s o f r e s h l y ionized
s u p p o r t i n g the idea t h a t the cometary cometary hydrogen atoms. At 1.1
m a t e r i a l i s made up o f low t e m p e r a t u r e m i l l i o n km f r o m t h e n u c l e u s , a bow
pristine solar nebula matter. When shock was r e g i s t e r e d . I n an i n t e r v a l
going around the sun, the outer layers o f 4 0 , 0 0 0 km, t h e v e l o c i t y o f t h e i o n s
a r e l o s t and new f r e s h m a t e r i a l is d e c r e a s e d f r o m 320 t o 260 km, and t h e
exposed. t h e r m a l v e l o c i t y d o u b l e d f r o m 50 t o
TOO k m / s e c . In addition, the
The l a r g e r s i z e o f H a l l e y ' s nucleus directions of m o t i o n of the ions
does not imply that the comet changed c o n s i d e r a b l y : the solar wind
p r o d u c e s s i g n i f i c a n t l y more m a t e r i a l . m o v e s a r o u n d t h e o b s t a c l e comet and
Earlier calculations about the t h e m o t i o n becomes t u r b u l e n t . The
c o n t r i b u t i o n o f c o m e t s t o t h e amount cold cometary ions prevent a
of i n t e r p l a n e t a r y dust in the e c l i p t i c p e n e t r a t i o n o f t h e c o n t a c t s u r f a c e by
p l a n e do a p p a r e n t l y n o t n e e d t o be t h e i o n s and t h e m a g n e t i c f i e l d o f t h e
altered, and t h e q u e s t i o n s t i l l solar wind. The f i e l d lines drag
r e m a i n s t o be a n s w e r e d w h e t h e r c o m e t s around the cometary ionosphere and
a l o n e can s u p p l y t h e interplanetary lead t o t h e f o r m a t i o n of t h e i o n t a i l
d u s t or whether a major contribution w h i c h i s mad'e up o f two h a l f - c y l i n d e r s
from asteroids i s r e q u i r e d as w e l l . with opposite polarity. At the
Ors. Kresak and K r e s a k o v a have c o n t a c t s u r f a c e , the magnetic field
discussed this problem in detail s t r e n g t h a p p r o a c h e s z e r o , and t h e i o n
during t h i s meeting. t e m p e r a t u r e decreases f r o m 2,000 K t o
a b o u t 300 K. The s o l a r w i n d m a g n e t i c
f i e l d cannot penetrate into the
The r o t a t i o n p e r i o d of Halley's.
i o n o s p h e r e , and t h e f i e l d strength
n u c l e u s i s e v e n now n o t definitely
reaches a maximum value of 60
established. The L y m a n - a l p h a i m a g i n g
n a n o t e s l a a t 1 6 , 0 0 0 km d i s t a n c e ( F o r
sensor of S u i s d i e . g . , detected a
 c o m p a r i s o n : t h e t e r r e s t r i a l magnetic
4
field at the poles ,s 60,000
nanotesla, the interplanetary
magnetic f i e l d i s 8 n a n o t e s l a ) .

GROUND-BASED MEASUREMENTS

More than 1000 professional

astronomers i n 51 c o u n t r i e s and
almost 100 0 a m a t e u r astronomers
provided a coherent set of qround-
based o b s e r v a t i o n s of H a l l e y ' s comet,
c o v e r i n g t h e p e r i o d from the comet's
r e c o v e r y on 16 October 1982 u n t i l the
present time. The most i m p o r t a n t
c o n t r i b u t i o n of the International
H a l l e y Watch (IHW) w i l l be t o p r o v i d e
a r e c o r d o f the 1982-1990 a p p a r i t i o n
i n d i f f e r e n t wavelengths and w i t h h i g h
temporal resolution. Ground-based
m e a s u r e m e n t s have substantially
complemented and extended the i n s i t u
" s n a p s h o t " l i k e s p a c e c r a f t data and
provided i n s i g h t into Halley's long-
term e v o l u t i o n and s h o r t - t e r m a c t i v i t y
variations. For i n s t a n c e , o n l y by
combining ground-based brightness
(product of size and albedo)
measurements at the time of r e c o v e r y
w i t h the space-based d e t e r m i n a t i o n s of
t h e n u c l e u s s i . e , was i t p o s s i b l e t o
d e r i v e the n u c l e u s ' a l b e d o .

A h i s t o r i c example of this
c o l l a b o r a t i o n is the "pathfinder"
concept: Targeting a spacecraft close
t o a comet i s a m a j o r problem s i n c e
the nucleus i s hidden by the dust and
gas i n t h e coma. Earth-based
astrometry of H a l l e y ' s nucleus
p o s i t i o n had an accuracy of about 500
km. S i n c e t h e two Vega s p a c e c r a f t
e n c o u n t e r e d H a l l e y ' s Comet b e f o r e
Giotto, a considerably improved
n u c l e u s p o s i t i o n was o b t a i n e d f r o m
Vega w i t h t h e h e l p o f NASA's deep
space n e t w o r k . Giotto achieved a
f l y b y d i s t a n c e o f 600 km w i t h an
u n c e r t a i n t y of o n l y 40 km.

CONCLUSION
When H a l l e y w i l l disappear again i n t o
t h e o u t e r s o l a r system by the end of
this decade - t h e Hubble Space
T e l e s c o p e , however, should be a b l e t o
f o l l o w t h e comet up t o i t s a p h e l i o n
and back t o p e r i h e l i o n i n 2 0 6 1 - i t
w i l l be t h e most t h o r o u g h l y s t u d i e d
comet e v e r . More data has a l r e a d y now
been c o l l e c t e d on H a l l e y than on a l l
o t h e r comets t o g e t h e r .

Th° f i r s t p r e d i c t e d r e t u r n of H a l l e y ' s
Comet d e m o n s t r a t e d t h e power of
s c i e n t i f i c i m a g i n a t i o n and knowledge.
The 1986 r e t u r n triggered an
u n p r e c e d e n t e d and unparalleled
international c o o p e r a t i o n on t h e
g r o u n d and i n space. I t has brought
together the l a r g e s t number of
s c i e n t i s t s ever t o combine e f f o r t s i n
a single astronomical p r o j e c t . It
m i g h t s e r v e as a model f o r future
i n t e r n a t i o n a l c o o p e r a t i v e programs.
 IUC 1 SEPT I OCT 1 NOV 1 PEC i JAN 1 APRl

T7
T 1 1 1 1 [ J

is

BOHUE 'USAI
60UMA INETKERLANDSI
BUS IMETHEHLANDSI
GREEN (USA)
KEITCH lENGLAfW)
UOfmS IUSAI
SEARGENT (AUSTRALIA)
VAN OE WFG (MTHlftlANOSi
LfCNT CURVE BY C.S MORMS/JPl

Light curve of Halley's Comet for 1985-1986, normaliBed to 1 AO (Courtesy C.S.

Morris).

— •
/ > OKI 73
* » UT-OttlO.iZ
•—-^~\ MM M/Q R*1500lan
c
(AMUW

MIS
X, 1 "

20 30 «0 SO GO 20 30 40 50 60
S 32 MASS CHANNEL MASS CHANNEL
SPIN
Z
AVERAGES

-10000 CA '10000 .25000

-25000

Left: Magnetic field and cometary ion observations) within 25,000 km from the
nucleus as measured by Giotto (from ESA BR-27, 1987). 16,400 km before closest
approach (CA), the magnetic field magnitude reached a maximum of 57 nanotesla
(magnetic pile-up region), decreased afterwards rapidly to essentially zero inside
the contact surface at 4,700 km, and increased again after crossing the contact
surface at 3,800 km after CA. At the same tim3, the ion temperature (middle panel)
and velocity (upper panel) decreased. When crossing the contact surface (C), the
temperature dropped by nearly 2,000 K; at the same time an outward flow of cometary
ions with 1 km/sec vss noticed.
Right: Ion mass spectra obtained from Giotto outside the contact surface (top) and
inside (bottom), revealing considerable changes in the Ion composition (from ESA BR-
27, 1987).
 Mass spectra of two dust particles observed from Vega, illustrating the extremes in
the ratio of light elements (C, H, 0, N) to heavier elements (Mg, Si, Fe). In terms
of ion counts, this ratio is 24 for the upper figure and 0.07 for the lower figure
(Courtesy J. Kissel).

12:34 20:18 05:16 ITTIH.M)

Cometary ions observed from Giotto's Implanted Ion Sensor in three different
directions (from ESA BR-27, 1987). The middle panel refers to the direction of the
solar wind: at large distances the solar wind is undisturbed. Closer to the nucleus
the solar wind is decelerated and the distribution broadens. Very close to the
nucleus the solar wind is deflected away from this panel's viewing direction (for
more details, see the special Halley volume of Astronomy and Astrophysics).
 THE PHOBOS MISSION
Boris valnicek
Astronomical Institute of the Czechoslovak Academy of Sciences
251 65 Ondfejov, Czechoslovakia

ABSTRACT
The complex space experiment Phobos will consist of tun space probes carrying more
than twenty experiments each. The primary purpose of tne mission, launched in
June 1988, is the exploration of the Mars satellite Phobos and of the planet itself.
Various methods are used, including landing on the satellite and activation of its
surface minerals by laser beam. During orbiting around Mars, the atmosphere of the
planet will be studied. The secondary purpose is to study solar activity during
the flight from Earth to Mars, gathering informations on solar wind, interplanetary
shock waves, and gamma bursts. Solar X-ray activity will be monitored and solar
corona observed in X-rays; stereoscopic studies of the Sun will be made.
The coordinator of the experiment is the Space Research Institute of the Academy
of Sciences of the USSR, the other participants are from Austria, Bulgaria,
Czechoslovakia, Finland, France, German Democratic Republic, German Federal Republic,
Hungary, Poland, Sweden, Switzerland and ESA.

THE PURPOSE OF THE PHOBDS MISSION

This is the first space expedition in which
a small body of the solar-system will be stu-
died from aboard a spacecraft passing above
the surface several meters only. The Martian
satellite Phobos has been chosen as a object
of studies because it is highly probably
a trapped asteroid body in primordial state
what can give usefull informations about
the conditions in which the Solar system was
formed.
The solution of scientific problems of origin
and evolution of Phobos requires many new
data, which can be obtained by direct measu-
rements. Essential are mass - and isotopic
- composition, different physical characte-
ristics of the surface, as spectral, elec-
trophysical and regolith thickness. The best
solution seems be the use of different dis-
tant research methodes.
Simultaneous study of the planet Mars is sup-
posed. This includes studies of surface, at-
mosphere, ionosphere and magnetosphere.
During all time of the active life of space
probes the parameters of interplanetary spa-
ce and of the solar-wind are registered. The
constant orientation of space-probes Phobos 77/)"
with one axis directed towards the Sun
offers the possibility for the observation Fig. 1
of the Sun.
This will be stable orbit for realization
THE CONCEPTION OF THE PHOBOS-MISSION AND of maximum of measurements (Fig. 2 ) .
THE SPACECRAFT This orbit gives the possibility to descent
at second circular orbit, identical with
Two spacecrafts are prepared fur launch in the aid of correcting engine and following
June 1988 (see Fig. 1 ) . They will reach the laser guiding telemeter for aproximately
Mars in 200 days, at the beginning of 1989 15 minutes to fly over the surface of Pho-
and circulate around the planet on long bos in the hihg-corridor 30-80 meters. Du-
elliptic orbit with pericenter 42P0 km ring this dnort period active experiments
(1 revolution 3 days). After 25 days this or- will be performed. The relative velocity
bit will be changed to the ellipse'with peri- of the spacecraft to the surface of Phobos
center 9700 km for 3D days. Finally, the will be 2-5 meters sec-1.
elipse will be transformed in circular orbit
with 9700 km pericenter (1 revolution
B hours).
 surface of the sa+ellite. During this 20
minutes interval following program must be
realized:
- study of the mass and isotopic composition
of Phobos regolith
- measure the topography and texture of the
surface
- electrophysical, spectral and polarization
characteristics must be determinated.
Following scientific payload will be applied
to perform this program:
laser-beam remote system, secondary ion mass-
-analyzer, radar system and videospectrome-
ter.
a/ Laser-beam mass spectrometer LIMA-D
The possibility to generate accelerated ions
under heating of the surface material is
used (see Fig. 4 ) .

MS
Fig. 2
For this mission a new generation of spacepro-
bes is prepared (Fig. 3 ) .

Fig. 4
Laser L is emitting light pulses of the du-
ration 10 nsec each 5 sec with energy 0,5 3
(wavelength 1060 nM). At the surface F of
the Phobos a light-spot of 1,5 mm is formed,
with energy density 10 9 W cm"2. Accelerated
ions are generated here and scattered omni-
directionally. Dne part of the ions is en-
tering the entrance of mass spectrometer
MS flying on the space-probe, focused in
Fig- 3 the electric field and registered by the
sensor. The good function of this complex
It has a 3-axis orientation, with the axis is ensured only when the light-spot of the
S directed to the Sun, to ensure good inso- laser-beam is still good focused on the
lation of Solar panels C- The part A con- Phobos-surface. To realize it, a laser ran-
tain scientifi-. equipment and at the base of gefinder is measuring with cycle 20 Hz the
the probe the engine and fuel containers distance spacecraft-Phobos and focusing
are placed. High gain parabolic antenna is system is automatically adjusted. Electronic
at the top of the probe for transmission of package E contains indispensable logic sys-
telemetric data. Accuracy of the stabilisa- tems for coordination of functions between
tion of the probe is + 1°. L, MS and range-finder and for processing
of the results which are prepared fot the
main memory of the spacecraft.
EXPERIMENTAL EQUIPMENT FOR THE STUDY OF
PHOBOS
The most important during the Phobos-tnission
is the hovering of the spacecraft over the
b/ Secondary - ion mass - analyzer DION
Secondary ions SI (see Fig. 5) are generated

IG

Fig. 6
Fig. 5
in regolith of Phobos by charged crypton ions
IF generated onboard of the spacecraft. Ion-
-generator IG is providing ion flux with ener-
gy 3 keV (5 mA, giving in a mean distance
50 meters with divergence angle 20° a ion-spot
about 20 meters in diameter. Secondary ion
energy is distributed over the range from
0 to hundreds of electronvolts. Injection pul-
ses 1 sec long are repeated every 5 sec °id
the quadrupole-mass-analyzer MS is recording
secondary icns. Each mass-spectrum is recor-
ded in the time not longer as 1 sec. The mass-
-spectrometer self can be used also without
ion-generator, with solar-wind ions as a pri-
mary ion-source.

c/ Radar system experiment GRUNT

The subsurface sounding of the soil of Phobos
will be performed using a three-channel radar
system, permitting the sounding in different Fig. 7
depths, depending from the frequency used.
So with the frequency 2 MHz the depth 1000 me- theobjectives is a tilting mirror M, which
ter can be reached. At 130 MHz it will be permits in the angle-interval 90° observati-
10-100 m and at 500 MHz 1-10 m (see Fig. 6 ) . on of the surface below the spacecraft. The
The frequency 2 MHz will be used also for information of this optical complex is re-
the sounding of the Marsian ionosphere. corded with videotape recorder with 2 Mbit/
/sec speed and the playback for the teleme-
d/ TV spectrometer system FREGAT tric transmission is working with 4kbit/sec.
Three channel TV camera (see Fig. 7) can in
3 different colours obtain the image of the For the function and good results of this
same area above which the spacecraft is fly- instrumental complex is mostly important
ing. As image detector CCD elements are used. the mode of the work of the spacecraft. The
One part of this device is a panoramic vi- orbit of the spececraft is in this case on-
deospectrometer VS with the rectangular slit ly 30 km higher as the orbit of Phobos
whose long side is in the direction perpen- (see Fig. 8 ) . For the observation must be
dicular to the translation motion of the spa- descending manoeuvre realized to the nea-
ce probe. It is working in 14 spectral bands rest proximity of the moon's orbit and the
in the range 400 - 1000 nM. Input objectives spacecraft mjst be hovering some 50 meters
of the cameras and of the spectrometer have above the surface of the moon under control
focal length 18,5 mm, relative aperture of the laser range-finder.
1:2,5 and field of view 350. i n the front of
 By means of the radar equipment the ionos-
pheric study will be realized. Magnetomet-
ric complex is applied for study of inter-
planetary magnetic phenomena and of the mag-
netic field of the planet self. Plasmatic

V—F-—-T> phenomena are studied by different methods

and five experiments are prepared for lar-
ge spectrum of measurements of ions and
charged particles in interplanetary space
during the flight and orbiting of the pro-
bes.
Because the lasting orientation of the pro-
bes to the Sun a system of Solar experiments
will be performed. The most important is
the complex solar telescope TEREK, working
as X -rays imaging telescope, white-light
coronagraph and EUV-spectrometer. X-ray
photometer is used for steady registration
of the integral X-ray flux and special in-
strument is used for the registration of
Fig. 8 solar oscillations. Also detection of cos-
mic gamma-bursts is prepared.
Ouring the period of the hovering over Phobos
will be let down also two small landers: one Total 23 experiment are prepared for each
will be jumping on the surface to have the Phobos-probe. This is very complex program
possibility change his place, the second one for the study of Mars, his moon Phobos,
will be fixed and long-living. Both landers interplanetary spa<~e, solar wind and the Sun.
are telemetring all informations to the
main station orbiting around the planet.
CZECHOSLOVAK PARTICIPATION ON THE PHOBOS-
PROJECT
OTHER SCIENTIFIC PROGRAM OF THE PHOBOS-MISSION
Czechoslovakia is realizing the general
Experimental instrumentation of Phobos space construction of the laser-beam generator
-probes will be used also for the exploration for LIMA-D experiment with focusing device
of the planet self. It will be the radar for the power-laser. This is very delicate
and TV spectrometer. Onboard will be equip- work because high precision of moving parts
ment for remote exploration of the thermic and controls is required.
properties of the planet by means of radio- Main parts of the solar program for the Pho-
metric method in infrared. Using excitation bos mission has been proposed of Czechoslo-
by galactic cosmic rays, the gamma-spectro- vakia, where is realized the imaging X-ray
metry of the surface material of the planet telescope and white-light coronagraph for
can be used. By the spectrometric observa- the TEREK-experiment. Also X-photometer,
tion of the SUn in the tangential direction using rich experience of former Prcgnoz-mi-
the study of chemical composition of the ssions, for integral flux of solar X-rays is
Mars-atmosphere is prepared (see Fig. 9 ) . prepared in Czechoslovakia and the partici-
pation in the measurements of plasma pheno-
mena exists.
Phobos project is good exemple of big inter-
national cooperation. Intercosmos and Euro-
pean Space Agency have united 12 countries
for realization of this scientific and tech-
nological project: Austria, Bulgaria, Finland,
France, German democratic republic, German
federal republic, Hungary, Poland, Sweden,
Switzerland, Sowiet-union and Czechoslovakia.
His realization will be nice document of the
goodwill of scientists for peacefull inter-
national cooperation.
General remark to the pictures: in all of
them E means Earth, S-the Sun, M-Mars,
F-Phobos.

;Fig. 9.

[10
C O M E T S
 THE ORIGIN AND EVOLUTION OF THE PORT CLOUD

W.M. Napier

Royal Observatory, Blackford Hill, Edinburgh, Scotland, UK.

Theories of the origin of the Oort cloud are examined in the light of recent observations of comets and of
star-forming environments, and some popular hypotheses are found to meet with difficulties. In particular chemical and
experimental evidence that comets grow in an extremely cold, quiescent environment is proving difficult to reconcile with
recent CO and IR observations showing that the environment of a star-forming region is characterised by turbulent,
high-velocity flows and that young stars are prone to recurrent, violent outbursts. The aggregation around young stars of
planetesimals pre-existing in molecular clouds avoids these problems. However formed, the Oort cloud is disturbed through
interactions with its galactic environment. A record of these past disturbances, episodic or regular, is in principle
recoverable through impact cratering and other geological signatures, and these terrestrial records therefore provide a
further new constraint on the structure and evolution of the Oort cloud. The concepts of r 'dense inner cloud' or a
'solar companion star' are difficult to reconcile with the impact cratering history. The debris from the very largest comet;
are expected to play a dominant role in producing galactic modulations of such fundamental phenomena as the rise and
fall of oceans, ice ages, geomagnetic reversals and the origin of life. A MS Myr galactic cycle in particular is predicted.
Power spectrum analyses applied to cratering, viilcanism and geomagnetic reversal records for the last -200 Myr reveal the
presence of a 16 t ! Myr cycle.

emplaced in the Ooi. cloud about 500 would be hyperbolically

ejected, and Safronov (1967, 1969, 1972, 1977) proposed instead
Introduction that most comets came from the Uranus-Neptune region. This
is efficient but slow, since on this hypothesis one has to wait for
The Oort cloud has been one of the most successful concepts the giant planets to accrete (--2 Gyr), comet growth itself taking
in cometary dynamics. For almost 40 yr, the idea of a stable, M0* yr (Hills 1973). However if the disc is sufficiently
primordial cloud of comets reaching half way to the nearest quiescent, dust will settle in a thin plane, gravitational instability
stars, and gently gardened by passing stars, has been the will take over and growth will proceed rapidly. Oort cloud
mainstay of cometary dynamicisis. It is true that the idea is dynamics based on the assumption of comet growth in a
based on *.i enormous extrapolation, from a few hundred quiescent, low-mass protoplanetary disc (M -O.I M o with H and
well-determined orbits to a supposed population "-10^' comets, He), has been developed by Fernandez (1980, 1985a) and others.
and there have been suggestions from time to time that the
observations really only require a few million comets to exist in An alternative class of models places the origin of comets beyond
highly eccentric orbits about the Sun. A system like this would the planetary regions. The first of these was introduced by
be quickly dispersed, however, and the idea that (say) MO'' Cameron (1962, 1973) who argued from the perspective of star
bodies were captured into highly eccentric orbits (e ISO.9999) a formation theory. A protostellar cloud, he considered, would
few Myr ago has never gained much acceptance. It is moreover collapse to form a massive disc (M M o ) and the growth of
natural to think of the formation of comets as being connected comets would take place in this disc, beyond the orbit of
in some way with the formation of planets. Neptune. Planetesimal growth took place rapidly because of the
high mass and turbulent velocities, and the Oort cloud was
Indeed part of the significance of comets is that they populated by mass loss from the early Sun during its T Tauri
represent a clue, albeit a cryptic one, to the formation of phase. Although the process of comet growth was described only
planetesimals in some environment past or present. The role of qualitatively, Hills (1981) produced a mechanism, based on the
planetesimals in stellar cosmogony is at present unclear: usually action of differential radiation pressure, for coagulating grains
they are seen as by-products of star formation, but there have into comets around the Sun during its T Tauri phase. More
been suggestions from time to time that their role is a more recently Bailey (1987) has suggested that comets might form by
fundamental one. In recent years, too, many new and the coagulation of dust in wind-driven shells around young
non-classical ideas relating to the origin and dynamics of the protostars.
Oort cloud have been aired (Table 1). One of these ideas,
namely that comet impacts may significantly influence Earth A third class of models postulates a truly interstellar origin
history, has meant that questions relating to the interactions f"i comets, generated either during solar passages through
between the Oort cloud and the Galaxy have acquired an nebulae (Lyttleton 1953), or by Jeans collapse of dust (McCrea
interdisciplinary significance. Oort cloud studies have thus come 1975), simple coagulation (Yabushita 1983) or radiati-e driving
to bridge a gap between star formation and galactic processes at (Flannery & Krook 1978, Napier & Humphries 1986). Other
one end of the scale, and the evolution Df life on Earth at the sites have been suggested but are not discussed here:
other. protoplanetary disc, solar nebula or molecular cloud seem to be
the realistic possibilities in the current state of knowledge. They
In addition to these new theoretical ideas, there have been are not, of course, mutually exclusive.
new observational advances, some at IUE or IRAS wavelengths,
and there have been experimental and in situ, measurements: There is evidence (hat comets must have grown in an
some of these results put constraints on the conditions existing at extremely quiescent environment. This follows in part from their
the sites of comet formation (Table 2). The purpose of this extremely fragile and fluffy structure, as evidenced by Brownlee
review is to describe briefly the current status of hypotheses particles and cometary fireballs. Further from the icy grain
about the origin, structure and dynamics of the Oort cloud, model of d'Hendecourt et al. (1982), the presence of volatile
putting some emphasis on the more recent work in this area. species in comets requires low velocity impacts between colliding
More comprehensive reviews are given by Bailey et al. (1986, grains: assuming that radicals comprise 1% of the icy mantle of
1988). a grain, they have shown that grain heating (T« ^ 2 5 K) during
mutual collisions at S40 m s~' would destroy most volatile
The comet forming environment species in an irradiated mantle. It is likely too that the comet
formation environment was very cold. S2 discovered in the
The location of the comet factory is usually taken to be the coma of IRAS-Araki-Alcock 1983 VII, probably as a parent
protoplanetary disc, the solar nebula beyond, or the molecular molecule, has been used as a fossil thermometer by A'Hearn and
clouds. Opik (1966, 1973, 1975) placed the comet factory in Feldman (1985). Grim and Greenberg (1987) have argued that
the Jupiter region where gravitational ejection is most rapid. aggregation time scales- must be taken into account before this
However Jupiter is such a strong perturber that for every comet can be done, but nevertheless find from their experiments that

13
temperatures much less than 100K, perhaps as low as 30-40 K, of 30 yr duration over the Myr lifetime of the T Tauri Sun,
are required for comet formation with S2 preserved. Krishna one finds that comets of - km dimensions in circular orbits
Swamy and Wallis (1987) have identified S2 in several other would have been evaporated out to 100 AU, comets cf 10 km
cornels including those of Halley and Encke. Assuming lhai dimensions out to 80 AU. It should be noted that relaxed orbits
comets form by the coagulation of grains, then, we are seeking in a protoplanetary disc would be approximately circular. Since
an environment, whether protoplanetary disc, circumstellar nebula ices are clearly abundant in the outer Solar System, and include
or molecular cloud, in which the grains come together at <40 such volatiles as CK4, one must either postulate ad hoc a dense
ms" 1 and perhaps T <40 K. intervening dust shield for the entire T Tauri lifetime of the
early Sun (although dust coagulation would proceed more rapidly
In recent years, high resolution millimetre and infrared in the inner protoplanetary regions), or assume that the ices
observations of star forming regions have become available and were stored in large comets (^10 km), or transported from
some observational progress in the star formation problem has elsewhere post - T Tauii.
been made. Current models for star formation begin with the
formation of a dense core in a molecular cloud, typically with The conclusion which seems to be emerging is that the
mass a few M o , T-10 to 15 K, nH-10 4 -10 5 cm" 3 . These turbulent, powerful outflows which are associated with star
cores begin to collapse from the centre out, the collapse moving formation from its earliest stages, and the occasional violent
outwards at the speed of sound. As collapse proceeds the more stellar flaring, are difficult to reconcile with the quiescent, cold
distant matter, with the higher angular momentum, is unable to environment required for comet growth by grain coagulation.
reach the protostar and it falls in orbits which result in the
formation of an accreting, growing disc. When the protostar has Nevertheless, there is evidence that, at least around some
reached a mass -0.3 M© deuterium burning begins, and s strong low-mass stars, planetesimals have appeared in a disc a few 10^
stellar wind results, which cannot escape because of the still AU. A systematic search of IRAS sources (Aumann 1985) has
Mailing material. As the infall rate declines, however, a narrow revealed that a number of them are associated with known dwarf
bipolar outflow of material develops, the opening angle of the and subgiant stars. So far four of these excess IR emitters have
wind increasing with time until eventually it extends in all been modelled as dusty discs, but allowing for selection effects
directions and further infall is stopped. One then sees, exposed, they may be common amongst F,G and K main sequence stars
a T Tauri star collapsing along its Hayashi track. Gaseous (Wolstencroft and Walker 1987). The dimensions of the particles
accretion discs may still exist at this stage, but the gas is later necessary to reproduce the far IR radiation are such that the
lost and dust discs remain around the newly formed main Poynting Robertson effect would have rapidly removed them, and
sequence stars. T Tauri stars themselves are the source of a this implies a replenishing source of larger dimensions. IUE
powerful stellar wind, of kinetic energy 10 4 3-10 4 7 ergs. observations of metal lines in Beta Pictoris show strong variable
Although this star formation sequence is somewhat conjectural, absorption which may be attributed to the frequent (10-100
high velocity molecular outflows are such common features in times/yr) infall of -km-sized planetesimak (Lagrange-Henri et aj.
young star -forming regions that they are likely to be a normal 1987); and the dust-free holes around the stars may at least
part of the first -0.1 Myr of a star's life (Schwartz 1983). speculatively be related to the clearing out of debris from an
inner planetary system as evidenced in the case of the Solar
IRAS 1629A is perhaps an archetypal collapsing protostar. It System by the late heavy lunar bombardment, of duration a few
is a cold (~40 K), luminous (-23 LQ) object discovered in the 10^ yr. Whether the planetesimals are cometary in nature is
Rho Ophiuchi molecular cloud by Walker et aj. (1986), and may unknown, however.
be a protostar only a few 10 4 yr old. The central point source
has a mass -0.24 M o . The material surrounding the source out Weissman (1984) has attributed the source of the small dust
to -3000 AU has n ^ MO* cm"^, and appears to be totalling at particles in the Vega disc to collisions between larger bodies;
-1 km s " ' . There is a simultaneous bipolar outflow. This however an accreting system is presumably a sink rather than a
object is very quiescent by the standards of most pre-main steady source of /an sized particles; on the other hand if the
sequence stars. Nevertheless the CS line widths indicate that the discs are fragmenting, then whence came the bodies which are
infalling material has a microturbulent velocity -0.4 km s" 1 , an now breaking up? A similar problem arises with the main belt
order of magnitude in excess of those just permitted by the asteroid system, which is much too 'hot' kinematically to have
grain coagulation models. Stellar winds seem to start up at the formed by accretion in a quiescent disc (Heppenheimer 1977).
earliest stages of star formation. These are exemplified by the In a system of colliding bodies, relaxation is attained when the
young stars in OMC-1, which have outflow velocities >\ 00 km energy input from mutual gravity balaces that lost from mutual
s~l, IRc2 for example being at the centre of a windblown cavity collisions (Safronov 1972). The energy input is dominated by
whose outflow, of velocity -100 km s" 1 , is channelled by a the largest planetesimals and so if it is accepted that comets
toroidal structure, ''"he driving force comes from within -0.5AU have grown through grain collisions <40 m s~', the largest ones
of the centre of lt*C2, and the flow appears to be turbulent, can only have been of -km dimensions. In fact although no
with cooler, massive clumps embedded within it. Whether these secure upper limit to comet masses is known the greatest
clumps were ejected by the stars or are independent blobs caught historical comets have probably been —100 km in diameter. This
up in the wind is unknown. HL Tau may exemplify a later would again seem to preclude an origin in a system approaching
pre-main sequence stage. This is a -1 M o star apparently a dynamically relaxed state, such as a circumstellar disc, whether
viewed through the plane of a torus of gas and dust of radius pre-main sequence or not, and including the Uranus-Neptune
-2000 AU and mass -0.01-0.5 M o , probably in Keplerian region.
motion. The temperatures of the gas and grains in the ring are
a few 10 K and there is a 3.1pm ice absorption feature present
These problems of comet growth and survival are avoided in
(Cohen 1983; Beckwilh and Sargent 1987). These properties
the third class of model, but one would then require that comets
perhaps resemble those associated with the early solar nebula, but
are formed in the interstellar medium prior to star formation and
once more the presence of jets in the system reveals that it is
are either pulled in during the protostar collapse phase or are
permeated by a strong stellar wind and it is not clear that the
captured post-main sequence (Clube & Napier 1984a, Napier
extreme quiescence apparently required for comet formation is
1985). The growth of planetesimals in dense molecular clouds
met in this system.
has been suggested to account for the lack of enrichment of the
interstellar medium with time, heavy elements being progressively
Herbig (1977, 1983) has pointed out that FU Orionis type locked up in large bodies (Tinsley and Cameron 1974, Greenberg
outbursts, involving luminosity increases of ^100 over a period 1974). The strong correlation between metal depletion and
of years, are a normal recurring feature of T Tauri stars (say density observed in cold molecular clouds may indicate that
every M 0 4 yr). He has argued that such outbursts would have comet growth is proceeding fairly rapidly in such regions, the
melted mm-sized dust particles in the inner Solar System. We dense knots presumably being precursors of star formation. The
can apply the same type of reasoning to the ice mantles of slow homologous collapse of a molecular cloud from 10 4 to 1
grains. It is easily found, from the evaporation rate of water AU would cause the indigenous planetesimals to spiral in, leading
ice at different temperatures as determined by Grim and to say a I M Q protostar surrounded by - 1 0 ! 4 comets orbiting
Greenberg (1987), that a single FU Ori outburst in the early within -5 AU. These would mostly be absorbed into the
Sun, of duration -30 yr, would have evaporated the icy mantles protostar or later destroyed, but some fraction of bodies at say a
of grains out to 200 AU. Likewise assuming 100 outbursts each f«w 103 AU would survive and be retained. If this admittedly
speculative picture is correct then the long growth time for stellar scattering masses (Sanders et aj. 1987). A half-life
planetesimals in the hazardous Uranus-Neptune region would not T 1^710 Myr, or -15% of the age of the Solar System, has been
be necessary. derived by Clube & Napier (1986). Hut and Tiemaine (1986)
also disputed the short Oort cloud lifetimes, deriving first Tj-20
The problem of growing large bodies in the interstellar Gyr and then —3 Gyr from their own analyses. However it now
medium has usually been seen as a severe obstacle to the seems that there were errors in these analyses (Clube and Napier
interstellar planetesimal concept. However the past few years 1986; Bailey 1986a); correcting for these, one finds that the
have seen a revival of a suggestion made by Spitzer and Whipple Hut and Tremaine study yields 670 < T j < 7 8 0 Myr, bringing
in the I940's that differential radiation pressure might force their study into line with the results of other workers.
grains together in the interstellar medium. This mechanism was
applied by Hills (1981) to a T Tauri star or collapsing protostar, A direct measure of the disturbing forces in the Galaxy is
but it has been returned to the interstellar medium whence it provided by the survival of binary stars. This has been
came by Flannery and Krook (1983) and Napier and Humphries investigated by Abt (1986) whose results are shown in Fig. 1.
(1986). The latter have argued that [he dust component of It appears that the maximum^separation of binaries varies with
molecular clouds is unstable in the presence of a radiation field. 3
time t roughly as t~°- . Amongst dwarf stars of solar age, an
This photon drive may be enhanced by up to two powers of ten upper limit -5000 AU is observed which, allowing for projection,
if impinging UV photons photodesorb mantle material. It was corresponds to an Oort cloud of radius 6000 AU. Of course a
found, from application of a generalised virial theorem, that in Sun-comet binary, being generally less massive than a G dwarf
3 3
cold (T ^ 20K), dense ( n H >> 10 cm" ) regions of a molecular double, is more fragile, and it appears therefore that the
cloud, planetesimals of > km dimensions may coagulate out in theoretical calculations of Oort cloud disruption are along the
MO 3 yr. right lines.

Schneider and Elmegreen (1979), in their catalogue of

filamentary dark clouds, point out the existence of long bead-like
dark clouds, comprising chains of small, discrete globules. In
addition they describe fila-.ientary structures without condensation
e.g. streamers in Of.'.iuchus. Often these filaments have a
windswept appearance or sharper edges along one side and often
they are signiiicantly aligned with respect to a star : Schneider
and Elmegreen propose that some highly directional force might
account for this. They suggest that this external force
accumulates material by sweeping it first into plane-parallel
layers, and the material then fragments into parallel filaments
before undergoing further gravitational condensation into
individual globules. All this, of course, is on - pc scales and
not directly applicable to comet collapse, but may support the
idea of radiative driving of grains. Random break-up of a
collapsing dust sheet or sphere yields a scale-free mass
distribution of planetesimals (a power law with index -1.75 to
-1.67). An upper limit to the possible masses may in principle
arise from the strong clumping of molecular clouds arising from
thermal instabilities : coagulation of grains within a clump
would create a body of lunar dimensions. There thus appear to
be two characteristic mass regimes associated with instabilities in
cold, dense nebulae : "stellar", arising from gravitational
collapse, and "cometary", arising from radiative collapse. There
is a case, therefore, for locating comet factories in the somewhat
less hostile environments of cold dense molecular clouds.

Oon cloud replenishment BO AO FO GO KO MO

Spectral type of the earliest star
't seems unrealistic to suppose that the Oort cloud comets
now observed, arriving from distances -40,000-60,000 AU from
the Sun, were placed there during the star formation process. It
has been proposed (Cameron 1973, Dermof.. and Gold 1978) that
one or more mass loss events from the primordial Sun might Fig. 1 Maximum binary separations after Aht (l')S6).
have thrown comets out from MO 3 AU in the early solar nebula
to their present distances of --5x104 AU. However, unless the
mass loss took place within a very narrow range of timescalcs, The long-period enmets, Ihrn, form ::n L*!.*!ahk\ ra]' :
any such events would have thrown the planets into highly dissipating system, but nevenlK-ie^ I^LV ,<;e tiivie. Se>\ :i
eccentric orbits also and it would therefore be necessary to possible explanations of this u<-nuiu\vi.iiu h.ivj Ke» suggcs;*.J.
postulate that !!••.• planets were formed after the great dispersal. Replenishment from a hypothetical .U.nse i^ner cloud is one
It is nm clear th it a realistic chronology can be so constructed. much discussed possibility. Another ^o.ssibili'.;. ii that :ho
long-period comets are somehow captured from inte'biellar space,
The long-standing problem of Oort cloud replenishment has say during passages though dense star-forming ay,ins. Or it
been exacerbated in recent years by the discovery of the may be that no replenishment is taking pl.tcc JIKI that the
molecular cloud system and the realisation that this system is observed comets are simriy a much-depiei'.j ienmanl of an
sufficiently massive to have swept away the long-period comets originally very massive cloud. Adopting a power iaw energy
several times over in the course of Solar System history. The distribution with index - 7 , various differential distributions
result can be derived analytically in several ways. One finds proposed in the literature are shown in Table 3 along with the
that over 4.5 Gyr the energisation of a long-period comet due associated distributions in a and r. (the quoted r distributions
to these disturbances is at least one power of ten higher than its are only approximate). The standard Oort cloud has 7 = 5/2.
binding energy. Refinements due to the finite size of GMC's The flat distribution of energy (7 = 0) due to Van Wocrkom
and the like do not substantially change the result (Clube & (1948), yields n(a)da = noa~2da and this is seen in the
Napier 1983 ; Bailey tS83; Napier 1985). A long series of simulations of Fernandez (1980), who followed the evolution of
analyses by several workers has led to widespread agreement that an initial ring of comets in the plane of the Solar System and
the half-life of the long-period comet system is <1 Gyr at i i with perihelia initially in the Uranus-Neptune region. A dense
30,000 AU. This conclusion was initially disputed by Fernandez inner cloud in the sense usually adopted (e.g. Hills 1981) has
(1985) on the grounds that the properties of the molecular cloud 7 < 0 , an extreme value of 7 = -2 being proposed by Bailey
system are very uncertain, but there now seems to be agreement (1986b) in order to directly replenish the short-period comet
to within a factor 3 or so between the 7-ray, CO, virial and system from a remarkably dense, small region.

15
 • The question of replenishment of the long-period comets
from an inner Oort cloud was investigated by numerical
simulations. These were fairly conservative, only close
encounters (<40 pc) being considered, and the GMC's being 1 1 I
taken as uniform spheres, so greatly exaggerating the softness of
penetrating encounters (the clumpy structures of GMC's yield Y=-1
dilution factors -0.1-0.01: loc. cjt.). The GMC's were taken
to have the bulk properties described by Sanders et al. (1987).
A transition matrix T was derived, whose elements were the
probabilities that a comet initially in energy state i is perturbed
to state j after 4.5 Gyr. The end state tjj of the Oort cloud
may then be derived for any prescribed initial distribution fc£o via.
en
o
: V
fcJl = X N o without further celestial mechanics.
0
• i 1
Although these calculations are very rough a number of 100
interesting conclusions could be drawn (see Fig. 2). First, it was Y=0
confirmed that if there was indeed a primordial Oort cloud, the
'observed' region 20,000 <a5530,000 AU has been depleted over
Solar System history, by at feast two orders of magnitude. The
standard Oort cloud, with y = 2.5, is in difficulties, and if seen
as a primordial remnant the initial mass of comets would have
been absurdly large, supporting the earlier contusions of Napier
50 -
A _

and Stiiniucha (1982), Clube and Napier (1982) and others.

Second, in addition to this depletion, the surviving cloud is
strongly mixed by GMC encounters. The GMC's act to push
0
\ ' 1
LC.iv.s inwards as we'l as outwards, driving them into a
tightly-bounri, fe.atively long-lived core of <;4000 AU radius and
enhanced density. Third, the iong-period comet system can in
150 -\ y=2
principle be replenished by a dense inner cloud (say y = -1), or
\ initial nla)
even a Van Woerkom cloud (y = 0) originally only a few times
more massive than the present one. The mass of the original
cloud must be a matter for speculation as the maximum mass of 100 \ final nla)

comets is not known. Assuming for example an upper limit of

\
10^2 gm, the mass distribution given by Hughes and Daniels
(1982), and 7 = 0, the original cloud would have had several
lO^M,^. It is not obvious that a dense inner cloud exists.
However constraints can be placed on the inner cloud by looking
50 -
\ -
at the effects of cometary impacts on the history of the Earth.
N
The Oort cloud and Earth history
12 24 36
The unseen inner regions of the comet cloud can be studied
by a Rutherford experiment, firing stars through it and observing a _^(x10 3 AU)
the scattered comets, the detection apparatus in this case being
the surface of the Moon and the geological record of the Earth
The impact record is highly incomplete and contaminated by a
non-cometary background, but the data are nevertheless at a Fig. 2 n(a) evolution.
level where one may put real constraints on the structure,
evolution and possibly even the origin of the Oort cloud.

The surveys of Shoemaker and Helin in the 1970's revealed

that the population of Earth-crossing (Apollo) asteroids was one encounter would yield craters at a mean rate of M per 300 yr
or two powers of ten higher than had been realised until then. for 4 Myr. With say a -50% non-cometary contribution to the
That the energy and frequency of impacts from Apollo asteroids background flux of impact craters ^ km in diameter, this would
were high enough to lead one to expect geological signatures was lead to the expectation that, in the list of Grieve et al. (1986)
first pointed out by Napier and Clube (1979), who also argued -8-10 out of 20 non-iron impactors would be concentrated at
that these signatures should be imposed on the Earth with one or two discrete epochs, and although the cratering record
galactic periodicites The basis for the latter was the assumption over the past -200 Myr is very incomplete, this is clearly not
that an appreciable proportion of the Apollo asteroids were observed. Oort cloud models with -y=0 can probably also be
probably degassed comets (Opik 1963) and that molecular clouds, excluded by this argument as they predict ~40:l enhancements
which were probably concentrated in spiral arms, would disturb over a 300 Myr period. The terrestrial cratering record is
the Oort cloud periodically. Clube and Napier also argued that consistent with a modulation in cometary flux of order -10:1,
depletion of the Oort cloud would be substantial and that but not much more. This lack of a strong 'flickering' in the
replenishment might come through external capture rather than record of impact cratering, even allowing a reasonable dilution by
internal unbinding. a steady asteroidal background, would seem to argue against the
existence of a very dense inner core, and the problem of
Hills (1981), in postulating an extremely dense inner cloud, replenishing the outer Oort cloud remains. Roughly put, if we
pointed out that brief, intense showers of comets would be have y < 0 there is a problem with the impact cratering record.
thrown into the inner planetary system through the occasional If -y * 0, there is a problem with replenishing the Oort cloud.
penetration of the cloud by a star. Over 100 Myr, there is an The latter is exacerbated by the fact that the lunar cratering rate
expectation that one star of mass ;>0.6Mo will pass within 7800 shows no signal of a secular decline over the past 3.9 Gyr
AU of the Sun. From Fernandez and Ip (1987) one finds that, (Fig. 3: Baldwin 1985). For comparison Fernandez (1980) found
for an Oort cloud with y ~ —2, the number of comets thrown that under the influence of stellar and planetary perturbations,
into the planetary system by such a passage would be -30 times the rate of passages of comets through the planetary system
that from the Oort cloud alone over the —4 Myr half-life of the varied as t~' over the Gyr of his numerical simulations with a
shower. Over a -300 Myr interval, there is an expectation of decay time -400 Myr. A comet source in the Uranus-Neptune
one encounter to within 4500 AU, leading to a shower of region was assumed. If an appreciable proportion of this past
intensity -300 timt, Ihe Oort cloud background. Assuming the cratering is due to cometary impacts then the replenishing
latter from all cometary sources live or dead to be -10 craters reservoir must be not only very massive, but also, probably,
Myr~l (for craters greater than 5 km in diameter), the latter external to the Solar System. It seems more likely therefore

16
 that successive Oort clouds of the standard kind (7 ~2-3) 2
Table 1 captured into the Solar System during the several penetration, f
star-forming regions. Oort cloud models with 7XD :
Some recent non-classical ideas on the Oort Cloud
generally difficult to reconcile with an origin by diffusion o:
comets from the inner Solar System; on the other hand, it has
yet to be demonstrated by detailed 3-bodied integrations that
capture of comets from GMC's takes place with sufficient
Proposal Comment
efficiency (but see Clube and Napier 1984a).
Dynamically unstable initially controversial but now
It might of course be that comets, aciive or degassed, are
seems well established
only a minor contributor to the cratering record and that
Baldwin's diagram says more about the main belt asteroids than
Episodic capture of comets 3-body problem; no detailed
the Oort cloud. However, the mass of material entering the
from GMCs calculations available
interplanetary system appears to be dominated by rare, giant
comets (say ;>J0 km in diameter), each of which, on
Galactic alignments good evidence; also a solar
disintegration, yields MO 2 - 10 3 short-iived Earth-crossing
motion component asteroids (Clube and Napier 1984b). The well-known difficulty
in providing an adequate supply of Earth-crossing asteroids by
Dense inner cloud (7<0) could yield short-period transfer from ihe main belt may thus be avoided by assuming a
comet flux; problem with major cometary contribution. The disintegration of a giant
cratering record comet in an Apollo orbit would yield climatic effects and dust
deposits on Earth, and Clube aid Napier have proposed that the
Terrestrial catastrophism highly controversial Held progenitor of Encke's comet was such a body (Table 4).
Encke's comet itself is about to become asteroidal (Ferrin and
(i) with galactic 15 and 30 Myr periodicities Gil 1986). Further, main belt asteroids would yield a declining,
modulations both proposed and disputed; but otherwise random source of impacts, and there is evidence
dominant role of giant comets that terrestrial catastrophes arrive on Earth according to a
pattern.
(ii) with solar companion severe problems witl? orbital
modulations stability and compatibility
The notion tlat terrestrial processes recur cyclically is very
with cratering record old, and inrtividiv.l workers, each in their own specialisation have
(Hi) with random impacts not consistent with claims in the past uncovered more or less qualitative evidence for it.
of periodicity in terrestrial Over 50 yr ago Holmes (1927), before the plate tectonic
or showers
revolution and radiometric dating of rocks, considered that sea
record
levels rose and fell in 6 30 Myr cycle which was correlated with
world-wide outbursts of volcanic activity. Dorman (1968), irom
a study of marine fossils, thought there was a 30 Myr
Table 2 world-wide climatic cycle. Seyfert and Sirkin (1979) found what
they called 'impact episodes', a tendency for impact cratering to
Some new observational developments of possible relevance recur at -26 Myr intervals. They correlated these episodes with
to comet cosmogony. plate tectonic and other phenomena. Although their approach
was again qualitative and they made no attempt to discriminate
Observations p_osible implications between types of bolide, there is a good correlation between
their impact episodes ana those found by Alvarez and Muller
detailed structure and tidal disruption of Oort (1984) by power spectrum analysis (Clube & Napier 1986). The
chemistry of GMCs cloud; site for growth one significant difference is that Seyfert & Sirkin find the Earth
of comets? to be currently immersed in an impact episode. A ~30 Myr
cycle is about the half period of the Sun's vertical motion in the
dust discs around main primordial relicts of Galaxy, and Clube and Napier (1984a) and Rampino and Slothers
sequence stars planet/comet formation? (1984) proposed that the Oort cloud disturbances were varying
systematically with this motion. The occurrence of galactic
young star-forming regions; turbulence/high velocities periodicities in the terrestrial record, through Oort cloud
bipolar flows in early Solar System disturbances, had been predicted by Napier and Clube (1979) and
and inhibition of comet Clube and Napier (1982), the possibility of 15 and 30 Myr cycles
growth? being explicitly mentioned by Napier (1983).

composition of comets: S2; low temperature It has been argued by Thaddeus and Chanan (1984) that the
isotope ratios. Brownlee coagulation? Sun's vertical motion is too small relative to the scale height of
particles the molecular cloud system for appreciable modulation of the
comet flux to take place. However for the periodic component
geochemicii anomalies at KT evidence of Oort cloud of the comet flux, what matters is the smoothed integrated effect
boundary and in polar ice; disturbances of molecular clouds, and this expresses itself as a part of the
'galactic' periodicities in vertical galactic tide. If this tide is generated by a smooth,
terrestrial phenomena plane-parallel continuum, then it varies linearly with the effective
mass density of local perturbers. This tidal background (Byl
1986) gives a flux of near parabolic comets into the planetary
system directly proportional to the local density. The cometary
flux therefore samples the instantaneous local density as the Sun
Table 3 moves up and down and, provided the 'missing mass' in the
Oort cloud distributions Galaxy has a half-thickness *60 pc say, 30 Myr periodicity in
the terrestrial record will be quite measurable. The effects of
galactic tides on cometary orbits (|' s tendency for aphelia to avoid
y = 512 7 = 0 7 = -1 •) = ~2 galactic poles) has been noted by Delsemme (1987).
1
n a (a) aS a-2 a"- a"» However the spatial structure of the galactic tide, and thus the
temporal variations in comet influx, are very uncertain: the
n E (E) E -5/2 E° E E2 vertical and horizontal distributions of the missing mass are
unknown and indeed its existence has been questioned (G
r r -3/2 r-4 r-5 r-6
<V > Gilmore pers. comm.). It may be that an appreciable fraction of
the mass of the galactic disc is 'granular1, being concentrated saj

17
T A B L E 4. Probable debris from the niosl recent giant short-period cornel (after Clulie * Niipiei i'«(,h, l.il'lt 3. ami "I™"
1988)

Object a(AU) i(deg)

meteor streams
1) S Taurids 5.2 153.2 temporal structure: peak • 1100-12UDAI >
1.93 .806
2) N Taurids 2.59 .861 2.4 162.3
3) 0 Taurids 2.2 .85 6 162.4 daytime
4) T Perseuts 1.6 .79 0 13 daytime
5) S Pisckls 2.33 .82 2 104
6) N Piscids 2.06 .80 3 130
7) S \ Orionids 2.IK .78 7 180
8) N \ Orioniils 2.22 .79 2 179

active comefs
9) Encke 1.2 .85 11.9 160 declining activity (few 102 yr)
10) Rudnicki - 1.00 9.1 154.7

asteroids
11) 2201 Oijato 2.2 .71 2.5 172 slight oulgassing probable
12) 1982 TA 2.2 .76 11.8 128
(3) 1984 Ka 2.2 .76 4.6 146
14) 5025 P-L 4.20 .895 6.2 145.8
15) Hephaistos 2.1 .83 11.9 258 largest known Apollo (M0 km)
16) unseen companion 2.4 .86 160 Whipple & Hamid (1952)

impactors
17) boulder flux April-June 1975
18) boulder swarm .tune 26-30 1975 (Dorman et al. 1978)
19) Tunguska object M0 Mt; June 30 1908 (Kresak 1978)
20) Bruno object MO5 Ml; June 26 1178 (Hartmann 1977)

larger complexes
21) Stohl streams April-June, Sept-December
22) zodiacal cloud lifetime M0 5 yr without replenishment
no current replenishing source (Kresak 1980).

in molecular clouds which are themselves probably concentrated

in spiral arms. This would yield a tensile tidal force which,
about a molecular cloud scale height, partially offsets the
compressive tide due to the smoothed component of the disc
(Fig 4). The 30 Myr modulation7Hl>en be itself modulated, the
end result being a M5 Myr cycle with weak and strong phases
interspersing. In a very incomplete record the 15 Myr
component could be missed and a 30 Myr one derived.
However the 15 Myr cycle is a uniquely galactic signature which
discriminates this hypothesis from all others, such as random
impact (Alvarez et a|. 1980) solar companion (Davis et al. 1984)
and so on.

In Figs. 5-7 are shown power spectrum analyses applied to

various terrestrial data for the past ~200 Myr. All of these
terrestrial phenomena are expected to be modulated by galactic
disturbances of the Oorl cloud (Clube and Napier 1982). Peaks
are evident at the expected locations, within the errors, the
16 ±2 Myr cycles having confidence levels -99% if they are
regarded as a priori predictions of the galactic hypothesis (Clube
and Napier, 1987). The geomagnetic reversal record is shown
explicitly in Fig. 8, where a weak 'interpulse' is marked against
the larger ~30 Myr cycle.

If these terrestrial cycles are truly galactic in origin, then the

'Rutherford experiment' as recorded in the terrestrial and lunar
cratering records uniquely constrains the unseen structure of the
Oort cloud. In particular the long-term steadiness of the lunar
cratering then implies the existence of a huge comet reservoir;
but if in the Solar System, it is difficult to see how this
reservoir was formed or how it could escape detection through 2 3
the generation of strong impact episodes. Age (Gyr)

Fig. 3 Lunar cratering record after Baldwin (1985)

18
 t L

\ ts> —

•mi
b.

Fig. 4 Smooth (a) and granular (b) tidal forces.

20 30 40 50
Period (Myr)

Fig. 7 PSA of Indian vulc.inisms from Pandey and Negi

(1987).

20 30 40 50
Period (Myr)
100 200
Time (Myr BP)
Fig. 5 Power sper'rum analysis of Fig. 0.

Fig. 8 Geomagnetic reversal record after Harland et aj.

(1982). A strong --30 Myr period (peaks joined by
solid lines) appears to be interspersed with weaker
'interpulses', marked by arrows.

Comet cosmogony is a fashion-prone field of astronomy and its

literature is strewn with the corpses of solar companions, dense
inner clouds and abandoned consensus. The emergence of new
observational data, such as those provided by the cratering record
and protostellar environments, may help to constrain the i.i >ny
theoretical possibilities. Some of the popular ideas of the last ^
30 yr already seem to be in difficulty.
20 30 40 50
Period (Myr) Acknowledgement

Fig. 6 PSA of craters from Shoemaker and Wolfe (1986). The author is indebted to Mrs Anne Bryans for her typing
efforts, and to Dr. M.E. Bailey for a detailed critique.

19
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20
 DYNAMICAL EVOLUTION OF SHORT-PERIOD COMETS

A. Carusi and G.B. Valsecchi

IAS - Reparto Planetologia, V. Universita 11, 00185 Rome, Italy

ABSTRACT. The dynamical evolution of short-period comets, and in particular of those belonging to the
so-called Jupiter family, is reviewed. Encounters with Jupiter play a dominant role in determining the
dynamical fate of these objects, although, in some peculiar cases, also Interactions with other pla-
nets may be important. Frequent although temporary librations around resonances with Jupiter are dis-
played by more than one third of short-period comets. Integrations of motion of observed comets, over
a time span comparable with their lifetime as active objects, are compared with previous numerical in-
vestigations, to get insight into the non observed phases of the dynamical evolution of these objects.

1. INTRODUCTION motions of observed comets and the results of Monte

Carlo investigations are compared, In order to get
The idea of the existence of a large reservoir of co- information about the frequency of different dynamical
mets surrounding the Sun at a mean distance of 50000 AU processes.
was proposed by J. Oort in 1950. Since then many
authors have investigated, both theoretically and by
means of numerical experiments, the origin, dynamical
properties and lifetime of such a cloud, as well as the 2. FROM LONG-PERIOD TO SHORT-PERIOD COMETS
interactions that it would have with the extra-solar,
galactic environment (Bailey, 1983; Bailey et al., The formation of the Oort cloud is currently consi-
1984; Cameron, 1973; Clube and Napier, 1984; Delsemme, dered as a by-product of the accumulation of giant
1985; Fernandez, 1980, 1982, 1985; Fernandez and Ip, planets, especially Uranus and Neptune. These planets,
1981; Hills, 1981; Lyttleton, 1974; Marsden and Sekani- at a late stage of their formation, should have expel-
na, 1973; Mignard and Remy, 1985; Napier and Staniucha, led a large number of planetesimals (the present co-
1982; Opik, 1973; Remy and Mignard, 1985; Safronov, mets), with velocities close to the escape velocity
1969; Valtonen, 1983; Valtonen and Innanen, 1982; Weis- from the solar system. The orbits of the small frac-
sman, 1982, 1985; Yabushita, 1979). tion of comets that remained bound to our star would
have been randomized, both In eccentricity and orienta-
Data coming from the Infrared Astronomical Satellite tion, by the perturbations originated by repeated pas-
(IRAS) have recently shown that jeveral stars, not far sages of other stars in the vicinity of the Sun. The
from the Sun, are embedded in a cloud of objects ra- result of this process would have been a more or less
diating at infrared wavelenghts, and it has been pro- uniform distribution of orbits with mean semiaxes of
posed that these may be clouds of "comets" similar to the order of 25,000 AU, and perihelion distances well
the one supposed to exist around the Sun (Weissman, beyond the planetary region. If no perturbations from
1984). objects outside the solar system were present, this
situation would be stable over very long time spans,
The structure and properties of the Oort cloud have greater than the age of the system itself, because
been reviewed many times (see, for example, Fernandez, encounters and collisions between comets In the cloud
1985; Weissman, 1985, and references therein con- are thought to be irrelevant for the evolution of th^t
tained) ; here we will only give a short account of what population.
are thought to be the possible dynamical channels con-
necting objects in the cloud to the observed, highly Four possible sources of perturbations on the co-
structured population of short-period comets. met's cloud have been proposed in recent years. Pas-
sing stars, of course» would induce orbital variations,
The possible end-states of the dynamical processes almost impulsive in nature, on a small fraction of
that transfer comets from the cloud to the inner solar objects on the same side of the star, with respect to
system are reviewed in the next Section, together with the Sun; the size of these perturbations would then
the single-stage and multi-stage capture mechanisms. depend mainly on the minimum distance of the star from
In Section 3 we will examine the population of short- the Sun and on its relative velocity. A second source
period (SP) comets in detail, looking for differences of perturbations comes from the observation that the
and similarities from a dynamical point of view. solar system must have encountered several times, in
the past, giant molecular clouds (Clube, 1985). The
Close planetary encounters and temporary satellite great masses of these objects would have caused large
captures are treated In Section 4, and librating mo- losses of comets from the cloud, especially at large
tions around resonances with the major planets in Sec- distances from the Sun; they may have even completely
tion 5. Since the dynamical evolution of SP comets has depopulated the cloud. A third source, that has been
been the subject of nuny numerical experiments in the invoked to justify the idea of periodic cometary show-
last twenty years, in Section 6 the Integration of ers on Earth, could be the presence, at a large distan-

21
 ce from the Sun» of a very massive planet, or even a the so-called Tisserand quantity, J, by the equations
second star (WIthmire and Jackson, 1984), whose period
has been estimated to be of the order of 20 to 30 U = V3- J
million years. Finally, Harrington (1985) has shown
that galactic perturbations may be able to randomize J = a r /a + 2 f a / a ? (1-e 1 ) cos i
cometary orbits in the Oort cloud.
where U is measured in units of the planet's orbital
Whatever the sources of external perturbations, it velocity, a, e, i are the semiaxis, eccentricity and
almost invariably turns out that the effects on the inclination of the comet's orbit and a p is the semi-
cloud of comets is smaller or at most comparable to axis of the planet.
that due to passing stars. For what concerns the
transfer of a comet into a SP orbit, we will then start The Tisserand quantity, a simplification of the Jacobi
with an orbit of very long period, e n u r i n g the plane- constant of the restricted three-body problem, has the
tary region for the first time after its removal into property of remaining almost constant after an encoun-
the Oort cloud. Such a comet, revolving on a quasi- ter, although its value during the encounter may change
parabolic orbit, is called a new comet (in the Oort substantially. Due to the ease of computation from the
sense). Conventionally, a comet is considered new if parameters of an osculating orbit, the Tisserand quan-
the reciprocal of its semiaxis at a great distance from tity has been used in the past to identify a comet
the planetary region, I/a, is between 1/100,000 and whose orbit was changed by an encounter with some major
1/25,000 A U " 1 . planet, taking advantage of the mentioned quasi-inva-
riance. Following Kresak (1972), we will make use of
The subsequent evolution of a new comet, as shown by this quantity in the following, as an orbital indica-
the numerical experiments by Everhart (1977), is close- tor.
ly related to the inclination to the ecliptic and the
perihelion distance of its orbit. In fig. 1 is presen- It should not be frequent that a new comet encounters a
ted a scheme, due to Everhart (1982), of the possible planet during its first revolution; instead, it will
end-states of the process of extraction of a comet from perform a number of them before such an event, and may
the Oort cloud, that will represent the start point for even be expelled from the system without encountering
the following considerations. any planet. This is due to the fact that, outside the
planetary region, the comet moves along an orbit whose
centre of motion is the barycentre of the solar system.
As the comet approaches the Sun, and crosses the orbits
of the outer planets, the centre of motion is shifted,
producing an indirect perturbation on the orbit. Only
inside the orbit of Jupiter the comet may be supposed
to move along a heliocentric orbit (due to the little
mass of the inner planets), and the shift of the centre
of motion repeats as the object recedes from the Sun.
These indirect perturbations (see Carusi et a l . , 1986,
1987) may be sufficient to provide the small
amount of energy needed to transform the new, quasi-
parabolic orbit into an hyperbolic orbit, so that the
UNSTABLE comet will be lost in the interstellar space.
HORSESHOES
TROJANS, ETC*"
Before a close encounter takes place, the orbit of
the comet may undergo several changes, due to the above
mechanism, and become an old comet of long period; the
same may happen if the comet encounters some planet at
a relatively large distance. If the encounter is
close, however, the comet inav still be put into a
c haot ic long-period unseen hyperbolic orbit, and then escape from the system (like
in the recent case of comet Howe Li) 7 or its orbital
Fig. I - Evolut ionary channels connect ing parabolic period may be shortened considerably.
to short-period comets (from Hverhart, 1982).
It is relevant, at this point, a consideration on the
values of the Tisserand quant ity with respect to the
The most important character of the orbit of a new • - major planets. It has been shown (see, for example,
met is its possibility to cross '. .e orbits >f major Carusi and Valsecchi, 1985) chat the dynamical evolut-
planets, which can produce, sooner or later, a close ion of a comet differs considerably if J is less than
encounter with them. Formally, this is possible if the 2, or greater than that. Comets with low, or very low,
perihelion distance of the cometary orbit is less than values of J have a high relative velocity at encoun-
the semiaxis of those planets, but the real possibility ters, and their orbits will not be changed by a large
of an encounter is limited by the mutual inclination of amount, unless the encounter is extremely close. In
the orbits and the orientations of the lines of nodes this last case, either the comet Is put into a hyper-
and apses. If the angles are in a suitable range, and bolic orbit, or Is definitely trapped in the planetary
then a close encounter may take place, the evolution of region. Considering the masses of the planets, and the
the comet's orbit is mainly governed by the relative probability of a passage at a given distance from the^i,
speed at encounter (U) which, in turn, is related to it turns out that Jupiter is the major source of this

22
type of orbit transformations (single-stage captures): or to a major change in the orbital elements due to a
its gravitational field is, in fact, able to produce - close encounter with a planet (mainly Jupiter). More
in a single encounter - a SP comet. As an example of than 80 SP comets have been observed several times
this phenomenon (although reversed in time), fig. 2 (P/Halley has been under observation for 22 centuries).
shows the consequences of a very deep encounter of
P/Lexell with Jupiter, in 1779; the comet has been put We have already noted that not all SP comets have the
into a very elongated ellipse. In fact, a small diffe- same dynamical characters, nor the same dynamical
rence in the timing of the event would have produced a origin. It may be of interest to analyze their orbits
parabolic comet (Carusi et al., 1982). It has been pro- in some detail, in order to elucidate the internal
posed (Everhart, 1977; Carusi et al., 1986) that SP co- structure of this dynamically important population of
mets with J < 2 were captured by Jupiter in this way; a minor bodies. This analysis is now facilitated by the
representative of this group of SP comets is P/Halley. existence of long-term integrations of comet's motions
(Belyaev f.t al., 1986; Carusi et al., 1985), the long-
est of which covers a time span (821 years) comparable
with the supposed lifetime of comets as active objects.
yum

Table I. Orbital parameters of Halley-type comets.

S "
4 s
S Name J a e i
2 I 177* \
\ P/Tempel-Tuttle -0.64 10.Z7 0.904 162.71
\ P/Halley -0.61 17.94 0.967 162.24
1 P/Pons-Gambart -0.45 14.89 0.946 136.45
(

X
P/Swift-Tuttle -0.27 24.33 0.960 113.56
-"
P/de Vico 0.37 17.99 0.963 85.11
- K
P/Hartley-IRAS 0.54 7.72 0.834 95.73
\
N |upit*r P/Pons-Brooks 0.60 17.13 0.955 74.18

\
P/Mellish 0.64 27.65 0.993 32.68
P/Herschel-Rigollet 0.64 28.84 0.974 64.20
- P/Wilk 1.03 32.74 0.981 26.02
f t»r 177* X IMII
-2 2 4 P/Bradfield 1.07 28.41 0.952 51.79
P/Brorsen-Metcalf 1.11 17.30 0.972 19.21
Fig. 2 - Encounter of P/Lexell with Jupiter in 1779. P/Olbers 1.25 16.92 0.930 44.61
The minimum distance of approach was only 0.0015 AU. P/Barnard 2 1.29 27.65 0.960 31.25
P/Vaisala 2 1.36 19.40 0.934 38.00
P/Westphal 1.36 15.64 0.920 40.88
The situation is considerably different when J is P/Crommelin 1.48 9.09 0.919 29.10
greater, or much greater, than 2, although this value P/Cubiago 1.52 15.72 0.929 22.32
must be considered as pure?, conventional. These co- P/Tuttle 1.60 5.72 0.823 54.46
mets, as a matter of fan?:, have low relative velocities P/Stephan-Oterma 1.89 11.25 0.860 17.98
at encounters, and may exhibit a number of dynamical
phenomena, such as temporary sa'-ellite captures or tem-
porary librations. These comets, through successive
encounters with the giant planets, can be gradually A first subgroup already mentioned, consists of the
transferred from Neptune, to Uranus, to Saturn and comets with J < 2. We will call them Halley-type (HT)
finally to Jupiter. Some steps may, of course, be comets (table I ) , although this designation has been
jumped, and at any point the comet can reverse its used in the past with a somewhat different definition.
inward trend, under suitable conditions; anyway, one of We have said that these comets have probably been
the end states of this evolution is an orbit in the so- transferred to orbits of short period as a consequence
called Jupiter family. Owing to the succession of of a single encounter with Jupiter. Moreover, as shown
interactions with several planets, each of them requi- in Carusi et al. (1986), their dynamical characteris-
ring at least a close encounter, this process has been tics are so closely resembling those of comets with
called multi-stage capture. It is thought that the longer periods (between 200 and 1000 years) that it
majority of SP comets was originated this way. seems natural to conclude that Halley-type comets are
the "tail" of long-period comets towards short orbital
periods.

3. DIFFERENT TYPES OF SHORT-PERIOD COMETS On the other extreme of J, close to 3 and on both
sides of this value, there is a group of comets charac-
Some 140 SP comets have been observed so far. Many of terized by having their orbits nearly tangential to
them have revolution periods such that a second passage that of Jupiter either in their perihelion or aphelion.
close to the Sun, since the time of discovery, has not P/Oterma and P/Gehrels 3 are nice examples of this
yet taken place: they are the one-apparition comets, peculiar group; their main dynamical feature is a very
imong these, however, are comets that should have been JLow velocity relative to Jupiter, which cause rather
observed more than once and the absence of their reco- frequent* deep and efficient encounters with drastic
very may be due either to poor knowledge of their or- changes of Che orbital elements. Due to the low en-
bits, or to a definitive extinction as active objects, counter velocity, the osculating orbital parameters

23
with respect to Jupiter become often elliptic, leading cific behaviours, presumably all temporary in nature.
to temporary satellite captures. Some comets of this An interesting subsample, whose dynamics nejds to be
type are listed in table II, all of them with 2.9 < J < studied in greater detail, is composed of comets with
3.0A. Another interesting feature of these orbits is semiaxes between those of Jupiter and Saturn (table
III). Their dynamical evolution is affected at the
same time by the two planets, and presumably represents
Table II. Comets with high-J orbits, often undergoing a rather frequent transient stage preceding the defini-
temporary satellite captures during close encounters. tive transfer to the Jupiter family.

Table III. Comets with orbits between Jupiter and

P/Schwassmann-Wachmann 2 3.00 3.48 0.387 3.73 Saturn.
P/Whipple 2.94 3.82 0.353 10.24
P/Oterma 3.04 3.96 0.144 3.99 Name J a e
P/Gunn 3.00 3.59 0.319 10.38
P/Shajn-Schaldach 2.93 3.75 0.406 6.15 P/ Schwassmann-Wachmann 1 2.98 6.09 0.105 9.75
P/Smirnova-Chernykh 3.01 4.17 0.145 6.64 P/Neujmin ] 2.16 6.85 0.775 15.03
P/Cehrels 3 3.03 4.04 0.152 1.10 P/Van Biesbroeck 2.65 5.36 0.550 6.60
P/Wild 3 2.93 3.62 0.368 15.46 P/Wild 1 2.42 5.61 0.647 19.89
P/Bus 3.01 3.49 0.375 2.58 P/du Toit 2.12 6.07 0.787 18.70
P/Russell 3 2.92 3.82 0.344 l'-.10 P/Sanguin 2.41 5.39 0.664 18.64
P/Russell 4 3.00 3.45 0.383 6.25 P/Gehrels 1 2.89 5.95 0.597 9.64
P/Kowal 1 2.95 6.11 0.237 4.36
P/van Houten 2.86 6.25 0.367 6.65
P/Chernykh 2.59 6.33 0.594 5.73
represented by the rather frequent exchanges of perihe- P/Bowell-Skiff 2.42 6.26 0.689 3.79
lion with aphelion, as a consequence of an encounter, P/IRAS 1.96 5.58 0.696 46.18
that is a clear signature of their stepwise capture P/Kowal-Vavrova 2.60 6.34 0.588 4.32
from a long-period orbit. P/Oterma is the only comet
for which the transfer o£ dynamical control from Saturn
to Jupiter, that took place rather recently, has been
reconstructed numerically (see fig. 3 ) .
4. CLOSE ENCOUNTERS AND SATELLITE CAPTURES

y(»u) The possibility of close encounters is obviously tied

to the orientation and size of cometary orbits. Among
8 x" • ' _^' N the known SP comets there are cases (like P/IRAS, for
example) of comets which cannot encounter Jupiter, due
V. to the high inclination and the unfavourable alignment
/ ^ ^s \
4 > of nodes. Other comets, like those of Halley-type,
c \ 1 '. only seldom pass close to a planet, since their orbital
• / '
I 1 /
periods are longer thar, those of other comets of short
:/
1
1 ° )\ I f ] period, and their low values of J would allow only very
t
fast encounters, anyway. An exceptional comet is
/ 1/ P/Encke, whose aphelion distance, 4.1 AU, is the smal-
•\ J . /
S • r lest of all SP comets. Since the perihelion distance
-4 •. N
of Jupiter Is 4.95 AU, P/Encke is never close to the
\
planet, their relative distance being 0.85 AU a.t least.
-8 ^ — — - "
Computer experiments (see for example Carusi and Pozzi,
1978; Carusi et al., 1979) show that the values of the
-8 -4 4 8 JCiAO)
"sphere of action", frequently encountered in litera-
ture, have little meaning and are of little help espe-
Fig. 3 - Orbits o£ P/Oterma in 1770 (a), 1933 (b), cially in cases In which the encounter velocity is low
1960 (c) and 1967 (d). Between (a) and (b) there have or very low. As a matter of fact, the efficiency of an
been 1 encounter with Saturn and 2 with Jupiter. (c) encounter in varying the orbital elements of a comet
and (d) are preceded by close encounters with Jupiter. strongly depends on the value of the Tisserand quantity
and, of course, on the minimum distance of approach.
We have already seen how a single encounter with Jupi-
The majority of SP comets with 2.0 < J < 2.9 belong to ter is sufficient to transform a very long period comet
the so-called Jupiter family. They are under the con- in a SP comet, or of changing a perihelion-tangent
trol of Jupiter, but their large relative velocity at orbit into an aphelion-tangent one. The last process*
encounter does not permit - unless the encounter is rather common among high-J comets, is responsible for
very close - substantial changes of orbital parameters. most cases of multi-stage capture; it shows also the
Many of them are in a temporary libration around low- great Instability of chaotic orbits.
order resonances with the planet. Further subdivi-
sions of these comets into homogeneous groups may be The frequency of close encounters differs widely from
disputable, although it is possible to single out spe-t case to case. The probability per revolution of a

24
 passage within a given distance from a planet increases Two comets (P/IRAS and P/Hartley-IEAS) with J < 2 have
with J, as well as the "efficiency" of Che encounter In encounters with Saturn and Jupiter, respectively. Both
varying the orbital elements of the comet. However orbits are of high inclination (45 degrees for P/IRAS
this is not a strict rule; we have already seen that and more than 90 for P/Hartley-IRAS) and then their
P/Encke, the comet with the highest value of J, cannot encounters are not very effective. While P/IRAS cannot
in fact encounter Jupiter at all* its aphelion distance encounter Jupiter in the present orbit, because of the
being decoupled from the orbit of the planet. In the unfavourable orientation of it, the opposite is true
long-term integration by Carusi et al. (1985) (that for the other comet, thus showing Che importance of the
contains the most extended sample of encounters oc- orientation in space of the two orbits (that of the
curred to observed comets) there are objects that did planet and especially that of the comet) in preventing
not encounter any planet over a time span of 821 years close encounters for a relatively long time, at least
(table IV). Many of them (18 out of 27) are HI comets, until the rotation of the line of nodes and of the line
of apses may allow a close encounter. At the same
time, shallow approaches to Saturn may cause a more or
Table IV. Comets with no encounters with the major pla- less pronounced variation of the Tisserand quantity
nets (within 0.5 AU) in the period 1585-2406. with respect to Jupiter; in the case of P/IRAS it has
been shown that this quantity was greater than 2 in the
Name Relevant orbital features past, before a close approach to Saturn in 1950 (Carusi
et al., 1985).
P/Halley Halley-type
P/Encke Low aphelion distance On the other extreme, the comets that undergo the
P/Tuttle Halley-type maximum number of encounters (greater than 0.1 per
P/Crommelin Halley-type revolution) have their values of J greater than 2.6
P/Tempel 2 1/2 resonance (see table V ) ; all of them have chaotic orbits, often
P/Pons-Brooks Halley-type wandering between the. 1/2 and 2/3 resonances with
also 6/1 resonance
P/Olbers Halley-type
also 6/1 resonance Table V. Comets which undergo more than 0.1 encounters
P/Westphal Halley-type per revolution within 0.5 AU from the major planets.
P/Brorsen-Metcalf Halley-type
also 6/1 resonance Name J Remarks
P/Schwassmann-Wachmann 1 High perihelion distance
P/Neujmin 1 Between Jupiter and Satur P/d1Arrest 2.71 chaotic
also 3/2 resonance P/Pons-Winnecke 2.68 irregular
P/Herschel-Rigollet Halley-type P/Finlay 2.62 chaotic
P/Stephan-Oterma Halley-type P/Neujmin 2 2 .90 chaotic, extinct?
P/Arend 2/3 resonance P/Wolf-Harrington 2 .81 chaotic
P/du Toit Between Jupiter and Saturn P/Honda-Mrkos-Pajdu?akova 2 .60 chaotic
also 5/4 resonance P/Churyumov-Gerasimenko 2 .75 chaotic
P/Peters-Hartley 2/3 resonance P/Schwassmann-Wachmann 3 2 .77 chaotic
P/Pigott 1/2 resonance P/Kohoutek 2.89 chaotic
P/Pons-Gambart Halley-type P/ Siairnova-Chernykh 3 .00 chaotic
P/de Vico Halley-type P/Helfenzrieder 2 .67 chaotic, lost
P/Swift-Iuttle Halley-type P/Lexell 2 .73 chaotic
P/Barnard 2 Halley-type P/Kowal 2 2 .78 chaotic
P/Mellish Halley-type P/Bus 2 .98 chaotic
P/Dubiago Halley-type
also 5/1 resonance
P/Wilk Halley-type
P/Vaisala 2 Halley-type Jupiter and sometimes displaying just one cycle of tem-
also 7/1 resonance porary libration about the first of these resonances.
P/Gehrels 1 Between Jupiter and Saturn P/Pons-Winnecke is the only comet of this group which
also 5/4 resonance exhibit a persisting libration, that is very irregular,
P/Bradfield Halley-type however. A peculiar case is represented by P/Lexell,
with three encounters with Jupiter before the injection
into an orbit with period of more than 280 years; the
number of encounters per revolution in this case is
one is P/Encke; 7 of the remaining 8 comets with 0 high, because the number of revolutions is very small
encounters (within a sphere of 0.5 AU) with the outer in the time span considered.
planets are in libratlon around some resonance with
Jupiter. Among them three comets (P/Neujmin 1, P/du For what concerns the "efficiency" of the encounters,
Toit and P/Gehrels 1) have semiaxes greater than that one may compute the absolute value of the cumulative
of Jupiter; the other four are equally divided between relative variations in orbital energy,5 lAE/E | . The
Che 1/2 resonance (P/Tempel 2 and P/Pigott) and the 2/3 minimum of this quantity is given by P/Encke (0.24) and
(P/Arend and P/Peters-Hartley). The last comet, the maximum by P/Gehrels 3 (7.41); it is worth noting
fcVSchwassmann-Wachmann 1> is very peculiar, since its that these two comets have some of the highest values
orbit is just outside Jupiter's orbit and its eccentrif- of J: 3.025 and 3.016 respectively (only P/Oterma has
tity is very small (below 0.1). B J-value greater than those: 3.04). With the except-

25
Ion of P/Encke, however, the less disturbed orbits have Not all temporary satellite captures are of the same
J < 2.6 (sometimes less than 2.2) and the most disturb- duration and with the same characteristics. In some
ed ones have J > 2.7 (often > 2.9, see table VI). It cases the comets do not perrorm loops around the planet
is natural to conclude that the size of the total per- (fig. 4 ) , or are so distant that the occurrence of
turbations on a cometary orbit is also strongly depen- elliptic planetocentric elements may be ascribed to
dent on the value of J, even on rather long time spans kinematical rather than dynamical reasons. Moreover,
including several close encounters. the durations of the captures differ from case to case:
the longest ones are those of P/Gehrels 3, which amount
Temporary satellite captures are a rather frequent to more than 31 years in total (more than 9 years as a
event among comets on high-J orbits. In fact, among maximum, see fig. 5 ) .
the 17 well determined events of this type found by
Carusi et al. (1985) relative to 9 comets, 12 are due
to only 4 objects: P/Gehrels 3 (5 captures), P/Schwas-

Table VI. Orbital perturbations over 821 years. The

quantity S|AE/E | Is computed summing up the absolute
values of relative energy variations every 800 days.

< 0.4 < 0.5 > 2.0 > 4.0

P/Encke P/Borrelly P/Brooks P/Kearns-Kwee

P/Tuttle P/Wild 1 P/Gunn P/Smlrnova-
P/Peters-Hartley P/du Toit P/Lexell Chernykh
P/IRAS P/Pigott P/Whipple P/Wild 2
P/Oterma P/Gehrels 3
P/Brooks 1
P/Wild 3
P/Wolf-Harrington
P/Ashbrook-Jackson
P/Shajn-Schaldach
P/West-Kohoutek-Ikemura rig. 4 - Jovicentric rotating pattern of P/Bus close to
P/Gehrels 2 Jupiter in 2021-2028. The comet does not loop around
P/Schwassmann-Wachmann 2 the planet, and the satellite capture is very short.
P/Bus

Table VII. Temporary satellite captures.

Name J Epoch of Duration

mln. dist. (years)

P/Schwassmann-Wachmann 2 2.97 1665 6.59

P/Schwassmann-Wachmann 2 2.98 1926 1.40
P/Schwassmann-Wachmann 2 3.00 1997 0.99
P/Oterma 3.02 1937 4.07
P/Oterma 3.03 1963 3.32
P/Cunn 2.99 1872 5.45
P/Shajn-Schaldach 2.96 1946 1.53
P/ Smi rnova-Chernykh 3.01 2030 5.80
P/Smi rnova-Chernykh 2.99 2077 2.16
P/Gehrels 3 3.02 1970 7.50
P/Gehrels 3 3.02 2062 9.77
P/Gehrels 3 3.02 2203 4.56
P/Gehrels 3 2.99 2305 4.46 Fig. 5 - Jovicentric rotating pattern of P/Gehrels 3 a-
P/Gehrels 3 3.02 2400 5.22 round Jupiter in 1963-1976. The satellite capture has
P/Giclas 2.88 2308 1.58 lasted for more than seven years.
P/Bus 3.01 2023 0.58
P/Russell 3 2.89 1941 0.73

5. RESONANT MOTIONS

smann-Wachmann 2 (3 captures), P/Oterma and P/Smlrnova- It is known since a long time that many comets of the
Chernykh (2 captures each, see table VII). Of the so-called Jupiter family llbrate around low-order rest-
remaining 5 events, 3 occur on orbits of still high J: nances with Jupiter's motion. Furthermore, there are
P/Gunn, P/Shajn-Schaldach, P/Bus, and only two with comets which have exhibited In the past horseshoe pat+-
rather "low" values of J: P/Russell 3 and P/Giclas. terns In the jovicentric rotating frame, and others -

26
with semiaxes greater than that of this planet - who distances.
librate around resonances with Jupiter that are very
close to resonances with Saturn, too. More recently
(see Carusi et al., 1986, 1987), it has been shown that
HT comets may librate around high-order resonances with 6. COMPARISON OF INTEGRATIONS OF REAL OBJECTS WITH
Jupiter, of the form n:l. MONTE CARLO RESULTS

Basing on the mentioned long-term integrations by Caru- The rapid development of computing tools, both hardware
si et al. (1985), and including the findings about HT and software, has allowed in the last twenty years a
comets, it appears that 48 out of 132 SP comets disco- number of numerical investigations on the dynamics of
vered up to the end of 1984 perform at least a tempora- SP comets. We will briefly review the most important
ry libratlon with Jupiter (see table VIII). This high of them, comparing their findings with the results of
value (36% of the total) Indicates that this process is long-term integrations of motion of observed comets.
very common among SP comets. 20 comets librate for
more than 400 years, and a minority of them for at These researches may be divided in two groups: in some
least 800 years. In one case (P/de Vico-Swift) the cases the motion of individual "comets", under the
comet has two temporary librations around two different gravitational influence of the Sun and some major pla-
resonances, namely the 1'2 and the 2/3. The first of nets, has been followed over a great number of revolu-
these resonances is by far the most populated, with 17 tions, in order to examine the general behaviour of
bodies on cometary orbits. In other cases many objects
have been examined over short time spans, to provide a
Table VIII. LibrationF around resonances with Jupiter. good statistical sample related to specific phenomena.
The long-term integration of real cometary orbits may
Name Res Name Res be thought of as a compromise between these two strate-
gies , providing both evolutionary tracks over substan-
P/Pons-Winnecke 1/2 P/Tempel 1 1/2 tial periods of time and samples of dynamical phenomena
P/Tempel-Swift 1/2 P/de Vico-Swift 1/2 relevant to the dynamics of these objects.
P/Kopff 1/2 P/Forbes 1/2
P/du Toit-tleujmin- P/Tsuchinshan 1 1/2 The process of multi-stage capture of long-period into
Delporte 1/2 P/ Churyumov-Gerasitnenko 1/2 short-period orbits has been modelled by Everhart
P/Clark 1/2 P/West-Kohoutek-Ikemura 1/2 (1977), who found a rather low efficiency in capturing
P/Kohoutek 1/2 P/Pigott 1/2 comets well inside the planetary region; the majority
P/Harrington-Wilson 1/2 P/Tritton 1/2 of comets would in fact be ejected into hyperbolic
P/Haneda-Campos 1/2 VI Howe11 1/2 orbits. However, once trapped between the orbits of
P/Reinmuth 2 4/7 P/Arend-Rigaux 4/7 Saturn and Jupiter, comets start to move on highly
P/Holmes 3/5 P/Perrine-Mrkos 3/5 chaotic orbits (Everhart, 1973), which display very
P/Faye 2/3 P/de Vico-Swift 2/3 different regimes of motion including temporary lib-
P/Schwassmann- P/Daniel 2/3 rations, temporary and generalized trojan and horse-
Wachmann 2 2/3 P/Ashbrook-Jackson 2/3 shoe orbits, temporary satellite captures. As we have
P/Arend 2/3 P/Peters-Hartley 2/3 seen, this is exactly what happens to observed comets,
P/Kussell 1 2/3 I'/Wild 3 2/3 a minority of which Is on rather stable orbits, at
P/Shoemalcer 1 2/3 P/Vaisala 1 3/4 least over the studied time spans. The motion of
P/Cehrels 2 3/4 P/Lovas 3/4 comets outside the orbit of Saturn has been studied,
P/Comas Sola 4/5 P/Whipple 1/1 in connection with the object 2060 Chiron, by Scholl
P/Boethin 1/1 P/Russell 3 1/1 (1979) and Olkawa and Everhart (1979); these resear-
P/du Toit 5/4 P/Gehrels 1 5/4 ches have confirmed that objects in such a dynamical
P/Gunn 4/3 P/Kowal-Vavrova 4/3 state can evolve towards Jupiter - and become members
P/Neujmin 1 3/2 P/Crommelin 7/3 of the Jupiter family.
P/Dubiago 5/1 P/Pons-Brooks 6/1
P/Olbers 6/1 P/Brorsen-Metcalf 6/1 The numerical simulations would also predict the pre-
P/Vaisala 2 7/1 sence of a large number of comets with perihelion
distances so large to inhibit the formation of the
coma. Most of these objects are unobservable with the
present techniques, but the finding is supported by the
comets, followed by the 2/3 (10) and the 3/4, 1/1, 6/1 discovery, in recent years, of objects with perihelion
(three comets each). In the case of 1/1, however, close to, or even outside, the orbit of Jupiter: these
there are two comets (P/Whipple and P/Russell 3) who could be the brightest members of that population.
move temporarily in a horseshoe fashion, of the type
described by Everhart (1973). Strong gravitational interactions with the major pla-
nets, occurring during close encounters, have been
The injection into, and ejection from, a temporary investigated by several authors, either using a Monte
libration is a process that needs further study; now we Carlo approach (Rickman and Vaghi, 1976; Froeschle and
can only say that it seems rather probable that a comet Rickman, 1980), or with a direct integration of a large
of the Jupiter family enters this regime of motion for number of such events (Carusi and Pozzi, 1978; Carusi
a fraction of its active lifetime, thus lengthening its et al., 1979; Carusi and Valsecchi, 1979, 1982a,b;
residence in the inner regions of solar system. This Carusi et al., 1981; Rickman and Malraort, 1981; Carusi
could accelerate its physical aging, since many of the et al., 1983). It is remarkable that all the patterns
objects in these orbits have rather small perihelion at close encounters, and the possible orbital evolut-

27
 ions after them, found in the case of real objects have Clube, S.V.M.:1985, in Dynamics of Comets: their Origin
also been found in these numerical experiments, thus and Evolution (Eds A. Carusi,G.B. Valsecchi; Reidel,
confirming that the most common dynamical phenomena Dordrecht), p. 19.
related to close encounters with the giant planets have Clube S.V.M.; Napier, W.M.:1984, Mon. Not. Roy. Astron.
been identified. Soc. 208, 575.
Delsemme, A.H.: 1985, in Dynamics of Comets: their Ori-
gin and Evolution (Eds A. Carusi, G.B. Valsecchi;
Reidel, Dordrecht), p. 71.
7. CONCLUSIONS Everhait, E.: 1973, Astron. J. 78, 3i6.
Everhart, E.: 1977, in Comets, Asteroids, Meteorites
As we have seen, most aspects of the dynamical evolut- (Ed. A.H. Delsemme; Univ. Toledo Press, Toledo), 99.
ion of SP comets are at least qualitatively understood; Everhart,E.: 1982, in Comets (Ed. L.L. Wilkening; Univ.
a definite improvement in our knowledge of this field Arizona Press, Tucson), p. 659.
would come from better quantitative assessments of the Fernandez, J.A.: 1980, Icarus ^ 2 , 406,
probabilities of the various processes, and this will Fernandez, J.A.: 1982, Astron. J. 87^, 1318.
require more sophisticated and extensive computations Fernandez, J.A.:1985, in Dynamics of Comets: their Ori-
than those performed so far. gin and Evolution (Eds A. Carusi, G.B. Valsecchi;
Reidel, Dordrecht), p. 45.
A further step may then be the interfacing of dynamical Fernandez, J.A.; Ip, W.-H. : 1981, Icarus V7_, 470.
studies with physical ones, as the space missions and Froeschle.C.; Rickman.H.:1980, Astron. Astrophys. 82,
the ground based observations give us more realistic 183.
models of the characteristics and the behaviour of Harrington, R.S.: 1985, Icarus 61^, 60.
cometary nuclei in the vicinity of the Sun. Hills, J.G.: 1981, Astron. J. 86, 1730.
Kresak, L.: 1972, Bull. Astron. Inst. Czechosl. 23_, 1.
Lyttleton, R.A.: 1974, Astrophys. Space Sci. 3^, 385.
Marsden, B.G.; Sekanina, Z.: 1973, Astron. J. 78, 1118.
Mignard, F.; Remy, F.: 1985, Icarus 63, 20.
REFERENCES Napier, W.M.; Stanlucha, M.: 1982, Mon. Not. iU,y.
Astron. Soc. Jj>8, 723.
Bailey, M.E.: 1983, Mon. Not. Roy. Astron. Soc. 204, Oikawa, S.; Everhart, E.: 1979, Astror.. J. 84, 134.
603. Oort, J.H.: 1950, Bull. Astron. Ins.. Neth. JJ., 91.
Bailey, M.E.; McBreen, B.,; Ray, T.P.: 1984, Mon. Not. Opik E.J.: 1973, Astrophys. Space Sci. 2_1, 307.
Roy. Astron. Soc. 209, 881. Remy F.; Mignard, F.: 1985, Icarus, 63, 1.
Belyaev, N.A.;Kresak,L.; Pittich.E.M.; Pushkarev, A.N.: Rickman, H,; Malmort,A.M.:1981, Actron. Astrophys. 102
1986, Catalogue of Cometary Orbits (Slovak Academy 165.
of Sciences, Bratislava). Rickman, H.; Vaghi.S.: 1976, Astron. Astrophys. 51, 327.
Cameron, A.G.W.: 1973, Icarus _18, 407. Safronov, V.S.: 1969, Evolution of the Protoplanetary
Carusi, A.; Kresak, L.; Valsecchi, G.B.: 1981, Astron. Clouil and Formation of the Earth and Planets (Nauka,
Astrophys. 99, 262. Moscow; 1972 transl. Israel Program for Scientific
Carusi, A.; Kresak, L.; Perozzi, E.; Valsecchi, G.B.: Translations, Jerusalem).
1985, Long-Term Evolution of Short-Period Comets Scholl, H.: 1979, Icarus 40, 345.
(Hilger, Bristol). Valtonen, M.J.: 1983, Observatory ^03, 1.
Carusi, A.; Kresak, L.; Perozzi, E.; Valsecchi, G.B.: Valtonen, M.J.; Innanen, K.A.: 1982, Astrophys. J. 255
1986, in Exploration of Halley's Comet (Eds B. Bat- 307.
trick, E.J. Rolfe, R. Reinhard; ESA SP-250), p. 413. Weissman, P.R.: 1982, in Comets (Ed. L.L. Wilkening;
Carusi, A.; Kresak, L.; Perozzi, E.; Valsecchi, G.B.: Univ. Arizona Press, Tucson), p. 637.
1987, Astron. Astrophys. in press. Weissman, P.R.: 1984, Science ^24, 987.
Carusi, A.; Kresakova, M.; Valsecchi, G.B.: 1982, Weissman, P.R.: 1985, in Dynamics of Comets: their Ori-
Asf-on. Astrophys. 116, 201. gin and Evolution (Eds A. Carusi, G.B. Valsecchi;
Carusi, A.; Perozzi, E.; Valsecchi, G.B.: 1983, in Dy- Reidel, Dordrecht), p. 87.
namical Trapping and Evolution in the Solar System Withmire, D.P.; Jackson, A.A.IV: 1984, Nature JJOjS, 713.
(Eds V.V. Markellos, Y. Kozai; Reidel, Dordrecht), Yabushita, S.: 1979, Mon.Not.Roy.Astron. Soc. JjLZ" 4 * 5 -
p. 377.
Carusi, A.; Pozzi, F.: 1978, Moon and Planets Jj), 71. t i s c u s s i o n :
Carusi, A.; Pozzi, F.; Valsecchi, G.B.: 1979, in Dyna- Olsson-Steel: How ma P/Halley captured? Encounters
mics of the Solar System (Ed. R.L. Duncombe; Reidel,
with Jupiter are of very low-efficiency since T ^ - 0 . 6 ,
Dordrecht), p. 185.
Carusi, A.; Valsecchi, G.B.: 1979, in Asteroids (Ed. T. Caruai: Although the efficiency ii- very low, P/Kalley
must have had several encounters rather close to Ju-
Gehrels; Univ. Arizona Press, Tucson), p. 391. p i t e r : niost probably the clo&est, and best oriented,
Carusi, A.; Valsecchi, G.B.:1982a, in Sun and Planetary of them huR brought the comet where i t i s nowg
System (Eds W. Fricke, G. Teleki; Reidel,Dordrecht),
Bananzkiewicz: Is i t possible that nongravitational
p. 379. effects could change the patterns of motion you have
Carusi, A.; Valsecchi, G.B.:1982b, in Sun and Planetary presented, e .-.pedal ly the resonant cases ?
System (Eds W. Fricke, G. Teleki; Reidel,Dordrecht),
Carur=i: I t i s c:ert:iinly poo.uble. A'e h-ive not modeled
p. 385. the nongravitatioruU forcer, becftuss they are unknown
Carusi, A.; Valsecchi, G.B.: 1985, in Dynamics of Co- far most comets. Taking the's into account, the patterns,
mets: their Origin and Evolution (Eds A. Carusi,G.B. especially in cases of resonances, muat be slightly dif-
Valsecchi; Reidel, Dordrecht), p. 261. ferent and this difference should accumulate with tine.

28
 LONG-TERM RESONANCES AND OBBITAL EVOLUTIONS OP HALLEY-TYPE COMETS

A. Carusi 1), L. Kresak 2 ) , B. Perozzi 3 ) , and G.B. Valsecchl 1 ) ,

1) Istituto Astrofisica Spaziale - CNR, 00185 Rome, Italy

2) Astronomical Institute - SAV, 84228 Bratislava, Czechoslovakia
3) Osservatorio Astronomico Collurania, 64100 Teramo, Italy

Backward integrations of motion of the Halley-type comets, covering over 11,000 years, are
used to investigate their librations around hign-order resonances with Jupiter. These occur
for comets moving in direct orbits with revolution periods between 50 and 90 years. The tact
that about one half of them is librating at a time explains the concentration of revolution
periods in this range. The librations are of rather uniform period and amplitude, and tend to
persist over about 200 revolutions of the comet. Their presence implies that the lifetimes of
these comets since their captures into periodic orbits of small perihelion distance mostly
exceed 300 revolutions. Possible exceptions among the 9 comets with present periods of 50 to
90 years are the already extinct P/Westphal, and also P/Ualley, for which a close approach to
the orbit of Jupiter 150 revolutions ago was identified.

1. INTRODUCTION In order to keep the integration time reasonably

short, it was decided to limit the number of per-
Currently we know 19 comets with revolution pe- turbing planets to seven, disregarding Mercury and
riods between 20 and 200 years (Marsden, 1986), Pluto; the mass of the former was added to that of
which are conventionally referred to as comets of the Sun. The nongravitational effects, which are
Halley type. Another three comets have periods of only known for five Halley-type comets of more
less than 20 years, but the low values of their than two apparitions (Marsden, 1985) and cannot be
Tisserand invariants with respect to Jupiter, T < extrapolated with confidence, were disregarded.
2, are indicative of their similar dynamical his- All the Halley-type comets included in the LTEP
tory (Carusi et al., 1986). In spit« of the very were integrated backwards from JD 2300000.5, which
limited statistical sample, it was recognized long was the end point of our previous computations.
ago that there is a significant overabundance of The starting positions and velocities of the co-
periods around 70 years, pointing to a mechanism mets were those obtained for this date in the LTEP.
concentrating the coaets into this region, or let- The starting positions and velocities of the pla-
ting them stay there for a longer time. An appro- nets were taken again from DE-102, with appropri-
priate mechanism was suggested in our previous pa- ate corrections taking into account that the Sun
pers (Carusi et al., 1986 and 1987), where we have and Mercury were replaced by a single body in their
found librations ojf some comets around the 5:1, barycenter. The integrations spanned over 4 x 10°
6:1 and 7:1 resonances with Jupiter, stabilizing days (nearly 11,000 years), from 1585 AD to 9367
temporarily their stay in this region. BC, and the CPU time on the FPS 364 was less than
The integrations on which this conclusion was 8 hours.
based (Carusi et al., 1985) spanned an interval of
3 x 105 days, 1585 AD to 2406 AD. This would typi- 3. THE MAIN RESULTS
cally include only two full libration cycles. In
order to get a better insight into this phenomenon In this paper we concentrate on the results on
we have performed backward Integrations for anoth- the nine comets with revolution periods between 50
er 4 x 10° days, 1585 AD to 9367 BC. The whole pe- and 90 years, in that range where the librations
riod covered by computations has thus become equi- were found (Carusi et al., 1986) : around the 6:1
valent to 30 typical libration cycles, and 1000 resonance for P/Brorsen-Metcalf, P/Olbers, and P/
revolutions of Jupiter, allowing to check the per- Pone-Brooks, that of 5:1 for P/Dubiago, and that of
sistence of the resonances and the transitions 7:1 for P/VSisala 2. The evolutions of the orbital
between different types of motion. Also, the ex- periods of these comets according to the extended
tended time span is about the same as the probable integrations are shown in Fig. 1. The periods are
active lifetimes of Halley-type comets, so that it referred to that of Jupiter, and computed at each
might encompaes some captures of these comets from aphelion passage from the semimajor axis of the
long-period orbits. osculating barycentric orbit. The values obtained
in this way are much closer to the actual duration
2. THE METHOD OF COMPUTATION of the revolution than the generally used values
of the osculating period at perihelion, since for
The longer time span to be covered by numerical most of the time the actual rate of motion of a co-
integrations required some major changes against met of Halley type is best approximated by this
the method used in the Long-term Integration Pro- barycentric orbit.
ject (Carusi et al., 1985). The use of planetary For the period of ± 400 years from now (Carusi
coordinates from the JPL Long Ephemeris DE-102 et al., 1987), P/Brorsen-Metcalf and P/Pons-Brooks
could not be maintained, because this only covers were found to librate around the 6:1 resonance all
less than one half of the time span required. It the time, while P/Olbers was escaping from it at
was therefore decided to integrate the whole sys- the end. In the extended backward computations, P/
tem of planets and comets in heliocentric coordi- Brorsen-Metcalf remains in this libration until the
nates using Cowell's method and, as before, the end of integration, but the behaviour of P/Olbers
RADAU integrator by Everhart (1985). and P/Pons-Brooks is reversed. The former librates
Since our computer had a 64-bit word length all the time, whereas the libration of the latter
(in double precision), the 15-th order version of can be only traced back to <u 16OO BC. The onset of
RADAU was used, putting the control parameter LL, libration at that time is followed by a progressive
on which the accuracy of the integration depends, diminution of the period of the libration cycle,
equal to 8. For more details.see Everhart (1985). and damping of its amplitude.
 7 8 6 4 2 0

W\ vv
6 6 6

P/HALLEY

MA/VWVVV\AAA/VWVWVVWV\/W

Figure 2. The same as in Fig. 1 for the other four

comets with revolution periods between 50 and 90
years. Note that the vertical scale for P/Westphal
7 is reduced by a factor of three.

The dynamical evolutions of the remaining four

comats, showing no signatures of librations, are
plotted in Fig. 2. The periods of P/Halley and P/
Pons-Gambart, moving in retrograde orbits, and of
Figure 1. The changes in the revolution periods of P/DeVlco, with inclination close to 90°, oscillate
five Halley-type comets subject to temporary lib- with moderate amplitudes without crossing their
rations around high-order resonances with Jupiter. neighbouring n:1 resonances. In somo sense, this
Horizontal scale, time in millennia BC; vertical is a direct counterpart to the piograde librators.
scale, barycentric revolution period at aphelion, The double-periodic oscillations of the period of
in units of the revolution period of Jupiter. P/Halley during the last four millennia are quite
interesting. They may explain the partial success
in linking up its different apparitions by empiri-
Another conspicuous example of long-terra lib- cal formulae, as first applied by Angstrflm (1862)
ration is P/Dubiago. Some differences against P/ and developed by Kamienski (1961). However, any
Brorsen-Metcalf and P/Olbers only appear when the extrapolation of this kind must break down comple-
horseshoe patterns reconstructed from the relative tely less than 60 revolutions back, when the pat-
positions of Jupiter and the comet, at its indivi- tern changes abruptly, and again 5 revolutions
dual perihelion passages, are intercompared. While from now, when the comet approaches the 6:1 reso-
the occupied arc in such a diagram exceeds con- nance with Jupiter (Carusi et al., 1987).
siderably 180° for P/Dubiago, it is smaller than Most chaotic is the motion of P/Westphal, the
this for the other two long-librating comets. To- revolution period of which varies quite irregular-
wards the end of the backward integration, nearly ly between 55 and 130 years. It must be emphasized
10,000 years ago, the libration of P/Dubiago va- that the past dynamical history of this comet is
nishes in two successive steps, indicative of its very poorly determined because its descending node
capture into resonance. P/VaisalS 2 shows, in ad- remains for the last five millennia wittin 0.5 AU
dition to the two cycles already recognized in the of the orbit of Jupiter. Thus it appears possible
LTEP (Carusi et al., 1987), only two incomplete that the comet was captured from a long-period
cycles immediately preceding. For the remainder of orbit during this time span.
the extended integrations it displays a chaotic
No similar crossings are indicated by the back-
behaviour, but its revolution period remains con-
ward integrations of the other eight comets, which
fined within rather narrow limits - only 2 to 3
suggests that they have already spent aiore than
times broader than the libration amplitude.
11,000 years, or at least 130 to 200 revolutions,

30
 Table I

Comet A q i to P R B E D N

27 P/flrorsen--Meteal 1 2 0.48/0.53 19/14 129/70 72/72 6:1 <-94OO =*24OO 360 33

15 P/Olbers 3 1.18/1.27 45/45 65/108 70/73 6:1 <-94O0 2300 390 30
14 P/Pons-Brooks 3 0.77/0.87 74/71 199/201 71/76 6:1 -1600 >24OO 440 9
519 P/Dubiago 1 1.11/1.06 22/20 97/92 62/64 5:1 -7700 >2400 340 30
521 P/Vaisala 2 1 1.29/1.41 38/37 335/328 85/87 7:1 1000 >2400 360 4
1 P/Halley 30 0.59/0.88 162/145 112/45 76/78 (6,7) - - - _
506 P/DeVico 1 0.66/0.72 85/82 13/10 76/77 (6,7) - - _
505 P/Pons-Gambart 1 0.81/0.91 136/133 19/358 57/58 (4,5) _ - _ _
25 P/Westphal 2 1.25/1.77 41/46 57/76 62/80 - - - - -

in periodic orbits similar to the present ones. Of the range of revolution periods between 50 and 90
course, for the one-apparition comets - in parti- years. Prom among the nine comets occupying this
cular P/Pons-Gambart - this conclusion has to be range at present, two - P/Halley and P/Pons-Gam-
taken with reserve, due to their poorly determined bart - move in retrograde orbits. Hence, for the
starting orbits. reasons explained in more detail elsewhere (Carusi
Most interesting is the ca&e of P/Halley. Kozai et al. , 1987), they are not liable to this type of
(1979) has suggested that its argument of perihe- libration. The repetition of similar patterns be-
lion librates very slowly between CJ = 47° and 133°. tween two neighbouring resonances n:1 is rather
Our integrations cover only about 30 % of Kozai*s the result of the opposite effect, repelling the
cycle, but at the end to stops a little below 45°. comet periodically from the resonance. This would
At the same time, the descending node approaches restrict the number of candidates for librations
the orbit of Jupiter within 0,15 AU, and remains to seven.
at this distance for a number of revolutions of The starting orbits of these comets are of dif-
the comet. P/Halley exhibits the largest progres- ferent accuracy, by which they can be divided into
sive variations of the orbital inclination, from two groups. P/Pons-Brooks, P/Olbers, P/flrorsen-
162° to 145°, going back in time; for all the oth- Metcalf and P/Westphal have already been observed
er comets the total change is ± 5° or less. As it at 3 or 2 apparitions, respectively, so that their
can be seen from Table I, its argument of perihe- present revolution periods are well determined.
lion is precessing most rapidLy, too. For the next The nongravitational effects are only known for
two comets with high precession rates, P/Brorsen- the former two comets (Marsden, 1985). Since their
Metcalf and P/Olbers, cc does not recede from 90° sum over one libration cycle amounts to less than
far enough to enable the comet to approach the or- 1/10 of the mean amplitude, it appears improbable
bit of Jupiter. that they would be able to destroy the libration
The total changes of the orbits of these nine pattern. The main source of uncertainty is that of
comets are summarized in Table I. This lists, in the present osculating periods of the three comets
succession : the names of the comets preceded by of only one recorded apparition; P/Dubiago, P/Vai-
their numbers from our catalogue (Carusi et al., sala 2, and P/DeVico. This makes about ± 2 years,
1985); the number of apparitions A, indicative of and equals to the mean amplitude reached by the
the degree of accuracy of the starting orbit; some librating comets during one cycle. Accordingly,
important orbital elements - perihelion distance the librations of P/Dubiago should only be real if
q, inclination i, argument of perihelion CJ, and the actual error is positive or small. Circumstan-
revolution period P - the first figure referring tial evidence, provided by the distribution of the
to the starting (present) orbit and the second to well determined periods of other comets with re-
that at the end of the extended backward integra- spect to the resonances, implies a probability of
tions, 9367 BC; the resonance ratio R around which well over 50 %. The capture of P/Vaisiilii 2 into
the comet librates, or was librating in the past, libration, found to have occurred 15 revolutions
or the resonance values of n in n:1 between which ago, is questionable. It might have talien place
it remained confined for the whole integration pe- much earlier, or not at all. The orbit of P/DeVico
riod (in parentheses); the approximate dates of is of very high inclination, vur>ing between 82°
the beginning and the end of libration, B and E; and 85°. Therefore, it appears highly questionable
the average duration of one libration cycle D (in whether the libration mechanism could worK in this
years); and the number of the libration cycles N case with any starting period. The evolutions of
identified in our computations. P/Pons-Brooks and P/Vaisala 2 suggest that a comet
has to spend some time in the vicinity of a reso-
Among the other comets of Halley type, not in- nance, until a suitable configuration triggers the
cluded in Table I, there are several interesting librations. On P/Pons-Brooks one can aJ so recog-
cases of temporary librations persisting over 4 to nize a progressive damping of the amplitude and
8 cycles. What they have in common is just a con- shortening of the cycle to its typical duration.
centration of the libration periods around ~500
years. Otherwise, there is a broad variety of the Even for the best determined orbits it is pos-
resonance ratios (7:4 for P/Hartley-IRAS, 5:2 for sible to rely on the positions of the comet on its
P/Crommelin, 3:1 for P/Stephan-Oterma, 9:1 for P/ orbital ellipse, and to identify its encounters
Bradfield, 11:1 for P/Swift-Tuttle), and resonance with the planets, only for a small fraction of the
patterns. The general impact of these resonances period covered by our backward integrations (see,
on the dynamical evolution of the system of comets e.g., Sitarski and Ziolkowski, 1986 for P/Halley).
is evidently of secondary importance, and they However, if there are librations preventing plane-
will be discussed in a separate paper. tary encounters, both of these restrictions lose
on their importance. Under such circumstances, the
4. DISCUSSION AND CONCLUSIONS available data make it possible to draw some gene-
ral conclusions on the resonance effects, in spite
The long enduring librations of the Halley-type of the limited number of known objects.
comets around high-order resonances with Jupiter, From among the comets with revolution periods
as demonstrated by integrations of their motions between 50 and 90 years, 40 % libra! is around high-
over 12 millennia, explain their overabundance in order resonances with Jupiter at a time. For the

31
comets moving in direct orbits, the share is over objects revolving in orbits similar to that of P/
50 c,i, and for i < 60°, 70 %. A typical duration of Halley in the critical period.
the librating motion is about 15,000 years, or 200
revolutions of the comet. An average libration cy- ACKNOWLEDGMENT. Our computations were made pos-
cle covers 350 to '(00 years, or a little over 30 sible by a grant from the Piano Spaziale Nazionale
revolutions of Jupiter. This is 3.0 to 2.5 times CNR, which is gratefully acknowledged.
longer than a typical cycle of a comet of the Ju-
piter family, librating temporarily around the 1:2
resonance, or of a steadily librating Trojan. On REFERENCES
the other hand, one cycle covers only five to six
revolutions of the comet. It is also interesting Carusi A., Kresak 1., Perozzi E., Valsecchi G.B.,
that, when all the Halley-type comets are taken 1985 : Long-term Evolution of Short-period Co-
together, the 20 % proportion of temporary libra- mets, A. Hilger, Bristol.
tors is just the same as in the Jupiter family of Carusi A. , Kresak: L. , Perozzi E. , Valsecchi G.B. ,
comets, and substantially higher than the propor- 1986 : in Exploration of Halley's Comet, ESA SP
tion of permanent librators among the asteroids. 250/11, p. 413.
The durations of the librations of Halley-type Carusi A., Kresak £., Perozzi L., Valsecchi C.B.,
comets indicate that their active lifetimes after 1987 : Astron. Astrophys., in press.
their captures from long-period orbits of large Everhart E., 1985 : in Dynamics of Comets - Their
perihelion distance are mostly longer than 20,000 Origin and Evolution, eds A. Carusi and G.B.
years, or 300 revolutions. Curiously enough, the Valsecchi, IAU Coll. 83, D. Reidel, Dordrecht,
only comet with revolution period between 50 and p. 185.
90 years which might be much younger, P/Westphal, Kamienski if., 1961 : Acta Astronomica 11, 223.
is the only one which has already disappeared. Kozai Y., 1979 : in Dynamics of the Solar System,
An object of special interest is P/Halley, for ed. R.L. Duncombe, IA1J Symp. 81 , p. 231.
which more reliable data on the past activity and Kresak L., 1985 : in Dynamics of Comets - Their
present mass loss exist than for any other comet. Origin and Evolution, eds A. Carusi and G.B.
At the end of our backward integrations* its peri- Valsecchi, IAU Coll. 83, D. Reidel, Dordrecht,
helion distance is 1.5 times larger than today, P. 279.
suggesting a slower disintegration rate. At that Marsden B.G., 1985 : in Dynamics of Comets - Their
time, the descending node remains fixed near the Origin and Evolution, eds A. Carusi and G.B.
orbit of Jupiter for a number of revolutions, per- Valsecchi, IAU Coll. 83, U. iieidel, Dordrecht,
mitting strong perturbations. This configuration p. 343.
substantiates the conclusion that the comet could Marsden B.G., 1986 : Catalogue of Cometary Orbits,
have been captured from a long-period orbit about IAU Central Bureau for Astronomical Telegrams,
150 revolutions ago. Due to a high relative velo- Cambridge, M^ss.
city, the encounter would have had to be a very Sitarski G. and Ziolkowski K., 1986 : in Explora-
close one. To explore this possibility in more de- tion of Halley's Comet, ESA SP 25O/III, p. 299.
tail, we plan modelling experiments with sets of

32
 PLANETARY UHIGIN OF FIREBALLS AND COMETS

V. Padevet,

Astronomical Institute, Czechoslovak Academy of Sciences, Ondfejov

All known groups of fireballs contain bodies which may reach the Earth s surface
as meteorites and are of planetary origin. Since some fireballs have cometary orbits
in the Solar System, then comets are probably of planetary origin. The possible ex-
plosion of a large planet is discussed again. This time on the basis of gravitation-
ally decelerated expansion of an originally superdense embryo.

l.The planetary origin of fireballs planetary material with typical cometary or-
bits in the Solar System (Ceplecha and McCro-
The original hypothesis of the primordial sky, 1 9 7 6 ) , we can present a second hypothe-
origin of comets assumed the existence of sis, i.e. that comets are probable of plane-
two types of materials in interplanetary mat- tary origin. The comets would have to be se-
ter: primordial and planetary. The primordial gregated from the early planets by an unkno-
material should be the remnants of an inter- wnprocess, as indicated by the age of the
stellar nebula, now mostly contained in co- meteorites: 4.6 x 10 years.
mets (Whipple, 1 9 5 2 ) . The planetary material Anders (1975) claims the origin of carbo-
represents all known types of meteorites (Ja- naceous meteorites to be on the surface of
kes, 1 9 7 8 ) . the planet close to the Sun, probably bet-
According to Ceplecha and McCrosky (1976), ween Mars and Jupiter. Van Flandern (1978)
there are two groups of planetary material considered the explosion of parental comet
(I, II) and two groups of primordial material planet with a mass equal to 90 Earth masses
(III A, III B) among the fireballs, particles in the same region. According to Weissman
with masses in excess of 0.1 kg. However, the (1985), the sum of the masses of all comets
testing of all four groups of fireballs with in the inner and outer Oort "s cloud is even
the aid of the theory of atmospheric terminal higher, comparable with the mass of Jupiter.
heights has disclosed that only planetary ma- However, according to Wood (1967), meteori-
terial probably exists among fireballs (Pade- tes originated from a larger number of smal-
vet, 1987). ler parental bodies. Nevertheless, this could
The theory of terminal heights predicts have involved only significant inhomogeneiti-
two basic types of fireballs: a) fireballs es in the early mantle of a single large bo-
with a subcritical entry mass may reach the dy (Nagy, 1975) with a cometary carbonace-
Earth as compact meteorites, b) fireballs ous and volatile surface layer.
with an overcritical entry mass disintegra- Various types of meteorites indicate an
te into dust alredy at high altitudes as a onion-like structure already of the early
result of the aerodynamic pressure being hig- parental planet with an iron core and sili-
her than the ultimate strength of the materi- cate mantle. If this structure is due to he-
al in question. All fireballs of Groups I and terogeneous accretion (Rudnik and Sobotovich,
II are subcritical. There is no doubt about 1984), the cause of the explosion Df the pa-
the planetary origin of the fireballs of Gro- rental planet of the comets cannot be found
up I, because three falls of meteorites have (Weissman, 1984). The explosive model is
already been recorded in this group (Pfibram, founded on an analogy between the interior
Lost City, Innisfree). The fireballs of Group of the planet and the onion-like structure
II cannot be carbonaceous Cl-meteorites, as of a Type II supernova. The gravitational
assumed by Ceplecha and McCrosky (1976), be- collapse of a massive star would generate a
cause they terminate as much as 30 km lower series of nuclear fusions, beginning with
than would correspond to their characteristic the formation of helium from hydrogen and
ultimate strength of 0.1 MPa. The author as- ending with the generation of iron from sili-
sumes that this group involves namely L-chon- con (Bethe and Brown, 1 9 8 5 ) . An analogous se-
drites of typically planetary origin. The ries of explosive fusions, but in opposite
most brittle Cl-meteorites of planetary ori- order of onion-skin generation, may take pla-
gin (Jakes, 1 9 7 8 ) , can only be found among ce in the expansion of a miniature superden-
the fireballs of Group III B. A part of these se embryo of a planet. If the original embryo
fireballs with subcritical masses may reach were of hydrogen and had not expanded too
the Earth's surface as meteorites, the other much, all the fusions as far as iron could
part of overcritical fireballs will not pene- have taken place in it, as can be seen in
trate deeper than the altitude of 55 km,which iron meteorites. Under rapid adiabatic expan-
corresponds to the characteristic aerodynamic sion, the pressure end temperature of hydro-
pressure of 0.1 MPa. The slightly stronger C2 gen in a larger volume decrease, so that the
-meteorites of planetary origin might belong fusion in the next layer ends with silicon r-s
to fireballs of group III A which are able to can be seen in stone ordinary chondrites. In
penetrate to depths corresponding to aerody- the yet higher and cooler layer the fusion
namic pressures of 0.6 MPa. ends with oxygen and later carbon, evidence
of which can be found in completely oxidized
carbonaceous meteorites. The expansion of the
planetary embryo ends by the creation of a
2. Planetary origin of comets hydrogen-helium atmosphere, partly preserved
in comets.
5ince the fireballs of Groups III A and
III B are formed of carbonaceous, surface, All the inner planets may have originally

33
been more massive than todays outer planets. tory of the collision of headon particles
Their outer layers of lighter elements may beams can be divided into three phases (see
have been segregated during their explosive Fig. l a ) . Just before the collision, when
evolution. According to McCrea (1972) inner d > ^ , a complicated interference phenomenon
planets can he formed from giant planets of is generated by the approaching leptuns,
the Jupiter type j f they lose 99% of the which has a nearly spherical envelope (see
light elements. Therefore, the masses of all Fig. 1 b ) . During the actual collision, when
early planetary pmbiyos could have grown mo- d=A , the lepton interference abject gains
notnnically with decreasing distance from in intensity and reduces to a disk formation
the Sun, which was the most massive of all of zero order and two rod-like formations of
planets. the first order positioned perpendicularly
and symmetrically relative to the disk.After
3. The explosive origin of the Solar System the collision, when d < A , two hadron jets
begin to emanate under angle & in the direc-
We can formulate a third hypothesis of tion of quarks and anti-quarks (Albrow , 1979) .
the explosive origin of the Solar System as
a whole from an interference embryo roughly
26 orders of magnitude smaller than the pre- (a)
sent radius of Neptune s orbit. The origin
of embryos of all cosmic objects can be sou-
ght in the early dense Universe and not la-
ter when the temperature haa already dropped
to such an extent that gravitational colla-
pse of the expanded mass could have occured.
Pre-galactic and pre-stellar disturbances in
the structure of the Universe which, accor-
ding to Gurevich and Chernin (1987), must
have been much more severe than the level of
thermal fluctuations throughout the Univer-
se's history, cannot be explained otherwise.
If the threshold temperature of 10l:iK was
exceeded in the Hadron era of the Universe,
thermal collisions exceeding 1 GeV in energy 1 . Icploni 2 . collision 3.h«drom after
occurred. These high-energy collision resul- before collision of leptont collision of lep
ted in the generation of clusters of new
protons and their anti-particles (Albrow,
1979) . These clusters of hydrogen nuclei (b)
formed the base of a new type of strong,
internally ordered inhomogenities comparable
in size with the wavelength > of de Bro-
glie s mass waves of particle occurrence
probability,

(1) = hp = hm - vV 2 )*
Fig.l The headon collision of electron-po-
where h is Planck s constant, c the speed of sitron beams at high energies
light, m the mass of the particle at rest
and v its relative velocity.
The disturbances in the distribution of Their mass waves interfere and first form a
particles generated by the interference of single hadron object of zero order in the
mass waves expanded much more slowly due to form o'f a disk (see Fig. 1b) . Its existence
their own gravitation than the surrouding follows from Eqs (1) to (4) for d < > , if
Universe, and could have been the foundation coordinates x and y in them are replaced
of superdense embryos ol galaxies, stars or by new coordinates x' and y' . As the jets
planets. of new hadrons recede from each other, all
The headon collision of electron-positron typical interference objects, including the
beams at high energies has the simplest re- spherical, which however grow weaker, can be
sult (see Fig. l a ) . The coordinates of the formed in the opposite order.
interference maxima are given by the rela- The superdense embryo of the cosmic object
tions is generated if the number of newly created
pairs of hadrons greatly exceeds the mass of
(2) x ~tx[a2- r " z ( , , A + Zian3 + 4 a 2 n 2 + l ) + the planet, star or galaxy. When the inter-
nal pressure and temperature decrease after
+ (n 2 + 2 a n ) ] * the particle pairs have been annihilated in
the embryo and after it has expanded, the
(3) y =t I" 1 (n 2 +2an) gravitational forces may terminate its fur-
ther growth. If the gravitation is insuffi-
under the condition that cient, the object loses its identity and is
dispersed in inerstellar or interplanetary
matter.
(4) E = d/?\ 2 n = 0,1,2,3, ...
According to the interference theory, the
where n is the interference order and a > 0 disk-like embryo has its internal structure,
is a continuously varying parameter. Colli- provided the interacting particle beams A, B
sions of local importance take place in the have non-zero radii d, (see Fig. 2).The disk
maxima of the interference phenomenon. is then divided into discrete interference
This theory describes the geometry of the rings with the radii
interference phenomenon caused by two wave
point sources at distance d apart. The his- (5) rk = ^F" 1 {k 2 + 2k[(ik)2-j]}-|k} ,
where REFERENCES
2 2 A 2 2 2 2 2 1
(6) J--[8F k -k -4F (t +4F )]{ 16F -4k J" . Albrow.M.G.:1979 , Nature 279, 2B9.
Anders, F. :1975 , Icarus 24, 363.
Radii r. form a harmonic series, whose num- Bethe,H.A.;Srown,G.:1S85, Sci.Am. 251, 40.
ber of terms is limited by the condition Ceplecna,Z. ;McCrosky,R.E.:1976, Ceophys .
Res.81 ,6257.
(7) 2F-1 > k = 0,1,2,3,... Gurevich,L.E.;Chernin,A.D.:1987, Proiskho-
zhdenie Galaktik i Zvezd.(Nauka,Moskva
where and k is the interference 1987), p.39.
order. Jakes,P. .-197B, Meteors and Lunatics, (MF
Prague), p.39.
McCrea,W.H.:1972, Symposium on the Origin of
the Solar System, Nice 1972,ed.H.Reeves,
Paris(Russian transl.Mir,Moskva), p.14.
Nagy,B.:1975, Carbonaceous Meteorites, (Else-
vier Sci .Publ.Co..Amsterdam, Oxford, New
York), p.27.
Padevet,V.:1987, Bull.Astron.Inst.Czechosl.
38, 156.
Rudnik.V.A.;Sobotovich ,E .V. : 1984, Rannyaya
Istoriya Zemli,(Nedra,Moskva), p.20.
Van Flandern,T.C.:1978, Icarus 36, 51.
Weissman,P.R. : 1984, The Origin of Comets:
Implication for Planetary Formation,
(at the Conference on Planets and Proto-
stars II, Tuscon.Arizona,January 4-7,
1984).
Weissmsn,P.R. :1985, The Oort Cloud in Tran-
sition. Cometary Science Team Preprint
Series,No .73, Jet Propulsion Laboratory,
Fig.2 The disk-like embryo and its internal Pasadena,California.
structure Whipple,F.L.:1952 , Astron.J. 57, 28.
Wood,J.A.:1967, Icarus 6, 1.
If the interacting beams display a discre-
te structure, instead of concentric pipes we
obtain a system of interference spots which
are already very close to the idea of super-
dense planet embryos. If the expansion rate D I S C U S S I O N
of the embryo of the whole Solar System does
not depend on r. , no agreement with the Ti-
tius-Bode rule can be achieved. Kresak: The geocentric velocities of long-pe-
To conclude it should be emphasized that riod comets are so high that their desintegra-
the present idea of the origin of planets tion products cannot survive the atmospheric
and the Solar System is the author's working passage as meteorites. So I do not see how the
program. It only explains the disk-like mor- laboratory analyses of meteorites might support
phology of cosmic objects. Only after the your point of view. The hypothesis of a plane-
mechanism of internal dynamics (spin) is dis- tary origin of comets is very old, but it was
covered, can be considered a well supported found untenable when reconciled with their
hypothesis. observed properties, such as the location,
mass and dynamical evolution of the Oort
cloud. There are additional arguments against
the origin of comets too close to the Sun.
Any revival of the planetary hypothesis would
require first to explain these fundamental
contradictions.

35
 PHYSICAL EVOLUTION OF COMETS

Hans Rickman

Astronomiska observatoriet
Box 515
S-751 20 Uppsala
Sweden

Mechanisms currently under consideration for the evolution of cometary nuclei are reviewed.
Attention is paid to processes that should have occurred in the past history of observed comets,
related to their origin or storage in the Oort cloud, but emphasis is placed on presently observed
evolutionary effects and in particular the late stages characteristic of short-period comets.
Evidence from brightnesses and nongravitational forces is discussed and support for a scenario of
dust coverage coupled to the evolution of perihelion distance is found. However, for the cases of
comets P/Halley and P/Encke where the perihelion distance is unusually small an ultimate fate of
complete mass loss or disintegration can not be excluded.

1. INTRODUCTION Shulman (1983). An important problem is to what

extent these energy carriers would have been "killed"
Comets are of long-standing interest in cosmogonical already before the formation of the comet nucleus,
theory. To reveal their physical nature appears a either by heating events in interstellar space or the
difficult, yet highly rewarding goal of research, and presolar nebula leading to organic residues like the
the same holds for the attempts to clarify their "yellow stuff" (Greenberg, 1982, 1986a), or by the
spatial distribution and dynamical characteristics. action of mobile quenching agents such as hydrogen
As progress has been made in these respects, the atoms (Wallis, 1986). Those which survive until the
cosmogonical interest in cometary nuclei has tended to birth of the nucleus are likely to give off their
focus on their "primordiality": their potential of energy later on, as the local t jerature reaches a
offerring pristine samples of pre-planetary matter critical value.
from the outer parts of the solar nebula.
The thermal evolution of the cometary nucleus thus may
How, then, do these bodies evolve? This is a be influenced by an internal heat source which becomes
fundamental and often posed question, obviously active at a certain cr' cal temperature. There may
stimulated by the fact that comets are one of the few be several such heat sources characterized by
classes of celestial bodies where one actually sees different temperatures and different energy yields.
evolution going on. But the standard problems of what Assuming the dominant mode of energy transport to be
characterizes the present evolution, and what are the the bulk conductivity of the solid material, the time
end states thus approached, is now supplemented by the scale of heat diffusion over the radius of the nucleus
equally important issue of what evolution has already can be estimated at ~10 yrs using the thermal
taken place (see Ueissman, 1986a). How pristine are diffusivity of compact ice (Klinger, 1981, 1985). If
the cometary nuclei and what are the processes by the structure of the nucleus is quite porous (Rickman,
which they may have changed since their time of 1986; Whipple, 1986), this may be somewhat longer, but
formation 41* billion years ago? it is certainly much shorter than the typical
residence time expected for Ocrt cloud comets. Thus
even if quite a substantial heating should have
occurred initially, the nuclei would have had time
2. EARLY STAGES OF EVOLUTION enough to cool down before entering the inner solar
system. On the other hand, thermal diffusion is slow
2.1 Evolution Driven by Internal Heat Sources enough that one may imagine a central part of the
nucleus where heat release has occurred practically
To discuss the present state of knowledge, or instantaneously, surrounded by a thermal discontinuity
uncertainty, as regards these processes which should expanding into colder, unaltered material (Fig.l).
have occurred very long ago, it is advantageous to Such an outward propagation will necessarily stop if
start from expected scenarios based on laboratory the nucleus has a strong underlying temperature
experiments or physical intuition. In what ways gradient so that the discontinuity reaches material
should a cometary nucleus evolve according to our that is too cold to be heated to the critical
understanding of a dusty snowball orbiting in temperature, but such gradients would be expected only
interplanetary space? And how could observations of under special conditions, if attention is restricted
present-day comets be expected to distinguish between to cometary formation in the outer parts of the solar
different alternatives? nebula.

One class of hypotheses deals with thermal evolution. In addition to the above-mentioned chemical
The cometary nuclei appear to have formed at very low transformations, there is a number of possibilities
temperatures (Yamamoto, 1985; Yamamoto and Kozasa, concerning low-temperature phase changes of water ice
1987) and thus their material may have included some (see Whalley, 1985). It appears difficult to specify
reactive or energetic components which may give off in detail the sequence of events that may have taken
latent energy by means of exothermal chemical place by consecutive reactions and phase changes upon
reactions or phase transitions. Some examples are an initial slight heating, e.g. by radioactive decay
free radicals formed by UV radiation in the volatile of isotopes with short half-lives. But one may expect
mantles of pre-cometary grains, as incorporated into the basic structure of the ice to remain amorphous
Greenberg's picture of comet origin (Greenberg, 1982, (Smoluchowski, 1985) since the crystallization
1986a); and the ion molecular clusters proposed by temperatures to cubic and hexagonal ices are as high

37
 Fig. 2. A cometary nucleus where melting occurred at
an early stage in a large fraction of the volume. As
a result, gravitational separation occurred so that
the silicate dust settled at the center as an inner
core surrounded by a dust-free liquid that later
Fig. 1. A cometary nucleus with a central region formed a compact ice mantle upon cooling.
(r < r c ) altered by an exothermal process with
critical temperature T c . The curve below indicates
a schematic temperature structure T(r) to be expected. have been practically independent of
insolation-induced heating. But as the comet finally
approaches the Sun, one may expect additional
as -150 K (Klinger, 1981; Prialnik and Bar-Nun, evolutionary effects from the heating of the surface
1987). This crystallization is rather expected to layer by sunlight. Of course a thermal wave will
occur in the later stages of evolution as the comet is penetrate toward the interior of the nucleus, and
captured into the inner solar system and the nucleus along vith this wave goes, probably, crystallization
is strongly heated from the outside by absorbed of the ice. One may easily speculate about observable
sunlight. consequences of this exothermal phase transition,
which may increase the local temperature by 20-30 K
Radioactive decay is an interesting possibility as a (Smoluchowski, 1981) and thus significantly modify the
stimulus for thermal evolution. Isotopes with sublimation rate if it occurs near the surface. In
half-lives much longer than the heat diffusion time particular, there have been suggestions as to the high
scale can not have any major effect, but Al might be activity of newcomers from the Oort cloud at large
a possibility, decaying in a mere 7-10* yrs. We are heliocentric distances (Smoluchowski, 1981); erratic
again facing a difficulty in estimating how much of activity like the outbursts of comet
this heat source may have been incorporated into the P/Schwassmann-Wachmann 1 in this distance range
comet nuclei: M A1 should have originated in a (Patashnick et al., 1974; Froeschle et al., 1983); and
supernova event closely preceding the birth of the the activity pattern of comet P/Halley including its
solar system (Lee et al., 1977), but there is an f perihelion asymmetry of gas production (Rickman et
obvious need to have comet nuclei formed within -10 al., 1985). But modelling is of course needed, and
years of this event for the heat source to be this turns out to be a non-trivial task. A very crude
significant. treatment was first done by Herman and Podolak (1985),
and recently important progress was also achieved by
Prialnik and Bar-Nun (1987).
In an extreme case this heat might have sufficed to
melt the ice in a large fraction of the nucleus The latter authors concentrated on the orbit of comet
(Wallis, 1980; Irvine et al., 1980), but in such a Halley, and from their work it appears that the phase
case one would expect both a fairly high density and a change quickly penetrates to a depth of nearly 100 m
chemically differentiated structure (Fig. 2), perhaps and then comes to rest until sublimation carries the
with a silicate core surrounded by an icy mantle, all surface close enough, whereupon a new penetration
wrapped up in an outer layer of more or less pristine event carries crystallization even further down.
material. One characteristic of cometary nuclei that After several such events occurring within several
now appears more clearly than before, using recent hundreds of orbital revolutions the nucleus appears to
observations of P/Halley and other comets, is that crystallize completely, and the interior then finally
they do not have this structure. In particular, their relaxes to the orbital mean temperature (Klinger,
densities appear far too low (Rickman, 1986, 1987; 1983) of appr. 80 K. Typical evolutions thus
Rickman et al., 1987). Thus there is some expected upon captures into Jupiter family orbits are
observational evidence against the existence of early still to be explored.
thermal events strong enough to have caused major
structural changes of the nuclei. But this evidence Other consequences of the thermal wave might include
does not put constraints on moderate thermal events thermal cracking due to the strong and rapidly
corresponding to phase changes or release of changing near-surface temperature gradients (Kubrt,
primordial chemical energy. In principle, 1984; Kiihrt and Mohlmann, 1984; Kiihrt et al., 1986),
polymerization of carbon compounds could have offerred or indeed the density change that may accompany the
a major energy source (Uallis, 1986), but the phase transition, but this idea should be reconsidered
formaldehyde polymers tentatively identified in comet in the light of recent data. In particular, can a
Halley (Huebner et al., 1987) may have been formed in very porous snow-drift-like mixture of grains be
a pre-cometary stage (op.cit.). expected to crack, or should one rather foresee some
other kind of structural modification in response to
2.2 Evolution Driven by Surface Heating the rapidly changing temperatures? In any case,
spacecraft imaging of the comet Halley nucleus does
According to a nowadays commonly accepted picture of seem to suggest a process related to cracking
comet formation having occurred relatively far from (Mohlmann et al., 1986), leading to a linear
the Sun (-10-1000 AU; see Weissman, 1986a; ramamoto network-type arrangement o£ the outgassing zones.
and Kozasa, 1987), the above described effects should Support for this kind of pattern is also found from

38
 the mapping of dust-emission sources (Selcanina and on C0 2 sublimation (Meech and Jewitt, 1987). There is
Larson, 1986a). hence some evidence that the new comet Bowell is
actually CO^-dominated. A problem is posed by the
The origin of such structures may be a very important very low expansion rate of -1 m/s of the coma
point to clarify, and this leads to one of the central (Sekanina, 1982a; Jewitt, 1984), since from the gas
issues of the problem of cometary evolution: the flux of a CC>2-sublimating nucleus grain speeds ~20
question of chemical differentiation of the surface m/s should be expected. One possible explanation of
layers. Since cometary material is a mixture this discrepancy may be that the nucleus is not
(although, perhaps a very intimate one) o£ components totally active but, perhaps, outgassing only in spots
of different volatility, and there is reason to covering <10 % of the surface area so that the gas
believe that the nuclei were formed homogeneous with flow is strongly diluted.
constant mixing ratios throughout, evolution would
result if upon approach to the Sun and heating of the 2.3 Cosmic Ray Effects
surface layer the more volatile components escape
preferentially so that they become depleted (Fig. 3). If such a small free-sublimating fractional area could
The largest dust grains, e.g., may be too heavy in be demonstrated beyond doubt for a new comet, it would
relation to their cross-sectional area in order to be have interesting implications for our picture of past
carried away by the gas flow from the nucleus surface cometary evolution. The effects of cosmic ray
and thus may form a residue remaining on the surface irradiation on cometary nuclei in the Oort cloud are
(Whipple, 1951; Shulman, 1972; Ip and Mendis, 1974), of course of relevance in this context. Such effects
thereby interfering with gas production in various have been recently explored by means of laboratory
ways. But a differentiation of the volatile experiments (see Johnson et al., 1986), and it appears
constituents with respect to depth might also occur to that during Vk billion years in the Oort cloud the
the extent that sublimation can proceed beneath the outermost 10 1 g/cml receive an integrated dose high
surface with escape of the gas through pores or enough to transform the material profoundly (e.g.
cracks. The recent arguments in favour of low Cooper, 1983; Ryan and Draganic, 1986). New volatile
densities o£ comet nuclei (Wallis and HacPherson, species are formed but also organic refractories, and
1981; Greenberg, 1986b; Rickman et al., 1987) tend to at a density of -0.2 g/cm3 as indicated by the
favour the idea of sub-surface sublimation even in the analyses of nongravitational effects (Rickman, 1987;
absense of cracks. Closely related to this idea is of Rickman et al., 1987) one may expect a crust of -5 m
course that of volatile pockets (Cowan and A'Hearn, thickness consisting of these irradiation products to
1982; Sole et al., 1986) where an excessive gas cover the surface of the nucleus (see Johnson et al.,
pressure is gradually built up close to the surface, 1986).
to cause an outburst of gas production as this gas
makes its way to the surface. An important question, still to be answered, is what
may be expected to happen to such a crust upon the
first approach to the Sun. Ve are faced with the
interesting though somewhat speculative ideas that the
volatiles may sublimate away during the first
|j |...I,4 I OUST ESCAPE A ) GAS C l o v l
perihelion passage (tfhipple, 1977; Johnson et al.,
1986) thus accounting for the well-known fading
i^.y ^ ' DUSI MAN1LE / / / / / /
T ti"
phenomenon first discussed by Oort and Schmidt (1951),
and that the refractories stay behind thus forming a
thick crust of dark, refractory material covering most
/ / / ' / / / / / | SUBLIMAMON / / / # * / A u_ft fLA-tMan'!
of the surface of a typical short-period comet
(Sekanina, 1986a; Johnson et al., 1986). It does not
^'1 x
DU^T i CIATHF1AU MAN1LE appear evident that this scenario actually applies,
but further investigation, e.g. by theoretical
modelling of the response of the irradiation-altered
crust to solar heating, will at least provide some
hints.

(nr.i t- fjftinnftiF t VOLMIIF rnnF ..

3. FINAL STAGES OF EVOLUTION

3.1 Grand Scenarios

Fig. 3. The surface layer of a cometary nucleus with
sublimation-driven differentiation. Heat and From the most basic properties of comets we can
material transfer processes are indicated to the immediately conclude that they do not last forever, at
left (after Houpis et al., 1985), and a possible least not in the shape in which we observe them. For
grain structure is indicated to the right. the final stages of evolution there are basically two
grand scenarios, which may be termed the "mass loss
model" and the "dust coverage model", respectively.
Generally speaking, as comets grow older, their
volatile constituents may be buried under a less 3.1.1 Hass Loss Model; Application to Comet Halley.
volatile mantle, certainly dominated by H.0 ice, which By gradual sublimation of surface layers, assuming no
may grow thicker and thicker (Houpis et al., 1985). refractories are left behind, the nucleus shrinks as
This, of course, may be viewed in conjunction with the the comet passes successive perihelia (Fig. 4). As
general conclusion that short-period comets are in
general dominated by Hx0 (Harsden et al., 1973;
Delsemme, 1985) while there is a possibility that
other volatiles control the remote activity often seen
in long-period comets, especially the new ones coming
from the Oort cloud (Marsden et al., 1978; see also
Sekanina, 1973). Recently, e.g., the record
heliocentric distance of comet Stearns 1927 IV was
finally broken by the observations of comet Bowell
1982 I at a heliocentric distance of 13.6 AU (Meech
and Jewitt, 1987). This is a new Oort cloud comet in
the sense defined by Marsden et . (1978) and it is Fig. 4. The mass loss model of cometary evolution.
interesting to note that the brightening and fading In this idealized version sublimation occurs iso-
rates of the coma during the whole apparition are in tropically and the nucleus shrinks until it becomes
good agreement with the predictions of a model based unobservable or disintegrates completely.
 this shrinking proceeds, the ratio of area to mass excluded that its strongly non-spherical shape is a
increases and thus the relative mass loss increases- result of localized sublimation rather than being
There are, however, some obvious modifications to this primordial. A major, single active spot seems to
idealized picture. cover an area of -20 km* (Keller et al., 1987),
corresponding e.g. to a circular region of Vk km
For instance, it is well known that comets are apt to radius, so within -10 revolutions one would have to
splitting (Sekanina, 1982b), and even though in most take shadowing by the crater walls into account -
cases as yet observed splitting did not imply the however, before this these walls would probably
sudden death of the comet, the increase of sublimation collapse since they are eroded by sublimation (Wallis,
area must obviously accelerate the mass loss. Ve may 1986).
probably view coraetary splitting as a part of a
general disintegration process (cf. Veissman, 1986b), The remaining lifetime of P/Halley - again if one
which ultimately amounts to the mass approaching zero, could extrapolate the present conditions far into the
or the size passing a limiting value where the gas and future - might be estimated as M/flH - 300
dust production rates get too small to cause revolutions. However, one must be very cautious in
observable cometary activity. applying this estimate, since it is only of zero order
and neglects any future changes of the
Perhaps more importantly, the shrinking process should free-sublimating area. Yet another reason to doubt an
not be seen simply as that of a sphere whose radius estimate of lifetime based on pure mass loss is
decreases gradually. Ve have learnt that the nucleus explained in the following subsections.
of Bailey's comet is far from being spherical (e.g.
tfilhelm et al., 1986) but also that it is far from 3.1.2 Dust Coverage Model. A different way to
being isotropic (Keller et al., 1986; Sagdeev et al., imagine the final stages of cometary evolution
1986). Gas and dust production is localized to a few involves dust choking. The kind of dust grains
major active spots, and the rest of the nucleus remaining on the surface of the nucleus even at the
appears inert. It is obviously important to know the orbital position of maximum gas flux will collect
typical lifetime of an active spot. If these move progressively, and thus they provide a means of
around fast enough, then the evolution is that of a covering the area of active sublimation more and more
nearly isotropic nucleus even over a short interval of until an insulating, or rather choking dust layer
time. However, if this is not the case, as seems forms and the active area turns inert (cf. Fig. 3).
indicated by the good agreement between the locations As evolution proceeds, one may thus imagine a nucleus
of dust activity in 1910 and 1986 (Sekanina and whose size changes only slightly but whose area of
Larson, 1986b), then one has to imagine that during free sublimation decreases steadily toward zero
quite some time mass loss is confined to some special (Fig. 5 ) .
part of the nucleus, thus digging holes at a
considerable rate.

Some present "best estimates" pertaining to the

properties of the nucleus of Halley's comet are given
in table 1. With a total (whole nucleus)
free-sublimating area averaging -60 km 1 over a whole
apparition, i.e., about 16% of the available surface
area, a total mass loss estimated at 3-1011 kg on the
basis of an average dust/gas mass ratio of 0.5 implies
a loss of -25 m of surface material in the active Fig. 5. The dust coverage model of cometary
spots. If one could extrapolate these present evolution. Latitude-dependent mantle growth
conditions far into the future, one would find that from patches coupled to spin axis precession
the depth of each crater reaches 1 km in -40 is indicated.
revolutions and then, if not before, the craters would
start to set their signature on the bulk morphology of
the nucleus. Considering the number of revolutions
that Halley's comet has already spent in its present This simple idea follows in a straightforward manner
kind of orbit (Yeomans and Kiang, 1981) it can not be from the basic concepts of a cometary nucleus
(Vhipple, 1950). Furthermore, evidence that activity
of cometary nuclei is restricted to minor regions has
been present since more than a century in the form of
TABLE 1. THE NUCLEUS OF COMET P/HALLEY jet and fan structures of cometary comae (Sekanina,
1987), and more directly it appeared in the early
1970's for comet P/Eneke by a comparison o£ its
photometric cross-section and free-sublimating area
Radii of best-fit ellipsoid: 8* 5 x 4} km (Delsemme and Rud, 1973). As noted above, imaging of
comet P/Halley has verified the existence of this
(Wilhelm et a l . , 1986) basic structure.
Volume: 550 km3
Theoretical modelling was started by Shulman (1972),
(Keller, 1987) and the first numerical results concerning the
evolution of a dust mantle were published by Hendis
Mass: 1 1 0 H kg and Brin (1977). Their model concentrates on grains
(Rickman, 1987) continually agitated by the gas flow so that a very
3 loose structure is formed. Attention is not given to
Thus mean density: 0 2 g/cm the secular behaviour and indeed no stcular growth of
the dust mantle is found when applied to the orbit of
Halley's comet. The gas flux always reaches too large
values near perihelion, and the relatively thin layer
Active surface area on I'l Mar 1986: to km2 already formed is blown away in the course of each
(Keller et a l . , 1987) perihelion passage (Brin and Mendis, 1979). The
Kendis-Brin dust mantle is thus a strictly periodic,
Estimated whole-apparition average: 30 km2 orbital one which does not explain the recent
spacecraft observations of Halley's comet, but an
Thus including night-side spots: 60 km2 interesting possibility remains in letting those
individual grains that are big enough stay on the
Mass loss per apparition: 3-1011 kg surface as the mantle is blown away. One might then
(based on average dust/gas ratio = 0.5) eventually explain the formation of a secular dust
mantle that indeed chokes off sublimation

40
 definitively. However, an obvious problem is to model very good discriminator of the two scenarios, the
the essentially unknown distribution of very large nongravitational effect on the orbital motion
grain sizes (McDonnell et al., 1986; Crifo, 1987). (principally, the advance or delay at perihelion
passage) may indeed be one. The nongravitational
In the similar "friable-sponge" model (Horanyi et al., acceleration (A) varies as f/R, so the mass loss model
1984) the possibility of secular mantle growth exists predicts an increase and the dust coverage model a
even for a Halley-type orbit, but only at the expense decrease, as far as the long-term evolution is
of assuming that the grains are very difficult to concerned. This should be understood as an "absolute"
break dovn so that mantle erosion is essentially acceleration normalized to a standard heliocentric
inhibited. If this is assumed, the dust mantle is distance in the same sense as the absolute brightness.
stable and grows by sublimation from the bottom until
its thickness reaches a final value large enough to 3.2.1 Measures of age. Cometary orbits typical of
choke off the sublimation completely by thermal the Jupiter family are subject to frequent major
insulation. However, even this asymptotic thickness perturbations at encounters with Jupiter
is very much smaller than that of the (Kazimirchak-Polonskaya 1972; Carusi and Valsechi
radiation-altered crust discussed above. 1987). Thus, e.g., the perihelion distances (q) and
therefore the aging rates change in a random manner.
A gas-diffusion model was described by Fanale and The dependence of aging rate on perihelion distance
Salvail (1984), but diffusion actually did not occur may not be the same for both considered scenarios, and
in their numerical experiments. A more recent and thus given a comet with a certain orbital history
more self-consistent model of this kind (Rickman and different ages may have to be ascribed to the comet
Fernandez, 1986) often gave a stable dust mantle for depending on which scenario is considered. However,
the orbit of P/Halley with a thickness depending on such a formally correct approach appears unnecessarily
the critical radius (Ip and Hendis, 1974) at the time complicated and in any case unfeasible.
of grain trapping. However, these models were
computed using an extremely small mean free path of Due mainly to the chaotic properties of cometary
gas diffusion through the mantle, and as a result the orbits (cf. Everhart, 1979) and the uncertain
cm-scale mantles found form a nearly complete obstacle extrapolation of nongravitational effects outside the
to gas production and easily remain stable. This observed intervals, the orbital histories of
assumption is by no means obvious and should be individual comets are basically unknown. Thus even if
checked further. one takes a very simple definition of "absolute age"
(Nn) as the number of orbital revolutions that the
In any case all the models so far developed are comet has spent with a perihelion distance small
unrealistic since they do not account for differences enough to allow significant evaporation of H a 0 ice (q
between different parts of the nucleus. Thus the ,£ 2.8 AU; see Delsemme 1985), there is as yet not one
whole nucleus is either free-sublimating or covered by single short-period comet for which N n is known.
a dust mantle. In reality the mantle should rather
ctart out in the form of patches (Shulman, 1972; cf. This is of course very unfortunate, but there is a
Ip and Rickman, 1986), and this scenario might explain short-term substitute for N^ which appears useful to
a wide variety of behaviours, including that of some extent. Let us define the "incremental age" (Nj)
P/Halley with a few active spots on an otherwise inert as the number of revolutions since the last
nucleus, but still has to be worked out. Another significant decrease of q (flq ^ -0.5 AU acquired
important question to answer is whether shore-period in one single encounter with Jupiter). This measure
comet nuclei such as that of P/Halley can really be of age can often be determined quite reliably from the
covered and deactivated to a large extent by a orbital evolutions given in the catalogues by Carusi
"sublimation-driven" dust mantle whose thickness is et al. (1985) and Belyaev et al. (1986) up to N z -
typically only a few cm (Sekanina, 1986a). 20-30, even though the dynamical models used are not
of ultimate accuracy.
3.2 Comparison with Observations There is an interesting difference between the
predictions of the two scenarios as far as N-£ is
As already noted, the observable lifetimes of concerned. In the mass loss model the evolutions
short-period comets are expected to be fairly short. predicted for A and B are monotonous, and
Specifically, a number of revolutions of the order of perturbations of q only amount to accelerations or
500 appears likely both from the number of decelerations of these processes. A and B should be
disappearances in the short-period comet population correlated with Nfl but probably not perceptibly with
(Kresak 1985) and from the net capture rate found by Nj since the two age measures appear to be mutually
Fernandez (1985). Even though both sets of statistics poorly correlated. The situation is quite different
are based on small numbers, the mutual agreement for the dust coverage model. The stability conditions
justifies a fair confidence in the quoted figure. In for a dust mantle may be strongly dependent on the
fact some support comes from orbital diffusion studies perihelion distance, and upon a significant decrease
of long period comets (Oort, 1950; Shteins, 1972) in q one may expect the relatively thin mantle formed
indicating a typical number of active revolutions of in the earlier orbit to be blown off, later on to be
the same order of magnitude. replaced by a new and thicker mantle. Thus the
evolution predicted for f is not monotonous - at least
Undoubtedly, the true reason for cometary lifetimes to not until the overall minimum of q is reached - and
be limited to & 1000 revolutions may be a combination nor are those predicted for A and B. Clear
or an interplay of both the above-described scenarios, correlations with Nj are hence expected.
and the actual mechanism may also critically depend on
the orbital evolution experienced by the comet. Thus 3.2.2 Evolution of brightnesses. The statistics of
it is not certain that a distinction between the two cometary brightnesses has been analyzed by Kresak
scenarios can be made to the extent that either of (1974, 1985, 1986; see also Kresak and Kresakova 1987)
them might be rejected in favour of the other. The and from these studies it appears as main conclusions:
problem is further compounded by the existence of 1) that the rapid fading of short-period comets
various uncertainties and observational biasses, to be claimed by Vsekhsvyatskij (1958) results mainly from
briefly discussed in the following subsections. instrumental effects and biasses related to observing
geometry; 2) that the true brightness evolutions of
Both scenarios naturally predict a long-term decrease different comets are rather characterized by a large
of the free-sublimating area of the nucleus and thus variety. Over a time span of - 10 revolutions there
of the absolute brightness (B), although on a shorter are some cases where a moderate fading can be
time scale there are some important differences to be discerned but even more cases where it can not. In
discussed below. In the mass loss model this is due connection with the identification of comet 1808 III
to a decrease of radius (R), but in the dust coverage with P/Grigg—Skjellerup, as an extreme though
model it is due to a decrease of the free-sublimating illustrative example, this comet is no longer a case
fraction (f) of the surface area. While B is not a of very rapid fading but instead one where hardly any

41
fading can be noticed at all (Kresak, 1987). other unknown or variable quantities as well: e.g.,
Furthermore, there are quite a few cases of the perihelion asymmetries of the gas production
brightening with no obvious reason, vhereamongst some curves, and the spin rates and spin axis orientations
comets that seem to have gone through dormant periods of the nuclei (Rickman et al., 1987).
after which they have been reactivated (Kresak,1986).
Therefore, the observed evolution of Az for individual
Such behaviour is not an immediate outcome of either comets can be used to construct precessional models
of the two scenarios but seems easily reconcilable for the individual nuclei (Sekanina, 1986b and
with the dust coverage model, whereas the mass loss references therein), but they give practically no
model does not at all predict this. As demonstrated information about the evolution of the "absolute"
by Fernandez (1985), comets with small fractional acceleration A. Apparently this is true whatever
free-sublimating area.*- are susceptible to large timescale one considers. However, the statistical
fluctuations of brightness even due to relatively correlation of A with Nj may be investigated, since
minor variations of this area. Such variations may be individual patterns of precession or light curve
caused, e.g., by collisions with interplanetary evolution may then cancel out. Indeed the result of
particles piercing the dust mantle (see below). such an analysis (Rickman et al., 1987) is a very
clear decrease of <A> with N lt by a factor two from
As explained in the preceding subsection, no the first three revolutions to those - 10
correlation can be observed between B and Nfl since the revolutions later or by a factor five with respect to
latter is unknown. An observation of a statistical those more than 30 revolutions later.
dependence of B on age would thus have to take the
form of either a correlation between B and N £ or an Again one may see this as a verification of the dust
ensembltof individual fading rates. The correlation coverage model. However, it is difficult to draw
between B and Nj, which is predicted by the dust quantitative conclusions owing to the above-mentioned
coverage model, appears impossible to observe due to observational selection effect. Since the observed
an obvious bias. Comets fainter than a certain limit sample is expected to concentrate on larger nuclei
are unlikely to be discovered, and thus if the with increasing Nj, part of the observed decrease of
brightness of each comet decreases with Nj it will be <A> should arise from this fact.
more easily discovered upon capture, when N x is low.
Hence at the smallest Nj our discoveries sample the 3.2.4 Dust Coverage and the Lifetime of Comet Encke.
distribution of nuclear radii down to the lowest There are thus some observational indications that the
limit. Some of these comets are subsequently lost due free-sublimating fraction of surface area on
to more or less coincidential reasons, but the short-period comet nuclei, and hence the absolute
smallest ones are most susceptible to this fate. They brightness and nongravitational acceleration,
are replaced by other comet discoveries at large Nj decreases markedly within a short time span (£ 10
where on the average larger nuclei are sampled. Thus revolutions) following a major decrease of perihelion
with increasing Nj there should be a tendency for the distance. However, it would be dangerous to
observed sample of comets to concentrate on larger extrapolate this behaviour to the scale of the whole
nuclei, to the effect that the intrinsic decrease of cometary lifetime. Even though dust coverage seems to
<B> is practically cancelled out. We shall return to be the process typically at work during short time
this selection effect in the next subsection. intervals, this is no guarantee against the ultimate
fate of many comets being governed by mass
The only conclusions possible from brightness data consumpt ion.
seem to be those based on fading rates of individual
comets. In spite of the above-mentioned problems, a
Let us briefly discuss the application of the dust
tew short-period comets are presently considered to
coverage model to Encke's comet as an individual case
fade at a measurable rate during - 10 revolutions.
of special interest. Some properties tentatively
The most notable case is that of P/Encke, for which
inferred for the Encke nucleus are listed in table 2.
Kresak (1965, 1974) finds a fading rate of about 1
There are now quite a few observations suggesting a
mag. per century. This means that its remaining
low albedo typical of cometary nuclei (Birkett et
lifetime might be estimated at a few hundred
al.,1987; Banner et al., 1987 and references therein;
revolutions, which is in good agreement with the
see also Rickman et al., 1987). Thus it appears
above-mentioned estimate of 500 revolutions for the
typical total lifetime of short-period comets.
However, extrapolating backwards one finds from the
lack of ancient observations (Whipple and Hamid, 1Q72)
TABLE 2: THE NUCLEUS OF COMET P/ENCKE
and the long time probably required for transfer into
the present orbit that even this modest fading rate is
considerably higher than the average one. This
conclusion will be further substantiated below. Comet Strongly n o n - s p h e r i c a l , slowly spinning _
Encke may survive longer than most other comets, but Typical photometric c r o s s - s e c t i o n : 1 km
this is not surprising in view of its small perihelion (Jewitt and Meech, 1987)
distance if the dust coverage model is considered (on
the other hand it would be somewhat surprising from If albedo = 0.03, then geomet. c r o s s - s e c t . : 33 km
the point of view of the mass loss model).
Thus volume: 110 km
A significant hint regarding the behaviour during
short time spans is that in a number of cases Maximum free-sublimating c r o s s - s e c t i o n : 1.3 km
decelerating encounters with Jupiter (i.e., reduction (Rickman et a l . , 1987)
of the perihelion distance) might have been followed
by an increase of activity lasting for a few Thus free-sublimating percentage: < U I
revolutions (Kresak, 1986). Apparently, if this can
be confirmed, we have a verification of the decrease
of B with N z predicted by the dust coverage model.
Mass: 2.5 10 1 3 kg
3.2.3 Evolution of Nongravitational Effects.
Nongravitational parameters are listed in Harsden's Thus mean d e n s i t y : ~ 0 . 2 g/cm
(1986) catalogue of cometary orbits for a large number
of orbital linkages of many short-period comets. The Mass loss per a p p a r i t i o n : 1 10 1 0 kg
Az parameters are by far the most reliable ones
(Rickman et a l . , 1987)
(Marsden 1974), measuring essentially the delay or
advance at perihelion passage (Rickman, 1986).
Nonetheless, they are no direct measures o£ the Thus relative mass loss: COM '*
nongravitational accelerations but depend on several
likely that the average geometric cross-section of the which in general does not intersect the orbit of the
Encke nucleus is ~ 30 km . It is not yet possible Earth), and in the dust coverage model an asteroidal
to estimate accurately the free-sublimating area of object of cometary origin (extinct comet).
this nucleus, but a free-sublimating fraction £ 5 X is Observations of "asteroids in cometary orbits" (Hahn
indicated by the results of several different and Rickman, 1985) may hence yield clues to the
investigations (Sekanina, 1986b; Jevitt and Heech, relative importance of the two scenarios. This issue
1987; Eickman et al., 1987). was reviewed by Rickman (1985) and the tentative
conclusion has not changed: a large percentage of
From the results by Rickman et al. (1987) it appears typical Jupiter-family comets develop into asteroidal
that the nongravitational effects on the orbital objects. These objects are apparently dust-covered
motion of comet Encke arises to a large extent from icy nuclei rather than silicate cores left behind
the perihelion asymmetry of the gas production curve, after total consumption of the ice. The possibly
and accordingly the mass of the nucleus Is fairly veil conflicting evidence found above fcr comets Encke and
determined in spite of uncertainties concerning the Halley is naturally explained by the low perihelion
rotational and thermal properties. The value implied distances of these comets which may render secular
agrees with the mass of a prolate spheroid of average mantle growth very inefficient. In this context it
cross-section 30 km* if the density is -0.2 g/cm 3 as would of course be very interesting lo know whether
recently inferred for Halley's comet (Rickman, 1987), 3200 Phaeton, the parent body of the Geminids
and it amounts to -2000 times the present mass loss (Uhipple, 1983), is of asteroidal or cometary origin
per apparition. (Davics, 1985). If it is an extinct comet, then
obviously dust choking can indeed occur even at very
We are thus faced with the following set of small perihelion distance.
observational data:
1) The perihelion distance (q-0.34 AD) is remarkably A vord of caution is, however, necessary. According
low. to present-day understanding the sublimation-driven
2) The orbital evolution is at present very slow, dust mantles should be very thin (perhaps only of
since the lov aphelion distance (Q=4.1 AU) implies centimeter-thickness) so that they are very easily
gravitational decoupling from Jupiter. pierced by impacting interplanetary particles of even
3) The nucleus is basically inert, probably minor size, and such impacts may occur quite
dust-covered to at least 95 X. frequently (Fernandez, 1981). Indeed, observational
4) The present relative mass loss per apparition is evidence tells us only that there appear to be some
only -1/2000. objects identifiable as at least temporarily extinct
5) The comet seems to fade by about one magnitude per comets. A continuation of Fernandez' work in
century. estimating collisional life-times vith the particular
The first conclusion to be drawn from this is that the purpose of finding the typical time scale for
present rate of fading is far too high to be explained rejuvenation of cometary activity is called for. We
by mass loss (items 4 and 5 ) . Obviously, also in view may be dealing vith a population of semi-extinct
of item 3, gradual dust coverage is implied. In fact cometary nuclei of which some have been observed as
the fading rate is in good agreement with the above asteroids such as 944 Hidalgo or 3552 1983 SA, some as
conclusion from the correlation of <A> with Nj. low- or intermittent-activity comets such as
However, we immediately face a problem if the present P/Arend-Rigaux or P/Neujmin 1, and perhaps some only
fading rate, interpreted by means of dust coverage, is as unconfirmed cometary objects either lost or later
extrapolated backwards in time. Capture of the comet classified as asteroids.
into an orbit vith the present perihelion distance
would then necessarily have occurred no more than Finally it should be stressed that we are still far
300-400 years ago, and this appears to conflict with from a real understanding of cometary evolution, and
item 2. Furthermore, it appears difficult to explain even when present evidence seems to favour one
how a comet with such a lov perihelion distance (item particular scenario, this evidence is rarely safe
1) could be subject to dust coverage at about the same enough for us to be confident about the conclusion.
rates a typical Jupiter family comet with q-1.5 AU. This of course means that a lot of Interesting vork,
Thus it appears more reasonable to conclude that the some of vhich has been hinted at above, remains to be
present fading is not typical for the secular done I
evolution of Encke's comet. As a consequence of this,
a slow capture process into the present orbit can be
assumed to the effect that the comet has spent a large Acknowledgement. I am very much indebted to my
number of revolutions vith small q. Thus a large younger colleagues Per Hagnusson and Mats Lindgren
number of revolutions can be expected for the future without whose help this manuscript could not have been
evolution too, and it is not unreasonable to estimate prepaied in time. Discussions with dr. L. Kresak
a total life-time of several thousand revolutions in (SAV, Bratislava) are also gratefully acknowledged.
agreement vith the relative mass loss rate. This work was supported by the Svedich-Czechoslovak
academy exchange programme.
It remains an open question vhether the fate of
Encke's comet is to shrink and eventually disintegrate
or vhether the small percentage of free-sublimating
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Similarity of Comets", ESA SP-278, in press. Shteins, K.A.: 1972, in "The Motion, Evolution of
KUhrt, E.: 1984, Icarus 60, 512. Orbits, and Origin of Comets" (Eds.
Kflhrt, E.; Hohlmann, D.: 1984, Adv. Space Res. 4, 225. G.A. Chebotarev et al., Reidel), p. 347.
KUhrt, E.; Hohlmann, D.; Giese, B.; Tauber, P.: 1986, Shulman, L.H.: 1972, in "The Motion, Evolution of
in "Exploration of Halley's Comet", ESA SP-250, Orbits, and Origin of Comets" (Eds.
vol. II, 385. G.A. Chebotarev et al., Reidel), p. 271.
Lee, T.; Papanastassiou, D.A.; Wasserburg, G.J.: 1977, Shulman, L.K.: 1983, in "Conetary Exploration I"
Astrophys. J. 211, L107. (Ed. T.I. Gombosi; Hungarian Acad. Sci.), p. 55.
Marsden, B.G.: 1974, Annu. Rev. Astron. Smoluchovski, R.: 1981, Astrophys. J. 244, L31.
Astrophys. 12, 1. Smoluchovski, R.: 1985, in "Ices in the Solar System"
(Eds. D. Benest et al.; Reidel), p. 397.
 Sole, H.; Vanysek, V.; Wolf, M.: 1986, in "Asteroids, Rickman: I took this value from the papers
Comets, Meteors II" (Eds. C.-I. Lagerkvlst et al., by Klinger and Bar-Nun.
Uppsala Univ.), p. 327. Shulman: The characteristic time at 150 K is
Vsekhsvyatskij, S.K.: 1958, "Fizicheskie Kharakteristiki only 10 s and it is about ID hours at 100 K.
Komet" (Gos. izd. fiz.-mat. literatury, Moscow). We need a cosmogenic time-scale of 10 hours.
Uallis, M.K.: 1980, Nature 284, 431. Ha.jduk: You have used the value 3 x 10 kg/
Wallis, H.K.: 1986, in "The Comet Nucleus Sample Return /rev. for the mass-loss of P/Halley. The "-JSS
Mission", ESA SP-249, 63. loss depends very much on the mass limits
Uallis, M.K.; MacPherson, A.K.: 1981, Astron. of the particles considered. To what upper
Astrophys. 98, 45. mass-limit do you refer your above mass loss
Ueissman, P.R.: 1986a, in "The Comet Nucleus Sample value? ..
Return Mission", ESA SP-249, 15. Rickman: The estimate of 3 x 10 kg is based
Ueissman, P.R.: 1986b, Nature 320, 242. on the assumption that the total dust mass
Uhalley, E.: 1985, in "Ices in the Solar System" loss is about one half of the total gas mass
(Eds. D. Benest et al.; Reidel), p. 9. loss. This would imply that the upper mass
Whipple, F.L.: 1950, Astrophys. J. Ill, 375. limit of ejected grains is of the order of
Uhipple, F.L.: 1951, Astrophys. J. 113, 464.
Uhipple, F.L.: 1977, in "Comets, Asteroids, Meteorites"
1 g on the average. But I would of course
(Ed. A.H. Delsemmej Toledo Univ.), p. 25.
expect that the instantaneous value of the
Uhipple, F.L.: 1983, 1AU Circular No. 3881. limiting mass varies in the course of the
Uhipple, F.L.: 1986, in "Exploration of Halley's Comet", apparition.
ESA SP-250, vol. II, 281. Simek: Do you suppose different size distrib-
Whipple, F.L.; Hamid, S.E.: 1972, in "The Motion, ution of ejected particles from the comet
Evolution of Orbits, and Origin of Comets" according to the number of cometary returns?
(Eds. G.A. Chebotarev et al., Reidel), p. 152. Rickman: Yes, in principle I expect that the
Vilhelm, K.; Cosmovici, C.B.; Delamere, W.A.; gradual dust coverage of the nucleus must
Huebner, V.F.; Keller, H.U.; Reitsema, H.; decrease the maximum liftable mass, which
Schmidt, H.U.; Whipple, F.L.: 1986, in "Exploration would imply a shift of the cut-off of the
of Hailey's Comet", ESA SP-250, vol. II, 367. size distribution. But one should also be
Yamamoto, T.: 1985, Astron. Astrophys. 142, 31. aware that this concept is based on a very
Yamamoto, T.; Kozasa, T.: 1987, ISAS Ras. Note 364. simplified model + hat might not be entirely
Yeomans, D.K.; Kiang, T.: 1981, Mon. Not. R. Astr. applicable to real comets.
Soc. 197, 633. Ibadov: What can you say about formation of
mass spectra of cometary nuclei? May we
expect existence of comets with dimensions
not only 1 - 1 0 km, but also 100 - 1000 km?
D I S C U S S I O N
Pickman: There may have been some very large
comets, e.g. 1729.
Vanysek: (Comments to all papers on evolution
Fechtig: Weissman has discussed a strong depen- of comets):The structure of cometary nuclei
dency of the pristinity of cometary nuclei on is essentially determined by the formation
the location of their formation. Do you agree process of these Dodies. The current hypothe-
with this opinion? ses concerning comets formation can be enco-
Rickman: Yes, I think that e.g. comets supposed passed in two different concepts: The comets
to have formed in the Jupiter-Saturn region are formed either in a cold or in a hoi en-
may have started out in a less pristine state vironment. According to the "cold" concept,
due to the energetic accretion process. But the cometary nuclei were accreted in distant
I should emphasize that I think the present- regions of the solar nebula (or even in the
-day pristinity of comets depends to a large dense interstellar clouds) where the temper-
extent on their dynamical evolutionary histo- ature was T«*riOOK. On the other hand, the
ry as well. comets may grown under relatively high
Babadzhanov: You find that the density of -j initial temperature (TCI2000K) in a medium
Hailey s and Encke's comet nuclei is 0,2 g/cm . with the physical characteristics typical for
But what about the density of the dust grains very inner part of the solar nebula. The dif-
in your comet model? -, ference in the formation processes should be
Rickman: The density of 0.2 g/cm is not di- discernible in the structure and chemical
rectly coupled to any particular comet model composition of the nuclei. Some of the recent
as far as the dust is concerned. However, observational results, as for instance the
I believe that a comet nucleus with such a discovery of the sulphur dimer in IRAS-Araki-
low density must be porous over a wide range Alcock comet, very strong indication that
of scales. In particular, it appears that a organic molecules are abundant in the dust
density of about 1 g/cm3 for cm-sized or larger particles, existence of the "CHON" grains
dust grains is not compatible with the inferred as well as presumably "interstellar" prop-
bulk densities. erties of parent molecules, imply that comets
are formed by cold coagulation of the water
Crifo: Many of the phenomena you discussed are ice and a heterogeneous mixture of organic
dependent on cometary mass-loss estimates. Can compounds, frozen radicals and refractory
you rite any indirect evidence coming e.g. material. Therefore the "cold concepts" are
from nongravitational forces that could place favorized against the "hot" alternative.
an upper limit to cometary mass-loss?
Rickman; As far as the nongravitational effect Nevertheless, chondritic meteoritic samples'and
is concerned, the answer is no, since this Brownlee particles of presumed cometary
depends only upon the gaseous mass loss. How- origin, were most likely formed in a hot
ever, from lifetime arguments using evidence hydrogen rich medium.Therefore, the hot and
for the previous existence of the comet this dense initially condition might be also an
may be possible (see comment to Crifo s paper acceptable starting point for a framenwork
in TS-2). of the "hot" concept. The formation of comets
Shulman: Why do you think that the crystal- is undoubtedly bound with evolution of solar
lization goes on at 150 K only? It is well system as well as with star formation general-
known from the physics of vitreous state ly. From the viewpoint of somewhat broader
that it takes place under arbitrary temper- perspective, the formation Df comets might be
ature .

45
 almost simultaneously i n i t. i a t o d u n d e r an
e n t i r e l y d i f f e r e n t •, t; t o f c o n d i I i o n : ; , d e p e n -
d i n g on the site w h e r e the p r o c e s s look place.
T h u s , it c a n n o t b e e x c l u d e r ) t h a t t h e r e are
at l e a s t two p o p u 1 a t i o n s of c o m e t s distin-
g u i s h e d by their dynamical f:liar;n:ti:i i i . t i c s
as we 1 1 as by the c h e m ioa I and structural
p r o p e r 11 e s . O n e p o p u l a t i o n c o n s i s t s o l uhitif-
f u r n n t i a trill b o d i e s f o r m e d in a , c o l d unviion-
m e n t n t a d i s t a n c e at l e a s t III A l ! I i oiu t i n :
Son . U y n a m i ca 1 I\ so . i i onu' t •, hi 1 I ' M r j I'M, III^HI:
1 V t o t h e " e e w " c o i i i i • I •. o f t l it • . l . i 1 , 1 , ! ! . i l M o r i
cloud. 1b o other' p o p u l a t i o n ) ! i n.ii'i., h i s a
(.•(initii l i e d "(ij(|li a m ) l o w " teii.'jieia t i n r h i ' - i i - i y
a n d d y n a m i c a l l y o r M l 1 n.j I e s ! i oin t h e i oiif i ,
p a r t o f a e o m e t a i y c l u u i l o \ 1 e o t o d o p to ib J
AU. I h u s G c o m e t s m i i j o t b o moi't: c o m p a c t anil
l e s s f r a g i l e a n d m o s t ol then: w e i o preooi-
s o r s of such typu of small b o d i e s as Apoliu
asteroids, I n o r i d - A r ie t i d S t r e a m oi comet',
l i k e P / f n c k e . h'och a s c e n a r i o d o e s n o t iei)iiiie
any e x o t i c niecihanism a n d may h e a s o u n d basis
l o r a Sf: I f - c o n s i s t ei 11. t h e o r y o I' (fir: o r i i j i n o f
c a m e ts .
 HALLEY DUST COMPOSITION

M. S o l e ' ) ) , E.K. Jessberger ) , P. H s i u n g 2 ) , and J. Kissel 2 )

2 2

1 ) Dept. of Astronomy and Astrophysics, Charles University

?•« 'dska 8, 150 00 Praha 5, Czechoslovakia
2) Mj>-Planck-Institute fur Kernphysik, Postfach 10 39 80
6900 Heidelberg 1, F. R. G.

Progress is reported in evaluating the mass spectra of cometary dust grains that have been obtained
Dy impact mass analyzers flown onboard the Giotto and Vega spacecrafts. Statistical analysis of
about 5000 spectra transmitted to the Earth in the more compressed modes 1-3 demonstrates that the
mean elemental composition is similar to that of Cl carbonaceous chondrites with the exception of
the light elements C, H, 0, and N which show nearly the solar composition. The isotopic ratios do
not differ from solar system values. Five classes of particles are suggested: 1) with dominant
Mg-Si element group, I) with dominant CHON abundances, 3) composites of classes 1 and 2, 4) grains
rich in carbon, 5) grains rich in iron and sulphur.

Time-of-flight spectra were registered in the

1. Introduction following modes:

The chemical compositions, masses, and densities of mode 3 Time (t**2) and multiplier output are sampled
dust grains in Halley's coma can be deduced from the (digitized and stored) for each ion current
data obtained by the impact mass spectrometers flown maximum. If no maximum occurs within 8.5 us
on board the spacecrafts Giotto and Vega 1,2. All a time sample was created.
three experiments (PIA and PUMA 1,2) are impact mode 2 Same as mode 3, time samples were created in
ionization time-of-flight (TOP) mass spectrometers of intervals of 1.06 us.
very similar construction (Fig, 1). Their detailed mode 1 Same as mode 2, but also ion current minima
description is given by Kissel (1986). More than 5000 were sampled.
mass spectra of dust grains were transmitted from all mode 0 Output signal from multiplier is sampled with
three instruments. The aim of this paper is to report a frequency of 15 MHz, the interval between
further progress in the evaluation of the data and to two samples beeing 66.7 ns. No time informa-
give a brief overview on the composition of cometary tion was transmitted. Spectra are not selec-
dust. ted according to quality.

The spectra of mode 1-3 were selected according to

quality (number of samples) before transmission to
the Earth, mode 0 spectra are unselected (each 26th
2. Experimental spectrum transferred is of mode 0). From the
instrumental point of view, all spectra are
Dust grains entering the spectrometer hit a metal classified into 10 classes including the results of
target with their high relative velocity (Giotto: 69 test procedures. The criteria for class assignements
km/s; Vega: 78 km/s ). The materials and shapes of include the number of trigger coincidences and the
the targets were as follows: number of peaks corresponding to the most abundant
elements. If many spectra were taken within a short
PUMA 1 silver plate, corrugated, (the normal line to time span, only those with high class were
facets divides the angle between entrance transfered. This implies a statistical bias towards
direction and the axis of the first drift more massive dust grains.
tubes into two equal parts of 30 deg)
PUMA 2 thin, slowly moving silver foil In the PUMA instruments ttw transmittance of the
PIA thin, slowly moving platinum foil doped with spectrometer was regularly switched between two modes
10X silver. with different ion energy windows: low energy window
(0 to 50 eV) resulting in so called "long" spectra
To recognize a dust grain impact, at least one of the and high energy window (0 to 140-190 eV) giving
following signals had to be triggered - a) the signal "short" spectra. Substantial differences of
from photomultiplier indicating a light flash from instrument transmitivity between long and short modes
the impact point, b) the current pulse occuring on occure mainly for light elements. They are discussed
the target and c) the signal from the acceleration in detail by Kissel and Krueger (1987a).
grid indicating passage of the ions through the grid.
Each of these events can start the time measurement The effective mass resolution in the mode 0 spectra
but a coincidence of three events makes the trigger is better than 1 amu as is the case in the more
more reliable. The threshold levels of triggering compressed spectra if recognizable peaks of major
signals were switched between two values differring elements are present. In about 10X PUMA 1 mode 1-3
by a factor of 100 and thus the instrument operated spectra and 20X PIA mode 1-3 spectra the absence of
in high or low sensitivity mode. strong peaks does not allow to correctly adjust the
mass scale. The uncertainty of the peak position,
The clock supplies the square of time elapsed since which cannot be assigned to any element at first
triggerring and hence it should be pro'portional to glance, is generally greater for masses above 56.
the mass of ions at the end of the path through the Also in well defined spectra the uncertainty still
TOF spectrometer. Positive ions released from the remains to be about 1 amu.
impact site are accelerated by the potential
difference between the target and the grid and are The main source of the mass scale adjustment in
directed to the first drift-tube. After completing spectra of mode 1-3 is the improper operation of t**2
the 1 m path through the drift tubes and reflector, generator and the subsequent digitisation. It has now
the ions are detected at the multiplier. The output been corrected by recognizing some regularities in
signal of the multiplier is a logarithmic measure of the t**2-values. The spectra most influenced by the
the ion current. jitter in t**2 generator are those of PUMA 1, but on
 PHOTOMULTIPLIER

Fig. 1 Arrangement of the time-of-flight dust impact mass spectrometer

the other hand they contain probably less biased Both components, the silicate rich and the CHON rich
values of amplitudes (digitized output from grains, differ also in the density which is 0.1-0.3
multiplier) than PIA spectra. Data from PUMA 2 are g/cm3 for the "organic" grains and 0.5-3 g/cm3 for
still beeing recovered from effects of the power the "silicate" grains which we believe is
supply drop. proportional to the content of iron. The masses of
mineral particles are generaly higher between
10**(-14) g and 10**(-12) g while organic grains have
densities 10**(-14) g or less. The selection rules
3. Isotopic, elemental, and chemical composition according to which the spectra were transmitted
probably suppressed small particles with few peaks
Tile peaks corresponding to major elements are well and consequently the frequency of these grains may be
recognizable in spectra of mode 0-3, both from PUMA 1 underestimated.
and PIA. The uncompressed spectra also show peaks of
less abundant isotopes of major elements, which Fig. 2 shows mean "short" and "long" spectra derived
correspond to their normal abundances. The isotopic from PUMA 1 mode 3 data. These spectra are mainly of
composition derived from PUMA 1 spectra mode 0 was class 7, i.e. they were triggered by 2 or 3
discussed in detail elsewhere (Jessberger et al., coincidences and generaly contain many peaks. Wi"l
1987, Sole et al., 1987). Some typical peak patterns the exception of mode 0 spectra about 3% of ail
in the corrected mode 1-3 spectra allow the isotopic others reveal only few peaks and there is no such
identification of C, Hg, Si, S, and Fe. The isotopic spectrum transmitted during close approach.
ratios of the elements are mostly compatible with
solar system values (Tab. 1), though the apparent The averaging procedure was applied to 1194 mode 3
12C/13C ratios cover a remarkably wide range. The PUMA 1 spectra, separately for long and short modes,
spectra with high energy window (PIA and PUMA 1 to show an example of mean composition. After the
short) rather closely reflect the solar isotopic correction for t**2-values, the amplitudes N were
ratios and therefore the contributions of multiply converted to ion numbers by 10**(N/DL) with
ionized atoms or of molecular ions are negligible, at decade-length DL set to be 25. The sum of the ion
least at mass numbers corresponding to the isotopes, numbers over all spectra, divided by the number of
e.g. 24, 25, 26, 28, 29, 32, 34, 54, 56. On the other spectra, was converted to the logarithms and
hand, some spectra with many peaks o£ probable subsequently the envelope curve was drawn.
molecular origin (mainly PUMA 1 long) show large
variations in ratios like 24/25 which varies from 4
to 100.

A large portion of cometary solid grains contains two

main components: "silicates" consisting o£ Si, Mg and
heavier elements, and "organics" made out of light Anorganic component
elements CHON. The plot of Mg vs. Si ion abundances
shows a clear correlation of both elements suggesting The abundances of heavier elements (Mg etc.) may be
that they belong to the same kind o£ material. On the consistently inferred both from long and short
other hand, there is only a weak correlation between spectra. Within a factor of 2 the silicate
composition is similar to that of Cl chondrites (Fig.
the Si and C abundances (Fig. 3 ) . Apart from the 4). The data do not yet allow to estimate mineral
hydrogen content which cannot be estimated precisely structures. Water molecule cluster Ag+H20 is found at
in long mode spectra, the main variation among masses 125 and 127 indicating possible presence of
individual grains is in the abundance of oxygen. The water also in the grains. The abundances of light
ion abundances of O/Si and 0/C correlate less than elements are solar rather than that o£ Cl chondrites.
e.g. Kg and Si.
 Fig- 2a The mean PUMA 1 mode 3 i "ctrum - long operational itode

Tig. ?b The moan PUMA 1 mode 3 spectrum - short operational mode

l o g ( K g / Cl

I -
II1
-
,1'

D -

111'
1

Z
-

-
1

I
lllfI
I1 111 IIP

3 —
i
log |Si/ O
11 (SI/ C)

-) -2 -I - 3 - 2 - 1

Fig. 3a Hg/Si ion ratio normalized to carbon Fig. 3b Mg/Si ion ratio normalized to carbon
(PUMft 1 mode 3 long spectra) (PUMA 1 mode 3 short spectral
 1 16 0 / 18 0 2 28
J sotopes Si/29Si 56
Fe/ 54 Fe

2
V26Hg 28Si/3OSj

Natural isotopic 90 500 7.8 19.6 22.6 15 .8

ratio 7.0 29.7

Mi'dri ion peak ratio 195 480 17 ( 4 ; 100) 28 (10;20001 18 *

It . l'ui'5 ( l;3000) 1100;-) 9 (4; 100) 26 ( 1 ; - ) (12;

" (iLMl 1 , , . , , , ; , i: ,,|.;no to the Its5 abundant I sntope usually not found !

Tab. ]

(!!> SOLAK PHOlOSt'HtHr

Organic component ® 11 HAU JSI

20- o
o
As it can be seen in the uncompressed spectra only, f-
two types of spectral features may be distinguished: 1
1. relatively broad profiles where peaks match the ®
10-
integer mass numbers. They are usually assigned
to atomic ions. m,•
2. Less frequent narrow profiles that sometimes do
not fit any integer mass number even if other
2-
m . _© • • . _.
M
_
peaks corresponding to elements are correctly
placed on the scale. The..*e narrow peaks cannot be
direct3y assigned to atomic ions since they
1-
• 0
a I y •
occur also at higher masses (above 5 6 ) . .5- • - •

• . - •
*

Accor ding to the- theory of ion formation processes

d u r i ng rhf? par t i c 1 c? impacf (Kissel and Krueger,
1987a ) , yo:ne mo ic-cu lea can be released from the grain .1-
surfa ces by desorpt ion. The ini tial energy spread of H C N 0 s Na K M n Cr Si Fe Mg N i Ca T i Al
mo 1 ecn}ar ions shouJd be lower than that of atomic
ions, This i .'••; cons is tent with the higher frequency of 330JT4 3.1 416 27 3.2 2 .6 •S .1 5
such peaks in long mode spectra. For example, peaks Afi JNOANCE in C1- mil C R I 1 I S
at ma sses 41-42, 46-47, 71-72, 79-81, 89-91 coincide
v i 111 sonr: molecular peaks found in PUMA 1 mode 0 VUI A T II I ! Y
spec t ra I)} Kissel and .Krueger (1987b) who discuss the
pi oba composi t ion of the irolecular species. Fiy. 4 "'lean e l e m e n t a l c o m p o s i t i o n o f H a i l e y ' s dust
in c o m p a r i s o n w i t h Cl ch'.in;:r i' i-b i PU:-'iA 1 ,
mode C'

3.
REFERENCES
On t h e b a r i s of corner e s s e d mass spec t r a t h e e l e m e n t a l
i on a b u n dan'•*_•.- v e t o evaluated. jessbergec, F..K.., Kissel, .i. , Fecluig, I! . Ki ueger,
The f o l l o w i n g f i v e
r 1 r'issps of f oil'."l.-iry g r a i n s a r e s u g g e s t e d ( i n p a r e n -
F.R.: ltflh, E m . Space Agency Spec. Pubi. ?•'.<?,
\ l i e s i s t lip 11 a p p r o / , i inn r e f r e q u e n c y i s g i v e n ) :
27
Jes>ibetge: , E.K., Kissel, J.: 198', Lunat ,ind Plaiiei.
1 . " s i l i . nt<>" g i a i n : - (WZ) Sri. Conf. XV1I1, The Lunai SriEin-e Ins'itute,
con.^ i .<; t i n s ; fr.a i n ) y of Hg, Si ( F e ) Houston, 247
Kissel, J-: 1936, E m . Spine Agency Spec. Publ . HIV 7,
} . "organ i -'" gra i n:-- ( 6%) 69
cons i •:' ing tiidi n 1; ol L iglit elements - CH0N Kissel, J., Krueger, F.R. : 1987a, Appl. Vhys. M2, 69
Kissel, J., Kruege:, F.K.: 1987b, Nature 32b, 755-760
.3. compos i te par t ic.les (70%)
Sole, H., Vanysek, V., Kissel, J.: 1987, Eur. Space
of ma t or i a I f rom cIasn 1 and 2 Agency Spec. Publ. 250, Vol. I, 373

4 . "pure1 carbon" pai t i c les C, (H) (1^)

DISCUSGI0H
5. "trollite" particle^ Fe, S ( 1%)
The actual population of classes 2, 4, 5 may have Ibadov; What can you aay about the existence of
tie en under es t i mated because of the selec t ion T,U1 ticharged ions (due to hi^h-velocity colli-
procedure before data transmission to Earth and also sions of com^tary dast particlf;? with interplane-
due to the procedure of mass-scale adjustment during tary bodies connidered thooro'icaliy in oar work)?
spectra evaluation. Some spectra (completing the •JOIC: r ultichar;^d :r,'u-nssi-j:r. ion." » r s detected.
classification to 100%) are difficult to interpret
because major e I emeur pe^ks are not recognizable.

50
 ON THE PHENOMENON OP ANOMALOUS DISTRIBUTION OP METAX ATOM EMISSION IN COMETARY HEADS'
S. Ibadov /
Institute of Astrophysics, Dushanbe 734670, USSR /

The theory of cooling of cometary dust by a gas outflowing from the nucleus is
developed and used for explaining the anomalous distribution of sodium atom emis-
sion in the head of Comet Mrkos 1957 d. The results obtained indicate the univer-
sal character of the phenomenon of anomalous distribution of metal atom emissions,
including the Na I lines, in the heads of bright comets and the possibility of
condensation of a cometary gas (HgO, C 0 2 etc.) in the neariiuclear region.
Key words: comets - metal atom emissions - anomalous distribution
1. Introduction 2. Cometary Dust Cooling by Gas
Outflowing from a Nucleus
Spectral observations of Comet Mrkos 1957 as the Cause of the Anomaly
by 5-ffleter Palomar telescope lead to the
detection of the phenomenon of anomalous The temperature of dust particles of co-
distribution of sodium atom emission, name- metary atmospheres T determines the rate
ly the displacement of intensity maximum of of their evaporation and therefore the con-
sodium atom emission toward the Sun to the centration of metal atomB in the cometary
distance nearly 2000 km from the cometary atmospheres, so that the spatial inhomoge-
nucleus (Creenstein, 1958; Greenstein and neity of T = T(r) may cause the correspon-
Arpigny,1962). ding inhomogeneous distribution of metal
Present approaches to the interpretation atoms in the cometary heads.
of anomalous distribution of sodium atom Conglomerate model of cometary nuclei as
emission in the head of Comet Mrkos 1957d a mixture of ices and solid particles now
may be divided in three classes: 1) opti- generally accepted allows highly intensive
cal, accepting the optical thickness of the ejection of gases (H ? 0, C0~ etc.) from nuc-
cometary coma in sodium lines to be very lei (see e.g. Biermafi and Trefftz, 1964;
large ( > 1) for nearnuclear region (i.e. Liller, 1960; Sagdeev et al., 1986; Whipple
for the cometocentric distance r < 2000 kin) 195O)i especially at small heliocentric di-
(Greenstein and Arpigny, 1962). We have to stances R £ O.T - 1 AU, i.e. where in comet
note, however, that such assumption is done spectra lines of metals (Na, Fe, Ni etc.)
without corresponding physical basis, name- are usually observed (see e.g. Greenstein,
ly without analysis of the possibility of 1958; Greenstein and Arpigny, 1962; Levin,
intensive release of sodium atoms in the 1964; Oppenheimer, 1980; Preston, 1967).
nearnuclear region; 2) kinematic.il, star- Along with this, according to recent calcu-
ting from the optical thin coma and attemp- lations (Bisikalo and Strel'nitskij, 1985;
ting to explain the anomalous maximum of Crovisier, 1984; Marconi and Mendis, 1983;
brightness as a classical Bessel-Bredikhin Marov and Shematovich, 1987; Shimizu. 1976)
envelope of Na-atoms which were ejected the temperature of cometary ges Te (r) has
from the nucleus towards the Sun and then, a deep minimum (T . = 10 - 50 K at r =
under the action of light pressure, move in 10 - 10 J km) because of a strong self-coo-
opposite direction (Wurm, 1963). However ling of gas due to its expansion and inten-
such explanation, as known (Dobrovolsky, sive IR-radiation of cometary molecules,
1966, p. 78), is contradictory to Kokhnach's and within the whole inner coma (r < 10' -
law, since in this case the maximum of bri- 10 * km) not exceeds the temperature of su-
ghtness have to be near the nucleus at arb- blimating surface of a nucleus of both the
itrary distribution of initial velocities telescopic and the bright comets; this tem-
of ejection; 3) atomic approach, proceeding perature is always low by themselves: To i.
from the view point that sources of Na- 200 - 300 K (see e.g. Sagdeev et al.1986).
atoms are, together with the nucleus, also
duet particles in the head of a comet (on In this connection we shall consider the
the role of dust particles as a main sup- establishment of the temperature of a dust
plier of metal atoms observed in the come- particle ejected from the nucleus into the
tary atmospheres see e.g. Delsemme, 1982; coma with an initial temperature T o taking
Bonn and Rahe, 1982; levin, 1964; Wyckoff, into account the cooling effect of crioge-
1982). The anomaly in the dietribution of nic gas flow.
sodium intensity may be explained if the The equation of heating of a cometary
presence of a small-moving dust envelope dust particle by solar radiation may be
- a dusty halo - in the cometary atmosphere written in the form
is supposed. However both th* absence of
well expressed correlation between the in- (1) Sicfzq dt = cm dT + ^ dt +
tensity of Na-spectrum and continuous spec-
trum and the gradual fall of intensity in + 63ikd2n V O^T-T) dt
the first 3000-8000 km from the nuc>us to- S S
wards the Sun observed do not allow us to where a is the radius of a dust particle,
confirm it with fully confidence. Thus, the x is the integral absorption coefficient
question on the mechanisms causing the ano- of eolar radiation, flow density of which
malous distribution of Ha I emission in the q varies with R as q = q 0 R~ 2 (qo= 1.36 10°
head of Comet Mrkos 1957d remains open. erg cm"' B~' is the solar constant); c, m
and t are the specific heat capacity, the

51
mass and the integral heat radiation coeffi- (cm3 K ) , * f / |= 0.1,
, V = 1 0 4 cm/s we have
cient of the grain; <f is the Stephan-Boltz- T B = 280 R-1/<f KK and
d l
lh = 1.1 10' RR33//22c m .
mann constant; k is the Boltzmann constant; Thus, in a "vacuum" regime within the zone
eC is the accomodation coefficient of molecu- of metal atoms apparition in the cometary
les of gas at the grain surface; n g is the spectra (R £ 1 AU; the length of the rela-
number density of gaseous molecule!; V g is xation zone is very small: lh - ro ~ 10-> -
their thermal velocity, corresponding to 10° cm, so that practically in whole head
temperature T_; the left-hand side of Eq.(1) of weak comets there ia the isothermic duBt
is the radiation energy absorbed by a par- with the temperature T(r > r o ) = T B .
ticle, rnd the terms on the right-hand side 2. In order to determine the relative role
concern the heating of the particle, its ra- of the radiational and molecular cooling,
diational and molecular cooling . we put in (4) q = 0 and neglect the terms
Eq. (1) is completed by the expression for containing T and T g . Then, after integra-
distribution of number density of molecules ting over T (from fg to T) and over t (from
in the flow escaping from the nucleus t = 0 to t ) , we get

(2) n,(r, R ) = n_(ro , R ) ( r o / r ) 2 . n +

(8) In
Here ru(r 0 , R) i s the number density of mo-
lecules' at the surface of the nucleus:
4 10 1 8 H d where l g ie the relaxation length of dust
(3) temperature, corresponding to its cooling
by gas:
/Q\ -^ cmV _ 2cJaV
is the,observ d dust production rate in
i j is the gas production MWafV^ 9UV g n g
cleus, J/L~ is the mean molecu-
lar weight, k s = S e ff/Si, S e ff is the area The condition of the dominating role of
of the effectively sublimating (subsolar) molecular cooling compared with the radia-
zone of the nucleus, S+ is the total area tional one, lg < lix, leads, according to
of the nucleus, ro is the nuclear radius. (6) and (9), to corresponding criterion for
Eq. (1) is reduced to nonlinear integral the density of ambient gas
equation
(* caV dt =
(10) n
" cr
2
) -6*ka n V «T-T g
o o o Here n c r is the critical density of gas,
corresponding to l g = l n , i.e. to equal ef-
(4) • ;
7 dt fects of molecular and radiational cooling.
From condition n K ( r c r , R) = n c r with us-
which we consider for two regimes: ing (2) we find the" critical radius r c r ,
1. The radiational cooling is essentially i.e. the radius of the zone within which
greater than the molecular one (weak cometa) the temperature of dust particles will be
Then Eq. (4) with quasiconstant coefficients controlled mainly by gas temperature:
(the velocity of grains outflowing from the
nucleus V; V & ; mj the density of grains S"
etc. weakly change with r) corresponds to (11) rcr
the problem of heating dust particles in a
"vacuum", and its solution has a form ( Iba-
dov, 1979): The critical temperature of grain T o r ,
T +T T 41 corresponding to quasistationary regime
(5) In — + 2 arc tg - =— . dT/dt = 0 at r = r c r , i.e. to thermal regi-
T
s" T me at which lg = lh and nR = n c r , may be
found on the basis of ( 1 ) ; (6), (9) and (10)
Here
1 = Tt; 1 cmV^_ _
(6) (12)
3 '
8
as seen from ( 5 ) , is the length of the re-
laxation zone, where the heating of the par- Prom Eq. (1) with using (2) T(r) may be
ticle from an initial temperature T o up to found for various values of r/r c r . As the
quasistationary temperature T_ takes place, result we have T(r = 3 r c r ) =• 0.99 T s , i.e.
namely T(l = l n ) « 0.9 T s , ana at the zone r = 3 r c r the temperature of par-
ticles is almost equal to the limiting maxi-
(7) T 8 = [fcq + 4WT 4 )/(4U)] 1/4 - mal temperature corresponding to quasistati-
onary vacuum regime.
Scheme of temperature distribution in co-
metary comae is shown in Pig.; 1 - dust tem-
ri = \1o/**/ = 280 K is the value of T s perature in atmospheres of weak comets, i.e.
ax » = I and R = 1 AU; the approximate equ- at "vacuum" approximation; 2 - dust tempera-
ality in (7) is applicable to the observab- ture in comae of bright comets, i.e. at con-
ility zone of comets, where Eq » 4 W T j . ' ditions of cooling effect of a gas (numeri-
For cometary particles having probable cal values of parameters as in the text be-
radius a = 10~4 cm by (6) and (7)_with cha- low); 3 - temperature of gaseous component
racteristic values of cd = 4.2 10' erg/ of comets - see e.g. Marov, Shematovltb,'!987.

52
T,K indicates the universal character of the
Dhenomenon of anomalous distribution of me-
tal atom emissions in the heads of bright
comets. This effect way be revealed in the
cometary atmospheres by spectral observa-
tions with sufficiently high spatial reso-
lution - of the order of 10 - 1000 km. The
resolutions ~10 - 100 km may be realized,
probably, during missions to comets. 0,'he
condensation of coinetary gases 1 B p o i b l
in the nearnuclear region.
The author is greateful to Prof. O.V.Dob-
rovolsky for useful discussions.

REFERENCES
Bierman, T.; Trefftz, E.: 1964, 2. Astro-
phys- 59, 1.
Bisikalo, D.V.; Strel'nitskij, V.S.: 1985,
The vapour pressure of condenced substan- Pisma v Astrcn. Journ. 11, 475.
ces depends on the temperature exponential- Crovieier, J.: 1984. Astron. Astrophys.
ly. So at coinetary conditions the maximal 130, 361.
release of metal atoms will be at the zone Delsemme, A.H.: 19G2, in Comets (ed. L.L.
of cometocentric distances of rmax s 3r c r . Wilkening; Arizona Univ. Press, Tucson),
Using Eqs. (3). (7), (10) and (11) we have 85.
Dobrovolsky, O.V.: 1966, Comets, Nauka,
Moscow.
(13) 2.5 Donn, B.; Rahe, J.: 1982, in Comets (ed.
max L.L. Wilkening; Arizona Univ, Press,
s Tucson), 203.
Greenstein, P.L.: 1958, Astrophys. J. 128,
Accepting for Comet Hrkos 1957d during 106.
17 - 19 August, when R = 0.559 - Q.599 AU, Greenstein, F.L.; Arpigny, C : 1962, Astro-
the values of H<i(R = 0.6 AH) = 109 g/s phys. J. 135, 892.
(Liller, 1960), ^ » 1, V g = 105 cm/s, SL = 1 Ibadov, S.: 1979, Dokl. • p.d. Nauk Tadzhik
= 0.1 (metallic particles), ./<• = 0.1, ,/Cg = SSR 22, 303.
20, k s = 0.1 by (13) we obtain r m a x = 1200 -: 1983, Dokl. Acad. Nauk Tadzhik SSR 26,
km. This value is near to the date of the 90.
spectral observations (Greenstein, 1958; Levin, B.J.: 1964, Icarus 3, "-97.
Greenetein and Arpigny, 1962). Along with Liller, W.: 1960, Astrophys. J. 132, 867.
that for Comet Halley 1982i near the peri- Marconi, M.L.j Mendis, D.A.: 1983, Astro-
helion by (13) we get rmax <* 100 km. Beca- phys. J. 273, 381.
use of gas-dust matter is ejected mainly Marov, M.Ya.5 Shematovich, V.I.: 1981, Kel-
towards the Sun, the maximum of metal atom dysh Inet. Appl. Mathem. USSR Acad. Sc.
emissions, including the sodium lines, have preprint No. §0, 3-26.
to be observed mainly in the Sun direction. Oppenheimer, M.: 1980, Astrophys. J. 240,
Moreover, the application of relations (7) 923.
and (12) to icy and quartz type particles Preston, G.W.: 1967, Astrophys. J. 147?,
(«e~0.0i) indicates the possibility of con- 718.
densation of gases H 2 0, CO2 type in the ne- Sagdeev, R.Z.; Blamont, J.; Galeev, A.A.;
arnuclear region and the amplification by Moroz, V.I.; Shapiro, V.D.; Shevchenko,
such way the dusty component of comets V.I.; Szego, K.: 1986, Nature 321, 259.
(Ibadov, 1983). These questions are in the Shimizu, M.: 1976, Astrophys. Space Sci.
stage of developing (see also Yamamoto and 40, 149.
Ashihara, 13S5). Whipple, P.L.: 1950, Astrophys. J. 111,
375.
ffurm, K.: 1963, Icarus 2, 29.
3. Conclusions Wyckoff, S.: 1982, in Cometa (ed. l.L. Wil-
kening; Arizona Univ. Press, Tucaon), 3-
The account of cooling effect of cometary Yamamoto, T.; Ashihara,0.: 1985, Aetron.
grains by gaseous flow from nucleus allows Aatrophys. 152, L17.
to explain most naturally the phenomenon of
anomalous distribution of sodium atom emis-
sion in the head of Comet Mrkos 1957d and

53
 D I S C U S S I O N

Crifo J.F. : Your proposed explanation for Na 5. Ibadov: Results of hydrodynamjc approach
anomalies being due to release from grains to gas-dust motion are used in our equations.
may be appropriate, but the way of your Cometary dust cooling by cryogenic gas
computation differs from known hydrodynamic outflowing from a nucleus occurs at suf-
methods (Finson and Probstein, Marconi and ficiently. high-,number density of molecules,
Mendis, Gombosi, Heilmich and Keller and n«S n os 10 cm , which corresponds also to
myself). What conditions do exist for come- lacaf thermodynamic equilibrium state, the
tary dust cooling by gas? flow is not free molecular on a scale of
coma.,Number density of dust particles
n?*10 cm- . So, for bright comets (for their
near-nuclear region) new solution of the
problem of cometary dust temperature appears,
which corresponds, particularly, to Na
anomaly.
 LABORATORY INVESTIGATION OP THERMAL CONDUCTIVITY OP DUST CRUST MODELS ON THE ICE COiffiT
liUCLEI SURFACES
Kh.I.Ibadinov, A.A.Rahmonov, S.A.Aliyev
Institute of Astrophysics of the Tajik Academy of Sciences, 734670, Dushanbe, USSR

For the purpose of studying the thermal conductivity of comet ice nucleus sur-
faces dust crust we have carried out the laboratory experiments on the cometary
nucleus models. The experiments were carried out under the conditions close to
those r-.z the heliocentrical distances from 1 to 3 A.U. The ice KpO which contai-
ned the particles cf quartz, graphite, nickel and organic substances Dl-alanin,
DL-treonin, L-valin has been studied. The dust matrices 5-15 nun in thickness have
been formed under the ice sublimation irradiated with a light beam. In most cases
the effective thermal conductivity of the matrices which included sublimation
products diffused in then is one or two orders less than that of H ? 0 .
Key r.-crds: dust crust - thermal conductivity - ice nucleus - laboratory modelling.

was necessary to obtain the mineral matri-

ces of necessary thickness in the process
f'ht xtssions of the cosmic apparatuses of sublimation of conglomerate ice cometary
Vega-1 ,2 (r:&f.1) and those of Giotto (Sef.2) nucleus under the conditions very close to
resulted in obtaining the confirmation of cometary ones and to determine the coeffi-
the statement that the hardmeltini: dust cient of this matrix thermal conductivity.
cru3t on the surface of the nuclei of some The samples of cometary nucleus models
p a n ; of periodical comets, the iialley Comet under investigation were prepared at the
included (I!ef.3, 4 ) . The dust crust play3 atmospheric pressure in the special cuvet-
an essential role in the evolution of a tes by freezing the mixture of distilled
ocnetary nucleuc and ether cometary pheno- water and impurities in the vapour of
mena and the study of the crust properties liquid nitrogen. In the course* of experi-
is of ^reat importance today. ments several variations of construction
j.'he author:; of the paper presented for
and the cuvette material and cylindrical
several years have- been carryinr out a num-
cuvettes made from phtoroplast and cork
ber of laboratory experiments aimed at the
have been found most successful. The
study in;- of p h y s i c a l , mechanical and ther-
rreatest number of experiments has been
mal i.y physical properties of the ice nuclei
carried out on the samples prepared in the
".cr.nt'ji-j surface of mineral crust. Zone of
cuvettes made from phtoroplast and corkj,..
che recultn obtained on the physical •xcd
v.-hose thermal conductivity (0.04 w V.~ K )
mechanical properties of duct matrices
is less than that of sand. The diagram of
•v'x'.elc r^ria or.jonie substance matrices are
a typical cuvette is shown in Fifl.1. The
• iven in (I;ef«>, (:) . ::fero v.re are :;oinR to
diameter of investigated rnodel.3 used to be
•:i;jcujG the- results of t'>.' experiments de-
30 as, their thickness ranged between 20-
v "tod the thermal con'juc vity of these
2~: mm. At least 4 thermocouples were moun-
••.".i.i'ices u;ef.1O).
ted in the cuvette and the maximum error
when measuring th.:. temperature of a model
did not exceed 1°K.
Z • y.-L ,..O~j\iZi G P JOf.'ih ^ A J < Y iiuGLEUo
k'.Vj 1'iir. i,APLiil:."Ji:;TAL :..t t:\QjZ

A.: K:I ico nuclerir base in o;ir experiments

we have taken M.,C the presence of v/'nich in
cci.iet.'iry nuclei' ::?.s oVtnined rr.jch indirect
evidence, d-.iria" tVic- cosnic \pp-?-?rt'-tu3 n i s -
3i.>:i co :!alle;,' Oornct (iief.l , 2). As hord-
melt in.-: impurity v;e used the dust particle.1;
of quartz V'j—?J ju. in si",e), ,-;ra-hite (10-
1 "Oj.i ), nickel (1-2 J-L ) and organic sub-
stance ijL-alanin, DL-treonin, L-valin. The
laboratory experiments (such as Kef.7, 3)
showed that under the certain conditions
come porous matrices can be formed on the
surface from the dust particles and organic
substances under the sublimation of such
nucleus model. The possibility that impuri- I L
ties chosen by us exist has been repeatedly
mentioned in literature but other versions
of hardnielting constituent of cometary
nucleus are quite possible in principle,
although as the experimental results showed,
it doesn't play the substantial part when Figure 1. Vacuum chamber for imitation of
solving the given problem. cometary conditions. 1 - chamber,
The experimental methods were due to the 2 - cryostat, 3 - glass windov;,
concrete aim of the experiment, thet is, it 4 - cuvette with nucleus models.
 The experiments have been carried out in
the high vacuum and low temperature chamber
(Fig.1) that made it possible relatively
uniform temperature field around the inves-
tigated models. According to the experimen- where 3£ is the coefficient of the ab-
tal methods already prepared nucleus models sorption of the model surface, Q. is the
after having been cooled to the temperature energy of light beam incident on the sur-
of 77°K were inserted into the chamber, that face and S is the area of model's sur-
hadgbeen pumped out until the pressure was face. The numerical value of ȣ for each
10 Torr and at the same time had been variation of nuclear model has been deter-
cooled by liquid nitrogen through the cryo- mined experimentally. The value of Q.
atat mounted inside the chamber. The solar has been determined by direct measurement
photon radiation imitation has been done by of light beam energy.
the superhigh pressure mercury lamp and the
irradiation of the models surface by visible
light was done outside the chamber through
the glass window after the limited vacuum
in the ohamber and equibalanced temperature
of nuclear models had been reached.
The specific feature of the experiment was
that in order to obtain reliable results
about the coefficient of thermal conductivi-
ty it was necessary to produce matrices with
5 mm and greater thickness under sublimation
process. The little thickness was respon-
sible for the error when determining the
irradiated parameter due to the errors made
in the determination of the thickness itself 40 SO 120 160 t, h
h and temperature T. To produce such matri-
ces is specific matter. The matrices are
being destroyed by the quasicontinuous flow
of sublimated gas, when the light beam in-
cident on the surface of a model is highly
energetic while under the conditions of low
energy the time of the experiment increases. Figure 2. Nucleus models temperature from
For instance, under the experimental condi- time dependence. The time of
tions, equivalent to the conditions at 3A.U. release of thermocouple from ice
to obtain dust matrices 5 mm thick it takes indicated by hand.
20-30 days of continuous irradiation of the
models by light when the dust concentration
in the model is average. The substantial
increase of dust concentration in the model It is known, that in the porous dust
makes it unreal. We in our experiments in- layer the heat can be transferred through
cline to the choice of optimal version. In the contacts between dust particles, gas
most cases we imitated the conditions of molecules in pores, by light irradiation.
location cometary nucleus at 1-2 A.U. which We have studied the effective thermal con-
made it possible to'obtain matrices 5-15 mm ductivity of a matrix when all 3 canals of
thick during approximately 10 days of the heat transfer could be active. The part of
experiment (that is 200-250 irradiation experimental results determining the effec-
hours by light beam) when the impurity con- tive coefficient o* thermal conductivity is
centration in the model was real. Throughout given in the Table 1.
all the experimental time the temperature of The result of our determination of the
the nuclear model was measured in 4 points thermal conductivity of ice H g 0 (3.6 w M" 1
of volume. To avoid the direct incidence of K~ ) coefficient coincides with the data
light the outside thermocouple was mounted obtained by other authors (Ref.9) by
at the depth of 1 mm from the model's sur- various methods and confirms the right
face. choice of the experimental method.
The thermal conductivity of matrices
(Table 1) proved to be one or two orders
3. RESULTS less than that of ice H_0 and is close to
that of very soft snow CO.12 w M~ T K ) or
In the course of experimenting on diffe- sand and depends on the porousity of a
rent variations of cometary nuclear model matrix. We didn't find the substantial
the numerical experimental data about the dependence Xeff on the matrices
temperature due to the matrix thickness and material. Prom the data presented in the
its character have been obtained by us. table it follows that in the course of
Pig<>2 shows the characteristic graph of calculations of the thermal regime of ice
nuclear model temperature dependence on comet nuclei possessing the hardmelting
time t. Throughout the whole experiment the surface crust one can take the coefficient
energy quantity of light beam incident on of thermal conductivity., of this porous
the surface of model remains constant. The crust as ~ 10" T w M" 7 K .
change of temperature takes place on the
surface of a model with the formation and
growth of a matrix, the sharp increase in
temperature coincides with the release of a
given thermocouple from ice. The distance
between the thermocouples & X and tempera-
ture gradient being known we can find the
coefficient of thermal conductivity af a
matrix X as
 Table 1.
Effective thermal conductivity of dust crust models on the ice comet nuclei surfaces

Middle p — .. Thermal
Matrices models temperature Porous,
% Density _3 conductivity. .,
of matrix, °K £ , kg m % ^ ^ w M *1 K -1

Graphite particles 235 80 460 7*10~o

Quartz particles 160 40 1360 8 # 10~,
Nickel particles 220 60 3100 10*10,
DL-elanin 250 98 24 6*10",
DL-treonin 240 97 35 6«10,
I-valin 240 97 36 6*10"^

4. REFERENCES
1. Sagdeev R.Z. et al., 1986, Nature, 321.
295.
2. Reinhard R., 1986, Nature, 221., 313.
3o Dobrovolsky O.V., Ibadinov Kh.I.,
Gerasimenko S.I., 1984, Doklady Akademii
Nauk Tadjik SSR, 2J_, No.4, 198.
4. Dobrovolsky O.V. et al., 1986, Proc. of
the International Symposium, Heidelberg,
Germany, 27-31 October 1986, ESA SP-250,
vol.2, 389.
5. Ibadinov Kh.I., Aliev 3., Rahmonov A.A.,
1985, Doklady Akademii Nauk Tadjik SSR,
28, Ho.1, 21.
6. Ibadinov Kh.i,, Aliev S.A., Rahmonov A.,
1987, Proc. of the International Sympo-
sium on the Diversity and Similarity of
comets, Brusselz, 6-7 April 1987, ESA
SP-278.
7. Ibadinov Kh.I., Kajmakov E.A., 1970,
Kotnety i Meteory, 22t 20.
8. Dranevich V.A., lizunkova I.S., 1982,
Kotnet. C i r c , No.286, 3.
9. Ivanov A.S., Gavrilov R.I., 1965,
Thermal physical properties of the
frozen rock, Pdoskou, Nauka.
10. Ibadinov Kh.I., Rahmonov A.A., 1986,
Komet. C i r c , U0.36O, 4.

57
A2
 ABE COMKTABY DUST MASS LOSS BATES
DEDUCED FBOM OPTICAL EMISSIONS RELIABLE ?
by
J.F. CHIFO
CNKS, LPSP, BP 10, F91371 VBRRIERES CEDEX2

ABSTRACT
We present additional evidence in support of our previous work (Crifo, 1987 b-
c) in which, fro* theoretical fits to Comet Halley near -to far- infrared
emissions, based on the in-situ flyby probes data, we estimated that the coiet
was losing half or Bore of its «ass under the fora of large (> 1 gram) grains of
snail (0.3 g cm~3) density. We confirm that the comet dust-to-gas iass loss rate
ratio lies sonewhere between the values 0.80 and 18.6, with a best estimate at
3.46. We discuss this result in the context of the general agreement that comets
loose less than half of their total Bass loss in dust, and this dominantly at
very small grain sizes. We trace this agreement back to overconfidence placed in
a model size distribution which inherently excludes substantial Haas loss in
large grains without appropriate experimental justification.

Finally, a spacecraft flying through the

I. Introductory definitions and remarks coma at a relative velocity much greater
than all V(a) may be hit by grains only up
We will characterize the size distribution to a certain radius aaiax with mass
of the dust released by the nucleus either m(aaax) defined by a collection
by the grain radius normalized probability equal to 1 during the whole
differential distribution Ho(a), or by flyby.
the grain mass normalized 'integral (or
"cumulative") distribution <Ci° (> •) • Due We g e n e r a l l y ( * ) have
to the mass dependance of the velocities V
imparted to the grains by the escaping aatax £ A < Aa a x ;
gas, the corresponding distributions in
the coma Y\ (a) andfo(> m) differ from J?o m ( a . a x ) < m(A) < ( Aa a x )
and X ° (Hanner, 1984, Green et al^.
1987). If power laws hold in some size Computations of the total optical emission
range involve integration of Yl (a) to A, and
computations of the total dust mass loss
Y)o(a) JCa- rate involve integration of Oo (g) to
A . Therefore, if A is indeed large
%»{> m)«C. •) oC •• and if power law applies, we see that
(Green et al., 1987) :
then one has the relations
1 The optical signal is bound (inde-
No - 1 N - 1 pendent of A ) if o > 0.67 (No > 3.54).
(1)
2 The dust mass loss is bound if
0.82 (No > 4).
d In V(a)
3(o - a o ) = N - N o = - u = (2) This already tells us that optical
d ln(a) sounding alone cannot give unambiguous
results concerning the mass loss, unless a
V(a) may depend upon the size distribution is reliably known, and particularly at
and therefore must be determined self large nesses. Confidence to be placed in
consistently by hydrodynaaic methods. such results should be proportional to the
Computations of these kind (Gombosi, 1986 confidence one can have in the value of a
; Crifo, 1987b) give the value u * 0.167 - especially near m (A).
0.18 for sufficiently large Basses.
At a given heliocentric distance, ro,
grains can be dragged away from the
nucleus only up to a maximum radius Aa»«
(ro) to which corresponds a maximum mass
• (Ax.) (Whipple, 1950). However, only
observations can tell us whether all
possible sizes are indeed represented in
the coma, thus we also define A, the * Following a strong and sudden decrease
radius of the maximum mass m(A) really in the gas production rate, A could exceed
present in the coma. Aata x

59
 II Theoretical determination of • (Aaax) required for the optical emission and loss
for comet Halley at ro = 0.9 AU rate to be bound !
Equating the surface gravitational force The two other methods imply a theoretical
and the gaa drag force, one gets the computation of the coma emission, and
following staple formula (Whipple, 1950, therefore have to specify a dust size
Goaboai, 1986) : distribution. Following the suggestion of
Hanner (1983) the following formula was
1 - » V« M, used :
• (A.,,) = - C d A (A..,) (3)
2 g (a)oe- - ao/a)« (ao/a)» (4)
where M« is the gas lass loss rate, g the with typical parameter values ao * 0.1 tim,
surface gravity, V« the initial gas M * 20-30, and, most importantly, H ~ 3 . t.
outflow velocity, V the maximum ^cross It was found to give "a very satisfac-
section of the particle, and Ca the tory fit to visual and infrared data"
corresponding drag coefficient at the (Newburn and Spirad, 1985, see also Crifo,
surface. Exploitation of this foraula is 1982, where a slightly different version
simple only for spherical grains on a of h ( a ) is used). The value for N was
spherical coiet. Still, in this case, justified by the tail analysis data.
considerable care Bust be taken to assess
properly the gas initial conditions (see It is indeed surprizing that this value
Crifo, 1987a) and cS. We have discovered for N is just marginally that needed to
that the free Molecular expression for C?, insure bound flux and mass loss. Realizing
used by Whipple, Goaboai, and others, lead this, Hanner (1984) looked for additional
to values of AB»> much greater than the justifications based on analysis of
gas collision freepath (Crifo, 1987a). observed IR emissions between 3 and 20 um
Therefore they are not applicable ! We in wavelength. She finds that indeed the
have therefore used for Ca more general condition N > 3.5 is required. And she
(but approximate) expressions valid for "notes (that this condition) indicates
spheres in the slip and transition regime that the mass is concentrated toward the
at any Mach number. The resulting a(A B a«) small grains", However, for this statement
-accurate to 60 X- is shown as a func- to be correct one must demonstrate that
tion of the assuaed grain density on
figure 1. the IR signal really requires the
algebraic expression (4) for fl(a) over
the seven decades in mass where the tail
Since in real the grains are not sphe- observations do not place such
rical, there is a much larger uncertainty constraints. From formula (4), however, we
resulting from the shape dependance of Co. see that tj(a) is proportional to a~" as
Consequently, we estimate that, for ro - soon as a exceeds a few times (M/N) ao,
0.9 AU and at p- 0.3 g cm'3, the range of i.e. a few microns (» 10"* gram). Owing to
possible values for i ( A n < ) is : the convergence of the flux integral, the
fluxes computed by Hanner (1984) are due
5 x 10 3 gram < n(A«»x) < 3 x 10s gram to grains below 10" 7 gram, and the
constraint on N aplliea to grains in the
Thus, in this range the exponent a must 9 7
range 10- -10" gran. In other words, the
increase, representing a smooth cutoff. We assumption that (4) holds up to m (Aaax)
ignore this effect in our computa-tions implies that the emission is due to grains
and take for m(A.«x) the nominal value below 10" 7 gram.
given by figure 1.
To constrain the production rate of grains
beyond this mass, it would have been
Ill Coaetary dust aass loss estimates necessary to vary the shape of H(a)
prior to coaet Halley flybys : values, or (e.g. the exponent N) above 10" 7 gram and
lower limits ? to look at the effect on the infrared
emission. We have done this (Crifo, 1987b,
Three different aethods were in use : (1) c and this work) and found that indeed
dynamical analysis of a few coaet tails values of K as small as 2.0 above «• 10" 5
(Finson and Probstein, 1968) ; (2) aodel gram lead to remarkable quantitative fits
fits to the scattered light continuum to comet Halley infrared spectra from 1 to
(Hewburn and Spinrad, 1985); (3) aodel 60 um in wavelengths !
fits to the IR continuua (e.g. Hanner,
1984). Following this evidence, we propose to
consider all dust-to-gas production rate
The first net hod allows derivation of ti(a) ratios based on fornula (4) or equivalent
on a restricted size range (a SlOOua for ones as "lower limits derived using the
antitails, i.e. in thio case grains of a contingent assumption that a unique power
few milligrams << a (Aaax) ! ) . The derived law grain size distribution applies over
values of No on the "large" (milligram) the mass range 10" 9 - 10 s gram". These
size side were 4.0 to 4.5 (Sekanina, "lower limits" were found in the range
1980), i.e. marginally above the value 0.05 to 0.3 with exceptional extreme
values 0.004 and 0.85.
 index as that can assume any value between
IV. Comet Bailey observations 0.35 and 0.55 (**)
IV. I Inr-situ dust analysis Extremely simple formulae were used to
relate the fluences to the size distri-
The "Vega" and "Giotto" in-situ detectors butions, to compute MG, and to compute
revealed O*(> m) distributions of the form the optical fluxes at Earth (see Crifo,
m"ol with ai * 0.8 - 1.0 over the mass 1987b). It is estimated that the computed
interval 1O"10 - 10"s gram (Mazets et al., optical fluxes are accurate to ± 50 * in
1986, Me Donnell et al., 1986 and 1987), absolute values, following neglect of the
corresponding to No values * 3.94 - 4.5, complex pattern of dust emission from the
confirming the results recalled in sec- nucleus revealed by the flyby cameras.
tion III. Between 10"5 and 10"2 gran,
however, the "Giotto" data reveal a It was assumed that, at each mass, the
softening of Ct(> m), az being there in dust was equally partitioned between dirty
the interval 0.33-0.59 (Me Donnell et al., (kv = 0.03) amorphous olivine and
1987). Also a difference of one order of amorphous carbon. The grain density p{m)
magnitude was found between the "Vega 2" was left as an unknown function to derive
and "Giotto" implied dust production from the fits, together with az and the
rates, in the mass interval 10~ 15 to 10"7 maximum mass m(A).
gran, raising the question of which one of
these results applies to average coma In Crifo (1987 b-c), the dust outflow
conditions. velocities were derived self-consistently
from a 79-fluid model taking into
IV.2 Giotto spacecraft deceleration account ^ (> m ) . The maximum mass
accessible in the model was 100 gram. The
The Doppler shift of the "Giotto" computed velocities were found in general
transmitter revealed the interception of a agreement with those of Gombosi (1986) who
total mass M° = 1.95 gram (Edenhofer et also has a broad size spectrum, but uses a
al., 1986), while scaling the detector small (0.3) dust-to-gas mass production
fluences to the spacecraft cross-section rate ratio. This agreement illustrates the
indicates a mass Mo = 0.235 gram only fact that the velocities are weakly
(Me Donnell et al., 1986). The "missing affected by dust loads concentrated in
mass" must be looked for in grains above large grains.
the detectors upper limit of 5.7
milligram. Evidence for the impact of a In this presentation we include recent
large (0.4 gram) grain is provided by the results obtained with an improved model
spacecraft destabilization just before using 87 fluids and giving therefore
closest approach (Griin et al., 1987). access to the maximum ejectable mass at
Assuming that the "soft" %,(> m) found .0.9 AU, i.e. » 30 kilogram.
above 10~s gram, holds to about 1 gram, Me
Donnell et al. (1986, 1987) were able to The optical computations were performed
account for the measured MD. It remained with extreme care, using as far as pos-
to investigate whether this unorthodox sible realistic complex indexes of
assumption was compatible with optical refraction and recomputing the resulting
data, in view of Banner (1984) grain temperatures (see Crifo, 1987 b-c).
considerations discussed in III. Mie scattering and absorption efficiencies
were computed using the new Complex
IV.3 Coma infrared emissions Angular Momentum method (Nussenzveig,
1983).
We have invested a large effort in ana-
lyzing the compatibility between remote In compiling experimental data, we
and in-situ observations of comet Halley interpolated between experimental points,
dust (Crifo, 1987 b-c, and this ignoring deliberately the experimenters'
presentation). We computed the infrared approximate "fits".
emissions from P/Hallley's coma using a
distribution f) (a) inspired by Me Donnell Our computations are strictly determi-
et al. (1986-1987) work, i.e. nistic, i.e. do not include adhoc scaling
factors. We require them to reproduce (1)
(l)below lO"5 gram it is either derived the shape of the continuum, particularly
from the Giotto fluences ("G" case) or in the "trough" between scattered light
from the "Vega 2" fluences ("V" case) or and thermal emission, and at long
from whichever of these fluences gives the wavelengths ; (2) the absolute value of
largest production rate at a given masp the continuum ; (3) the observed emission
("sup (G, V ) " case, or upper envelope). features in the so-called "silicate"
emission region.
(2) above 10"5 gram, in the "V" case is
the power law extrapolation of the Vega 2
data (i.e. <xz • 0.9), and in the "G" or ** We here indicate that the results
"sup (G, V)" cases it is a power law with presented in Crifo 1987c are computed with
02 = 0.35, value not given in the text of
that paper.

61
 IV.3.1 fits to emissions at vo > 1 AU best n(A) = 100 gram the lower value m(A)
= m(a»ax) = 2 gram. In this case r = 0.80.
We performed theoretical fits to data It is as well just possible to use the
acquired over the wavelength interval 1 to highest possible value m(A» B x), for which
65 nm, at r» = 1.28 AU before perihelion, r = 18.6 ! Until additional experimental
by Tokunaga et al. (1986), Campins et al. data provides new constraints, this must
(1986), Herter et al. (1986) and Glaccum be taken as the present range of
et al. (1986), and to data extending from uncertainty concerning r !
1.5 (Jin to 30 urn, al r,, - 1.15 AU post-
perihelion, taken from Gehrz et al. (7)Beyond 1 AU, the "s ilicate" emission
(1986), Green et al. (1986), and Knacke et features present in th e 10-20 kim region
al. (1986). are "small" or even ah sent, which makes
the fits relatively easy because a
Our conclusions were the following .' relatively large ratio of large to small
grains is allowed However, as
(l)Best fits are always obtained assuming^ demonstrated by our si ilar work on comet
(m) - c s l e = 0.3 g cm"3 (to ± 50 %) . In Kohoutek at small heli ocentric distances
particular, the "ESA WG" proposition of a (Crifo, 1987 c ) , di fficulties may be
decrease in density with increasing size expected when observati ons reveal "large"
is excluded. emission features. Th erefore we have
extended our earlier work to include
(2)The "Pure Giotto" ("G") distribution observations of comet Halley at smaller
cannot account for the observed emissions, heliocentric distances.
because it implies a ratio of large to
small grains such that no emission feature IV.3.2 Fits to emissions at r<> 0.9 AU
is visible.
Figure 3 shows spectra of comet Halley at
(3)A choice of "sup (G, V ) " distributions »• 0.9 AU from the Sun obtained pre-
provide equally good best fits. They perihelion by Tokunaga et al. (1986), and
differ by their combinations of (az , m(A)) post-perihelion by Hayward et al. (1987)
values, as indicated in Table I. We note and Hanner et al. (1987). In their
that a maximum value of az is found, publications, the authors show a continuum
implying a naxinum value for No (3.04). which is not a measurement result. Thus,
This conclusion is exactly opposite to the we have retained only their data points
one of Hanner (1984), illustrating the and interpolated linearly in-between. We
correctnes of our analysis made in section have indicated by a dotted line the
III, that her conclusions apply to <zi approximate expected shape of the
only. continuum in the "trough' region, based on
the Tokunaga data, in order to avoid
(4)Considering the ± 50 % uncertainty in misinterpretations.
the absolute values of our model fluxes,
the range of acceptable parameters On figure 4 A-B-C-D we reproduce the two
broadens considerably. In particular, the post perihelion experimental curves and a
"pure Vega" ("V") distribution becomes choice of model computations. Figures 4A
acceptable. This illustrates the poor and 4B show the predicted spectra obtained
capabilities of the optical sizing with the "V" distribution and with "sup
technique by itself, already discussed in (G, V ) " at az ~ 0.425, assuming various
Crifo (1987 c). values for m (A). The continuum fit looks
good, as far as one can judge considering
(5)We find that the MD requirement the small number of data points. But the
implies az = 0.425 ± 0.012. This value contrast of the computed "silicate"
lies in the middle of the interval 0.33- emission features looks weaker than in the
0.59 indicated by the Giotto data. Me data. Therefore, we show on figures 4C and
Donnell et al. (1987), from the same 4D the contribution to the computed fluxes
requirement, compute 02 - 0.50. This of the dirty olivine component of our
difference probably can be traced back to nodel. In other words, if we assumed that
our neglect of "momentum enhancement the dust was 100 X dirty amorphous
factors" in computing Ha . Momentarily, one olivine, the corresponding computed fluxes
can take the interval 0.5-0.412 as would be those of figure 4C and 4D,
bracketing the uncertainty range for az. multiplied by 2. This produces suitably
Figure 2 shows fits of preperihelion data contrasted features -but, now, the
with az = 0.425 and various m(A), from continuum below 8 un is not correctly
which everyone can form his own conviction reproduced. It has long since been shown
concerning the choice of the best fit (see e.g. Crifo, 1982) that only a mixture
value a(A) - 100 gran. of dielectric and absorbing grains can
lead to correct continuum fits. Replacing
half of the dielectric grains by absorbing
(6)The computed dust-to-gas mass loss ones, however, dins the emission features
rate ratio corresponding to this best fit significantly.
is r = 3.46. However, keeping the value 02
= 0.425 constant, the mentioned ± 50 %
uncertainty in absolute flux computations Since changes in the silicate/carbon ratio
makes it possible to use, instead of the have opposite effects on the fits to the

62
continuum and to the emission features, we ratios determined in any other comet. This
do not think that auch a mixture is not interpreted as an indication that
represents the real situation in comet comet Halley is atypical, but as an
Halley's coma. It should be understood indication that all previous
only as a computational necessity in the determinations have a common built-in
absence of an adequate formalism making it artefact. It can indeed be identified as
possible to compute the emissions from the artificial assumption that a size
real grains which, we believe, must all distribution based en a restricted set of
include both silicates and absorbers observations concerning only small and
(Crifo, 1987c). The fractional ion between intermediate mass grains holds as well for
silicate and carbon grains does not appear large and very large grains. Accordingly
physically plausible and is not well all estimates based on this assumption
supported by the in-aitu grain elemental should be considered as lower limits only.
composition data (Jessberger et al.,
1S86). It is reasonable to think that the
complex refractive index of inhonogeneous
aggregates mimics the absorbing signatures
of each of its components, i.e. resemble
that of silicates in the 10-20 nm region, Assumed Best fit
and that of carbonaceous matter elsewhere.
A two-component model approximates this »(A), r gram
situation but not perfectly. gram

For the same reason, no natter how good

our fits are, they should not be used to 0.35 3 1 .78 12
claim that precisely amorphous carbon
and/or dirty aaorphous olivine exist in 0.40 30 2 .84 3.8
Halley'a coma ! Any other absorber and/or
dielectric with rest-strahlen bands may 0.425 100 3 .46 2.2
provide eventually as convincing fits.
0.450 >{A..x) 7 .60 1.32
It nay be appropriate to make a final
remark. The contrast of the emission 0.50 NONE - 0.52
features fluctuates at a given ro (tiehrz
and Ney, 1986) and perhaps also their
shape (Hanner et al., 1987). Perfect
fitting of one given observation is Table 1
therefore meaningless. Contrast fluctua-
tions have been tentatively attributed to For each assumed value az , the requested
changes in the silicate/carbon content value of B ( A ) is indicated, and the
(Gehz and Ney, 1986). Me have indicated resulting dust-to-gas mass loss rate
above why we dont believe that the coma is ratio, r. The computed values of Me allow
a mixture of well contrasted dust grains. the final choice of as.
Instead, these fluctuations could be well
reproduced by minor fluctuation, in the
ratio of large to small grain coma
contents associated with the time REFERENCES
modulation of the emission. But since our
model is stationary it does not include
such effects. Campins, R. and 7 co-workers : 1986, ESA
SP-250 (*), Vol. 2, p. 121-124
Crifo, J.F. : 1982, in : Cometary
V. Conclusion Exploration, ed. by T. Gonbosi, CRIP,
Budapest, p. 167-176
Quantitative analysis of a large set of Crifo, J.F. : 1987a, Improved gaskinetic
optical observations of comet Halley treatment of cometary water sublimation
provides vigorous support to tue sug- and recondensation, with application to
gestion by Me Donnell et al. (1986, 1987) comet P/Balley, Astron. Astrophys. (in
that comet Bailey dust size distribution press)
flattens at masses above 10~5 gram and Crifo, J.F., 1987b, optical and
extends beyond the gram range. While the hydrodynamic implications of Comet Halley
small mass exponent ai is near 0.9, the dust size distribution, ESA SP-278 (**)
optimum value of the large mass exponent Crifo, J.F. : 1987c, to appear in :
O2 is near 0.425. With these values, the Proceedings of the International Symposium
fits to the comet emissions considered in on "Optical particle sizing : theory and
this work indicate that the dust-to-gaa practice", ed. by G. Grehan and G.
mass loss rate ratio in the comet is at Gouesbet, University of Rouen (France)
least 0.80 and at most 18.6, with a best Edenhofer, P. and 7 coworkers : 1986, ESA
estimate at 3.46. The upper limit is set SP-250 (*), Vol. 2, p. 215-218
by the optical data and by the Finson, M.L. and Probstein, R.F. : 1968,
hydrodynamics and the lower limit by the Ap. J. 154, 353-380
Giotto deceleration requirement. These Gehrz, R.D. and Ney, E.P. , 1986, ESA SP-
values are well outside the range of 250 (*), Vol. 2, p. 101-105

63
Glaccum, W., Moseley, S.H., Campins, H. FIGURF3
and Loewenstein, H.F. : 1986, ESA SP-250
(*), Vol. 2, p. 111-116 Please notice that the Figures are given
(iombosi, T.I. : 1986,ESA SP-250 (*), Vol. in the order 1, 3, 2, 4.
2, p. 167-172
Green, S.F., Me Donnell, J.A.M.,
Pankiewicz, G.S.A. and Zarnecki, J.C. :
1986, ESA SP-250 (•), Vol. 2, p. 81-86
Green, S.F., Me Donnell, J.A.M., Perry,
C.H., Nappo, S., Zarnecki, J.C. : 1987,
P/Halley dust coma : grains or rocks ? ESA
SP-278 (**)
Griin, E.N. Massonne, L. and Schwehm, G. :
1987, New properties of Cometary dust, ESA
SP-278 (**)
Hanner, M.S. : 1983, in : Cometary
Exploration, II, ed. by T.I. Gombosi,
CRIP, Budapest, p. 122
Hanner, M.S. : 1984, Adv. Space Res. 4, 9,
189-196
Hanner, M.S., Tokunaga, A.T.,
Golish, K.F., Griep, D.M. and Kaainski,
CD. : 1987, Infrared emission from
Halley's dust coma, Astron. Astrophys. (in
press) o oi ' ""b'.T
Hayward, T.L., Gehrz, H.D. and Grasdalen, ASSUMED GRAIN SPECIFIC MASS (g.cnfJ)
G.l. : 1987, Mature 326, p. 55-57 FIGURE 1 . Maximum mass of a spherical grain ejectable
Herter, T., Gull, G.E., Campins, : 1986, from P/Halley at 0.9 AU from Sun . M is the assumed
ESA SP-250 (*), Vol. 2, p. 117-120 nucleus mass , Q the water molecule loss rate, and R
Jessberger, E.K., Kissel, J., Fechtig, H. the distance from nucleus center of mass . For non-
and Krueger, F.R. : 1986, ESA SP-249, p. spherical grains , m(A ) can differ from the above
27-30 values by up to X8 or 2 8.
Knacke, R.F., Brooke, T.Y. and Joyce, R.R.
: 1986, Ap. *. 310, L 49-53
Me Donnell, J.A.M. and 7 coworkers 1986,
ESA SP-250 (*) Vol. 2, p. 25-40
Me Donnell, J.A.M. and 27 Co-authors :
1987, The dust distribution within the
inner coma of comet P/Halley 1982i :
encounter by Giotto's impact detectors.
Astron. Astrophys. (in press)
Mazets, E.P. and 14 To-workers : 1986, ESA
SP-250 (•), Vol. 2, p. 3-10
Newburn, H.L. and Spinrad, H. : 1985,
Astron. J. 90, 12, 2591-2608 c 10-16
Nussensveig, H.M. : 19£3, Recent deve-
lopments in high frequency scattering, in
: Proceedings of the Fifth Rochester
Conference on Coherence and Quantum Optics
Sekanina, Z. : 1980, in : solid particles
in the Solar System, ed. by I. Halliday
and E.A. Me Intosh, p. 237-250 x 10-17
Tokunaga, A.T., Golish, VI.F., Griep, D.M.,
Kaminski, C D . and Hanner, M.S. : 1986, 1. 2. 5. 10. 20.
WAVELENGTH ( Micron )
Astron. J. 92 (5), 1183-1185
FIGURE 3 . Observed emission from P/Halley at 0.9 At!
Whipple, F.l. : 1950, Ap. J., Ill, 3752
from Sun . The curves are linear interpolations bet-
ween the points of Tokunaga-et al.,1986 ( C ,preperi~
helion ),of Hanner et al.,1987 (B , post-perihelion )
(*) Proceedings of the XXth ESIAB and of Hayward et al,1987 (A , post-perihelion ),nor-
Symposium on the Exploration of Halley's malized to a field of view of 5 arc second.
Come.t, Heidelberg (D), October 27-31, 1986
(**) Proceedings of the International
Colloquium on the Similarity and diversity
of comets, Bruxelles, April 1987
 -16
10

-16
10

,-(6
10

-17
10

.-18
10

-19
10
1. 5. 10.
WAVELENGTH ( Micron )
FIGURE 2. Model fits to P/Halley emissions at 1.25 AU from Sun , Pre-Perihelion.Curve A is
the composite o£ experimental data ( see text ).Curves B are computed with r sup(G,V)' and
Q(.=0.425,and m(A) as indicated.

FIGURE 4 A FIGURE 4 B
-15 F -15

-16

-17 • _

-15

-16

-17
H>. 20. 30.
« A V ij • .- • .N G T H ( M i c r o n )
: fits to P/liai ley rHissions at 0.9 AU Post-Perihelion . Curves A and B are identical to
>, and curves C are model computations . Figures 4A and 4C_are computed with the 'Vr distri-
inci 4U with 'sup(G.V)' usingC<2=0.425 and m(A) = l,10,I0 ,10 and 10 gram. Figures 4C and AD
: mis-, Lon (Carbon + 'ilivine },Figures 4/4 and 4B the Olivine component only (50% of the mass).

65
 D I S C U S S I O N

H a j d u k : I agree e n t i r e l y that the d u s t / g a s Ri c k m a n : Some c o n s t r a i n t on the dust p r o d u c -

r a t i o , including c o n t r i b u t i o n of large par- 11on rate might come from the value of M/4M
t i c l e s , should be increased by about one order (the ratio of the n u c l e u s mass to fie total
of m a g n i t u d e , in comparison with the values mass loss per a p p a r i t i o n ) . Let us e s t i m a t e
currently ijuuted. H'I t ir, it p o s s i b l e to
\ ilues of 0.8 to 19 as the mass at M-lxlQ 1 4 kg and the yaseous mass
interpret M
t nucleus density of loss at 4'^ -1?x 10 i kg. 1 hen front your m i n i m u m
(J. i !j value nf M./M - 0 . 8 , one f i nds &t-U i. Ox 10 kg
C r if o \ uptiuji I i t .J require dust density and M/£Ma» 2ti'O. But from you m a x i m u m value
of 0.3 g/cnr* - 'iOS.. If the ratio M d / M is nf M^/M = 2 0 . the result is A M = D . 2 x 1 0 1 2 kg
l a r g e , then this will also be the n u c ? e u s
d e n s i t y . But J find impossible to d e t e r m i n e and M/flM «*24 .1 ven though M/&M i L- not a r e -
liable estimate of the r e m a i n i n g l i f e t i m e ,
M./M hr-'ter than within the limits 0.H to I think the latter value a p p e a r s u n c o m f o r t -
19. This u n c e r t a i n t y follows from the ignor- ably low. since orbital s t u d i e s indicate
ance of what is the maximum mass in the coma that the comet has already passed at least
(it is s o m e w h e r e between a few grams and a few many hundred r e v o l u t i o n s in its p r e s e n t
tens of ki 1 ograrns). Also we do not know for orbi t.
surr; what is the slope of the dust d i s t r i b u t - C r i f o : It would indeed be s u r p r i s i n g that
ion beyond a few g r a m s , b u t , as my Table I
i n d i c a t e s , this is a less severe source of M./M were precisely equal to the upper limit
u n c e r t a i n t y than the p r e v i o u s o n e . 2 0 : we know n o t h i n g about the dust s i z e
d i s t r i b u t i o n aboveasl g, a n d , as I m e n t i o n e d ,
the slope e x p o n e n t is at least expected to
increase above 1 kg due to size d i s p e r s i o n
e f f e c t s . On the other h a n d , it would also
be s u r p r i s i n g that M . / M were equal to O . B . ,
b e c a u s e this would imply that the dust d i s -
t r i b u t i o n has a sharp cutoff just p r e c i s e l y
at the m a x i m u m that G i o t t o could i n t e r c e p t !
 IMAGE PROCESSING OP V^GA-^V OBSERVATIONS
D. Mohlmann
Institut fur Kosmosforschung
DDR 1199 Berlin, Rudower Chaussee 5

Abstract. Methods of processing of VEGA-TV observations of the nucleus of P/

Halley and derived scientific results are summarized. The existence of lineamen-
tary surface structures ia interpreted as an indication for boundary zones bet-
ween km-sized blocks, building the cometary nucleus. The consequences for come-
tary origin are investigated.
1. Observations and interpretation ved from Sekanina and iarson (1986) by tra-
Two of the VEGA-2 close enteounter images of cing the foot-points of jets from observa-
P/Halley are most appropriated for studying tions, made in 1910, is given with Pig. 3,
properties of the cometary nucleus. The ima- where the "open window" indicates that re-
ges were taken 1.5 sec before and 98.7 sec gion of the nucleus, which has been seen
after closest encounter from distances of by the VEGA-spacecrafts during close en-
8.045 km and 11.060 km respectively. The counter.
angle spacecraft - nucleus- sun was for the- These linear structures are interpreted
se two images 28.4° and -23.0° respectively, as an indication for a block-atructure of
so the dayside of the cometary nucleus with cometary nuclei. The contact zones between
its great activity bacame visible (in con- these km-sized building blocks are the
trast to GIOTTO images). Consequently, the (brighter) zones of enhanced cometary acti-
nucleus is visible only through the scatte- vity, as it is inferred by the "active"
red light from the near-nucleus dust, which lineamentary zones.
is most intense above the "active" dayside.
Special image processing software has been
used indentify shape of and structures on
the cometary nucleus. The main steps of this 2. Origin cometary nuclei
processing have been described by Mohlmann The above described model of a cometary nu-
et al. (1986). They refer to image restau- cleus, made of relatively large km-sized
ration, noise-reduction, gradient- and blocks with contact zones between them,
Laplace filtering and overlay-techniques can be understood as an indication for a soft
with false-colour images. accretional growth of cometary nuclei from
The essential result can be in Pig. 1, these building blocks ("cometesimals"). It
giving a synthetic image of the nucleus and is especially the fact that these cometesi-
its direct surroundings. The outer white mals survived this growth by impacts and it
line indicates limb and terminator. Dark is the existence of the relatively thin im-
lines (which are brighter in reality) are pact-caused and impact-modified contact zo-
indications for lineamentary surface struc- nes, which indicates that these accretional
tures. Ehey are described directly with impacts were "soft". Consequently, the im-
Pig. 2, as they were derived from the above pact velocities should have been remarkably
mentioned two images. The comparison with small. A maximum value for this velocity
lineamentary structures, as they were deri- can be estimated by comparing the total
binding energy of a km-sized cometesimals
and its kinetic energy which is released by
the impact process.
The cohesive strength " T " of binding of
cometary matter has been shown to be the
order of T = I O 4 Pa (Wetherill and Re Velle,
1982). If the total binding energy E t = T.V
of a cometesimals of density g equals the
kinetic energy Ek = ^•l?l^ of the impact
with relative velocity v,the impacting co-
metesimal would be destroyed totally. Con-
sequently it follows for the real impact
velocity r-t
^>; < ( 2 Z /f)
(1)
With a density f = 0,2 g cm" 3 =2 • 10 2 kg/cm3
follows

< 10 m/sec. (2)

Pig. 2 Comparable lineamentary structures This is a remarkably low impact velocity.

on the "-1,5 sec. image" (above) and This value can be modified if it is assumed
the "+99 sec. image" (below) of that the kinetic energy can be transformed
VEGA 2 partially also into heat. But very proba-

67
bely this process is very ineffective. This Fig. 3 "'.Vorm-like " structures of :;ones of
should be due to the relatively low cohesive enhanced activity (from Sekanina
strength of cometary matter. and Larson, 1986) and related iden-
Difference velocities of the order of some tification of that part of these
meters per second (or less) are typical for structures, which was seen by
regions, for out in the Solar system, with ViiGA 2
distances exceeding 103 AU.

But there is the number density to small to The internal velocities in this cluster
have a sufficient number of collisions. can be estimated by
On the other side, this range of veloci-
ties should be typical for the growth-phase V
of planetesimals from first-generation pla- 4 (3)
netesimala, formed from an unstable thin ( /-= 6,674 • 1 0 - 1 V / k g s 2 , 2~Se t:>/^
preplanetary disk, as it ha3 been described
by Goldreich and Ward (1973). The contrac-
surface mass density of the disk,
-typical scale for instability).
«°
tion of these clusters of fragments depends The resulting conclusion is, that come-
on the rate at which gas drag damps, and on tary nuclei were formed in the outer plane-
their internal rotational and kinetic ener- tary system by the Goldreich-V/ard-meclianism
gies. for the formation of planetesimals. Comets
are the planetesimals of the outer planetary
system.

References
P. Goldreich, Astrophy. Journal, 183, Sekanina, Z. Astron. Journal.
W.R. Ward 1051-1061,1973 Larson, S.M. 462-482, 1986

D. Mohlmann in ESA-SP-250 11,330-340, Wetherill, G..V. in Comets (L.L. ..UI.I-

1986 ed.),
et al. and ESA-SP-250 111,313-315, Re V e l l e , D.O. p p . 2 9 7 - 3 ^ 2 , L h , : \ . ...f
1986 A r i z o n a P r e 3 3 , I'38?

68
 Pig. 1 Synthetic image of the nuoleua of P/
Halley, based on the "-1,5 aeo. image"
of VEGA 2

DISCUSSION

Napier: Safronov finds that the mutual impact Gru*n: Vou cannot .o much the simi
velocities in a dynamically relaxed system are larity of your liname ? ~tures with the
determined by the largest bodies present and results Sekanina got i_ ..lysis of the
are of the order of their surface escape velo- 1910 observations, because L .3se results were
cities. If there were 50 to 100 km comets obtained by assuming a fixed spin axis. But
around during the coagulation of Halley s comet Sekanina himself points out that recent
then the/vkm-sized bodies should have been observations indicate a much more complex
colliding at substantially more than <vlm/s. rotational state of the nucleus (Nature 325,
Conversely, impacts at less than lm/s imply p. 3 2 6 ) . Therefore, at least the combinations
that the majority of accreting bodies would of loci of sources which were observed at
be much less than a km in diameter. different times cannot be correct. The map
Md'hlmann; The internal relative velocity in a published by Sekanina (AJ 92, p. 462) must
cl' ter of the "first generation" planetes- be incorrect, because observations covered
imaiS can be estimated from the potential a time span of several months.
energy of this, cluster, leading to/y/j^2JK Mflhlmann: I agree with you, but I think that
(£=6.674 x 10 m /kg sec ,23^10 kg/m and Sekanina s rotation period (and the axis of
JfcPlO m - according to Goldreich and W a r d ) . rotation he used) were not too wrong.So, the
Equating this with the internal kinetic energy, topological character of his results should
this leads to the order of m a g n i t u d e ~ l m/s survive, when more precise values are used.
for the relative velocities. This value coin- Consequently, the detailed identification
cides indeed with the escape velocity from 1 km should not be correct, but similarities
to 10 km sized "building blocks". Greater shoi'ld remain. This has been assumed in
bodies probably did not exist in this cluster. comparing Sekanina s results with those of
VEGA-TV image processing.

69
 SPECTRAL OBSERVATIONS OP COT.tET HALLEY (1982 i) IK DUSHANBE
O.I.i.Mamadov
Institute of Astrophysics, Dushanbe, USSR

Numerous spectrograms of Halley's Comet have been taken by the author during
October 1985 - May 1986 with the Hissar astronomical observatory 70-cn reflecting
telescope AZT-8 and SR'-1 spectrograph giving a dispersion of 160 A/mm. A two cas-
cade image intensifier with fiber optics and Kodak 103 aG emulsion have been used.
On the baBis of four red and near I& spectra taken on 16 December 1985 with 5 to
40 min exposures a set of provisional identifications shown in the Table was given.
Key words:Comet Halley,- IR Spectra,- K_ molecule
We have taken Halley's spectra using the The author expresses his thanks to prof.
new spectrograph SPM-1 (flat replica, 600 O.V.Dobrovolsky for helpful discussions.
lines per mm, dispersion 160 A/mm) attached
to the telescope AZT-8(mirror diameter 70cm,
Cassegrain focus 13 m ) of the Hissar obser-
vat ory.
The spectrograph is equipped with a two \ obs. { Identification
cascade intensifier having fiber optics.
First spectra were taken during the 16-17 9007
October 1985 nidht, Preperihelion observa- 8982
tions were run till 16 December; that post- 62
perihelion from 19 April to 5 May 1986. The 28
observational nights total to 15, the number 14
of spectra received is about 50. The slit 8865
wir'thoWas 5", the spectral range was 6000- 37
9000 A and slighly broadened with growind 21
exposition. This region containing many pure 10
known bands such as the red system of CN, 8780
Phillips system of C 2 , emissions of H 2 0+, 56 C2(2-0)
NH, etc. is very interesting.
For express identification we have choosen
the spectra, taken on 16 December 1985 8679
totalling to 4 and having different exposure 17
times: 5, 10, 20 and 40 min. Registrogram 09
of the 10-min. exposure spectrum is shown 8595 CO(1,O)
on the Figure. This day the comet Bhowed a 87
strong continuum and many weak emissions. 70
In the registrogramme middle (at > 7619 A) 62
a strong telluric Ojabsorbtion bahd is seen. 40 N2(3,2)
Other indentification are: red CN system 22
bands (2-0, 3-1); Cj.Phillips system bands 04
(2-0, 1-0, and 2-1); Cj Swan system sequence 8491
(av= -2); bands of H , 0 + (0,5,0; 0,6,0; 80
0,7.0; 0,8,0); telluric 0z system (1,0; 0,0; 58
0,15 and water steam abeorltions at 7200 48
and 8300 A. A total of about 200 emission 41
peaks are identified on the 5-min and 10-min 33
exposure spectrograms (see table). Designa- 23
tions of CO emissions were given according 14
to Cosmovici et al. (1982). 05
Except the known substances we have identi- 8369
fied also Hi and 71* . These identifications 75 N.,(4,3)
were oerformed using the spectral tables by 62
Peerse and Gaydon;i949) (Russian issue). 55
Identification of N^is the first one made 46
on ground and confirmed (Tentatirely) in 23
ppace: Giotto registerred mass-spectrograph- 12
ically the proballe presence of N t , as was 8299
stated by Eberhardt et al (1986). 94
It should be mentioned that Danke et al 88
(1981) have found in an other comet a strohg 81 CO (6-1) A
red CN (1-0) emission ineted of the 0^(2-0) 75
feature missing on their spectrograms - 65
Some distortion of the field of wiev of our 60
image intensified is not excluded, but a 44
careful examination showed it to be small 35
and not to be leading to misidetification 27
of futures covcerned. 16
03 JN' (5,4)

71
 obs. iIdentification A obs» r Identification
8182 7273
68 63 CN (5-2)
26 33 CO ( 6 - 0 ) A
18 23 CO (6-0) A
09 18
01 00 H,
8086 CH.C3-T) 7182
69 CN(3-1) 60 CO (11-3) A
60 47
46 ffo(6,5).CW (3-1) 27
04 CN (4-1)
25 7093
84 CN (4-1), Cj(0-10)
19
05 73 H ^ (0,6,0)*
7997 64 H20+ (0,6,0)
82 53 H4O+(O,6;O)
72
66 44 HjO + (0,6,0)
48 HjO + (0,6,0)
38 35
30 12
14 HCN 6990 H^O* (0,6,0)
01 CN (2-0) 76 H 4 0 + (0,6,0)
7889 CO (5-0) A
70 CIT (2-0) 59 H0+(0,6,0)
57 CN (2-0)
42 35
35 CO (5-P: 4, CH (5-3) 24
29 12
09 6899
7787 83
76 74
68 64 OH
61 40 CO (10-2) A
46 20 CO (10-2) A
39 6794 N2(4,1)
28 78
19 56 HjO+(0,7,0)
06 43 CO (7-0) A
7694 23
70 09 0,7,0), CO (7-0) A
65 6692 (0,7,0)
52
33 72 H20+(0,7,0) ,
17 60
01 CO (7-1) A 56
50
7593 36
83 14 NHi(0,7,0)
56 C0(7-1) A , CN (6-3) 00 HiOf(0,7,0),
39
17 6592 H^Of(0,7,0)
05
7497 H^V fa,5,0) 52 HJLO"* (0,7,0), CO (9-1 )A
87 43 % ( 7 , 4 ) , H^O*(o,7,O)
63 H x 0 + (0,5,0) 10 H ^ (0,7,0), CO (9-1) A
50
42 6490
HjO+(0,5,0) 72
25 65 1^(8,5), CO (3-0) T
16
CO (3-0) T
05 H y (0,5,0) CO (3-0) T
7393
87 N2(5,3) 6394 Na(9,6), CO (11-2) A
80 5 /01/, CO (11-2) A
71 52
58 CO (9-2) A 42 NHx(0,8;0)
50 1^(0,5,0) 31 H 2 0 + (0,8;0), CN (5-1)
41
34 CO (9-2) A 22 Nj/io;?)
19 CO (9-2) A 14 CO (8-3) T
02
7295 6299 / 0 1 / , NH a (0,8,0), E
82 CN (5-2 86 NH z (0,8,0), Hx

72
 obs, r_ Identification oba. Identification
6265 6171
61 CO (8-0) A 64 H 2 0 + (0,8,0), H^
59 N, (11,8) 30 N 1^(0,9,0), C A ( 1 - 3 )
28 19
08 H t 0 + (0,8,0 N 1^(0,9,0), H^
6191 H,.O+(0,8,0 (0-2) 6099

3-0 2-0
0,7,0 0,6,0 0,5,0

6000 6500 7000 7500 8000 8500 9000

Registrograrome of Comet Halley spectrum taken on 16 December 1985

with 10 mim exposure. „

REFERENCES
Cosmovici, C,B.S Biermann, L; Arpigny G;
1982, Proc. of ESO Workshop The Need for
Coordinated Ground-based Observations of
Halley'a Comet (EdsiPiVeron et al.;
Paris - 1982).
Danks, A.C.; Dennefeld, M.j 1987, Astron.
J. 86, 314.
Eberhardt; Pis Krankowsky , D; Sohnlte, w;
et al: 1986, in 20th ESI AB Symposium on the
Exploration of Halley's comet. Heidelberg
Cermany - 1986.
Mamador, O.M.: 1986, Comet circ, No 362,
Kiev - 198b.
Pearse, R. and Gaydon, A.: The identi-
fication of molecular spectra, London - 1941.

73
 PRE- PERIHELION PHOTOMETRY OP GOIIBT HAIJ.RY At THE SKA1HATE" PLE30 OBSERVATORY

J.

Astronomical Institute of the Slurak Academy of Sciences,

Skalnate1 Pleso Observatory, 05960 Tatranska Lomnica, Czechoslovakia

A second part of the pre-perihelion photoelectric measurements of P/Halley obtained at the

Skalnate' Pleso Observatory is presented. Tha observations cover 9 nights from November 8, 1985
to January 5, 1986. A set of focal diaphragms of the following diameters was used: 29.53",
48.98", 81.08", 137.34" and 220.53". Results of this paper are magnitudes in focal diaphragms
in the filters Cont. 365.0 run, Cont. 484.5 nm, CO , C_, C and CN. Coma diameters, photometric
parameters and continuum colors are also determined.

1. Observational technique et al, 1987).

In accordance with the recommendation of the
The photoelectric observations were made with discipline specialist team for photometry and po-
a photoelectric photometer, installed in the Cas- lar ia« try net, the observations have been made at
segrain focus of the 600/7500 mm reflector at the the poor atmospheric conditions, too. This must be
Skalnate Pleao Observatory. An EMI 6256 B type taken into consideration in the interpretation of
electron multiplier was used as a radiation detec- the results.
tor. The optico-mechanical parts contains a eet of
focal diaphragms with the following diameters: 2. Comparison stars and extinction changes
29.53", 48.98", 81.08", 137.34" and 220.53". The
diaphragm diameters were measured with the Abbe Comparison stars have been chosen from the list
comparator. Five basic IHW filters and the CO one recommended by A'Hearn and Vanysek (1984). The
are installed in the optical part of the photome- magnitudes (listed in Table 1) according to the
ter. A detailed description of the photoelectric IHW list of Standard stars (Peierberg, 1985) have
photometer system is published elsewhere (Klocok only been used for processing the observations

Table 1
Magnitudes ot standard stars

HD Interval UC CH C
3
co+ BC C
2
used 365.0 387.1 406.0 426.0 484.5 514.0

186427 Whole 7.68 7.96 7.35 7.23 6.50 6.46

25680 NovS-18 7.27 7.47 6.99 6.86 6.15 6.09
2186B7 Dec22-Jan5 7.83 7.97 7.57 7.45 6.30 -
3379 Dec12-13 5.88 5.88 5.88 5.88 5.88 -
16906 Whole 4.71 4.68 4.67 4.66 4-65 4.66

For all the nights the extinction coefficients were determined as follows:

Table 2
Extinction coefficients

1985/86 Date k(Cont. 365.0) k(Cont. 484.5) k(CO + ) k(C 2 ) k(CN)

Nov 8/9 0.400
Nov 11/12 0.627 0.254 0.32^ 0.160 0.477 0.479
Nnv 16/17 0.782
Nov 17/18 1.287
Deo 12 0.714 0.696 0.670 0.870
Dec 13 0.206 0.295 0.750 0.396 0.470
Dec 22 0.080 0.947 0.200 0.333
Dec 30 0.316
Jan 5 0.804 0.398 0.625 0.573 0.652
mean of + 0.062
standard error
i 0,079 1 0.095 ± 0.025 i 0.091 + 0.113

The values of Table (2) show large night to metric nucleus in the direction of right ascen-
night changes of the extinction. Htese rapid vari- sion. It was supposed that the image of the comet
ations of atmospheric conditions excluded applying was approximately circular. The tail did not con-
the mean value of the coefficient. tribute to the brightness in the direction of
crosB-section. The diameter of the coma was meas-
3. Coma diameters ured with the aid of the diurnal motion, by stop-
ping the telescope drive. Each registration was
The diameter of the coma was measured by means repeated independently several times, in order to
of photoelectric cross-section through the photo- eliminate the effects of inaccurate setting on the

75
 surface Image of the ooma. The largest value of night.
the coma diameters was chosen for each individual
Table 3
Diameter of the ooma (sec of arc)
1985/86 Date Oont 365.0 Cont 484.5 C C CN
2 3

Nov 11/12 66 + 16 123 t 34 68 i 3 289 ± 124 190 + 89 215 i 49

Nov 15/16 - - - - 185 i 28 223 + 56
Nov 16/17 - - 75 i 22 - - 197 i 59
Nov 17/18 - 127 t 59 - - 197 i 50 328 + 116
Dec 3/4 - - - - - 295 ± 9
Dec 12 - 118 i 26 - - 274 2 35 419 t 2b
Dec 13 107 + 6 151 i 35 - 108 ± 10 237 i 32 611 ± 92
Dec 22 95 ± 27 137 i 31 - 44 i 12 164 i 30 613 ± 3b

4. Magnitude data in the Cont. 365.0 filter. The last column gives
the m' magnitudes
4.1. Continuum 365.0 nm
m* = m - 5 log A (1)
The observed quantities were reduced for the
differential extinction using the extinction coef- where & is the geocentric distance and m the
ficients derived. Table (4) gives the night aver- magnitude at the largest diapnragm.
age magnitudes obtained with different diaphragms

Talole 4
Continuum 365- 0

1 QOE; /HA Dot

Magnitudes at diaphragms (standard errors in parentheses)
i joy /ao imt.9 2 9 .53" 48 .98" 8"I.0Ei1* 137 •34" 220.53" m'

Nov 11/12 ' 12.66 (0.04) 12.10 (0.09) 11.33 (0. 01) 10.64 (0.02) 10.07 (0.06) 10.56
Nov 16/17 13-02 (0.05) 11.78 (0.02) 11.13 (0. 04) 10.44 (0.04) 9.76 (0.04) 10.54
Nov 17/18 13.50 (0.15) 12.37 (0.08) 11.38 (0. 10) 10.62 (0.04) 9.92 (0.03) 10.73
Dec 12 10.26 (0.08) 9.68 (0. 01) 9.16 (0.02) 8.72 (0.04) 9.2b
Dec 13 - 10.68 (0.04) 10.10 (0. 03) 9.58 (0.01) 9.25 (0.01) 9.74
Dec 22 11.12 (0.07) 10.47 (0.02) 9.92 (0. 04) 9-52 (0.01) 9.09 (0.01) 9-16
Jan 5 9.14 (0.06) - 7.98 (0. 02) - 7.38 (0.02) 6.90
4.2. Continuum 484.5 nm

The columns in the Table 5 have the same meaning as those of Table 4.

Table 5
fiO'l t i nuu.ro 464-5
I diupi^ rror a In p«j-ent-i.
.-53" .y i.Ofl" 137.34 ;•/-

No-. - . - . . ' -i <-'3) 1:1 ,I.U !'., . •••)>-) 10 . 14 ('* . : > • > ; .!;(> ( O . 02 ) 25 (u.o.t) •1 .St.
No- I '. / ; 0 . .72) : ; 4C fO .07) 10. .55 ( 0 . , O i ) y ,9u (0. 2, 44 ( 0 . 0 2 ) M •; ; 3

Pec I2 ('J. 105) f i • SO '. 0• O j ) b. 40 ( 0 . •03) 7 • J •- ( C• 01) Y. 52 ( 0 . v.. 1 ) e . O'b

ijoo 1 j - 9 -4fa • 0 .01) 8.65 J.01)
(•=<• a• 3!i ( 0 . 0 1 ) 7. 99 (•=0.0:) • 4b
'xic 22 - - B.• 35 ( 0 . ,02) 7 ,68 ( 0 . 0 1 ) 7. 57 (0.01 ) •/ .'04
iJtjc 30 b. 40 (0. 01) b . 0 4 ( 0 .03) 7.. b2 ( 0 . 0 1 ) 7 -2b ( 0 . 0 2 ) 7. 02 ( 0 . 0 1 ) 6 -76
Jan 5 6.<f6 ( 0 . 1 0 ) - 7.. 0 4 ( 0 . ,02) - b. 5b (O.O1 ) 0 .10

+
t Emission CO

T>J remove the •j.nderlying continuum we used the nathod of A'Hearn (19&4)- We a&xii<u:d tiiat the filters
for the continuum (3b5-O and 484.5) wore not contamined by any emission band3. Let the magnitude at the
emission bonds be represented by
" ''•el
(2)

where ,\ = 426.0 nm, A c 1 = 365.0 nm, X „ = 484-5 nm.

The average value of A for 6 solar analogs is A p 0 + = (0.16 + 0.03) mag.
Then we used X to determine the cometary magnituae m ^.(X ) which would have been observed in the
absence of any emission band:

(3)
•^-02 ^c1 ''>-c2 ^ d
The magnitude of the comet duo solely to the emission feature alone is then given by

76
 m ^ C i ) - - 2.5 log (4)
The CO magnitudes calculating according to the equation (4) are listed in Table 6.
Table 6
Emission CO

1965/86 Date Magnitudes at diaphragms (standard errors in parenthes 3es) n1'

29 .53 48.96" 81.08" 137 .34" 220 . 5 3 tl

Hov 11/12 12 .71 (0. 09) 11. B1 (0.02) 11. • 70 (0.01) 11. 69 (0.01) 12. 18
Dec 13 12.15 (0.01) 11. • 77 (0.03) 11. 35 (0.01) 11. 01 (0. 01) 11. 50
Jan 5 10 • 47 (0. 01) 10..32 (0.01) 9. 20 (0. 02) 8. 72
4.4. Emission C.,

I- = (0.24 t 0.02) mag.

2
The C 2 magnitudes calculating according to tie equation (4) are listed in Table 7.
Table 7
Emission C?
Magnitudes at diaphragms (standard errors in parentheses)
1985 Date 48.96" 61.08" 137 .34" 220 .53" in'
2J .53

Hov 11/12 11.30 ( 0 . 16) 10.2 2 (0.06) 9. 26 (0.02) 8 . 34 (0.01) 7.55 (0.01) 7.20
4.5. Emission C-
I c = (0.08 1 0.02) mag.
The C magnitudes calculating according to the equation (4) are listed in Table 8.
Sable 6
Emission C,

1965/86 Date Magnitudes at diaphragms (standard errors in parentheses)

29.53" 48.98" 81.08" 137.34" 220.53"
Nov 11/12 12, .11 (0 .09) 1 1 . 03 ( 0 . 01) 10.50 (0.02) 9.66 (0.01) 9.51 ( 0 . 01) 10.00
Dec 12 - 9. 31 ( 0 . 02) 8.66 (0.01) 8.06 (0.02) 7.60 (0. 01) 8.14
Dec 13 - 9. 72 («cQ .01) 9.14 (0.03) 8.57 (0.01) 8.18 (-=0 .01) 8.67
Dec 22 - - 8.85 (0.01) 8.49 (0.01) 8.32 ( - 0 .01) 8.39
Jan 5 9..77 ( 0 .04) - 7.91 (0.01) 7.80 ( - 0 .01) 7.32

c1.6. Emission CH

Ac(f = (0-50 i 0.02) mag.

The CN magnitudes calculating according to the equation (4) are listed in Table 9-
Table 9
Emission CN

1985/86 Date Magnitudes at diaphragms (standard errors in parentheses)

29.53" 48.96" 81.08" 137-34" 220.53"
Nov 11/12 11 . 1 0 (0.05) 10.20 ( 0 . 04) 9.32 (0.01) a. 40 ( 0 .01) 7.74 (-0..01) 8.23
Deo 12 _ 7.96 ( 0 . 03) 7.10 (0.01) 6.19 0.01) 5-43 (0.! 6.02
Dec 13 - 8.27 ( 0 . 02) 7-34 (0.02) 6.51 (0 .01) 5.79 (-0..01) 6.28
Dec 22 - - 6.68 (0.01) 6.24 ( 0 .01) 5.73 (-0.,01) 5.80
Jan 5 7.07 (-0.01) - 5.16 (0.01) 4.09 (0.01) 3.61
5. Changes of the brightness Table 10
The photometric parameters 11 and n , defined Photometric parameters
by the relation II (mag)
Region r (AU)
M m' - 2.5 n log r (5) Cont 365.0 5.0 + 0.6 7.84 ± 0.31 1.76-0.94
where r is the heliocentric distance and m' the Cont 484.5 5.0 + 0 . 4 6.68 + 0.16 1.81-0.94
magnitude reduced to unit geocentric distance (Sq. C0 + 5.1 i 1.7 9.40 ± 0.66 1.76-0.94
1) are listed in Table 10. Coefficient of correla- 3.8 + 0.7 7.55 i 0.23 1.76-0.94
tion between the quantities m' and log r is CH 3 6.5 ± 0.7 4.34 ± 0..24 I.76-O.94
0.95 - 0.98 .

77
 6. Continuum colors color.
(2) The behaviour of the coma diameters, during
The colors of the cometary material can be re- the period of observations, shows that with
presented as color excesses (A'Hearn, 1984): exception of Cff-coma, diameters of observed
comas did not depend on the heliocentr? • dis-
JS(U-B) -[m,,, (365.0) - ffio<>(484.5)] - tance.
(3) The photometric exponent only for Ctt-emission
- [ m o (365.0) - m o (484-5)] (6) shows that the increase of the brightness was
steeper than for continuums.
The solar color was taken to be the average color (4) During the whole observing period, practically
of the solar analogs whole observed brightness of "-he comet origi-
nated in CN-emission.
tov (5) Comparison of the measurements with different
focal diaphragms givi'S a higher conceu tratioj
Table 11 of the brightness C o.r.d C0 + comas to the
U-B color brightest point in the coma than in the C_
and Ci; Cumas.
1985/86 Date B(U-B) (6) In contrast to the J-H and Il-K colors (Toku-
naga et al, 1986) the U-B color varied con-
Kov 11/12 - 0.56 mag. siders. 1y during the interval of observations.
Dec 12 + 0.01
Dec 13 + 0.07 6. References
Dec 22 + 0.33
Jan 5 - 0.39 A'Hearn, M.P.: 1984, in Solar system photometry
handbook, ed. R.M. Genet (Willmann-Bell, Rich-
7. Conclusions mond).
A'Hearn, M.F., Vanysek, V.: 1984, The letter of
(1) A progressive Increase of the brightness Photometry and polarimetry net dated 30 Novem-
caused by approaching of Comet Halley towards ber 19B4, 3-
the Earth and the Sun is overlapped by sudden Peierberg, M.A.: 1985, The letter of Photometry
outbursts. For example, there was an outburst and polarimetry net dated 8 November 1985, 1.
before December 13> 1965. ffhis outburst was Xlocok', I., Zverico, J., Ziznovslty, J.: 1987, Contr.
detected as a local maximum of the brightness Astron. Obs. S^alnate Pleso 16, 43.
on the both emissions C,, CH and continuum* Tokunaga, A.T., Qolisch, W.P., Griep, D.H., Kamin-
on December 12. The out Cure t was confinwd «lci, C., Hanner, J4.S. 1 1986, Astron. J. .22,
independently by Watanabe et al (1986) in (;„- 1183.
emission. Toicunaga et al (1986) also pointea Watanabe, J., Kawakami, H., Tomita, K., Kinoshita,
out that on 12 December the comet was brighter H., Nakamura.T., Kozai, f.: 1986, in ESA SP-
at all wavelengths compared to 13 December. 250, Vol. III., eds. B. Battrick, E.J. Rolfe
On 12 December the comet had the bluest <I-H and R. Reinhard (ESTBC, Noordwijk), 267-

78
 SPATIAL DISTRIBUTION OF NEUTRAL AND IONIZED GAS IN THE HALLEY COMET COMA AFTER
THE PERIHELION*

R. Falciani 0 ) , MFestou <2), L.A. Smaldone (3), and G.P.Tozzi (1.4)

(1) Osservatorio Astrofisico di Arcetri - Largo E. Fermi 5 - 1-50125 Firenze - Italy

(2) Observatoire de Besancon - 41b Av. de l'Observatoire - F-25044 Besan9on - France
(3) Dip. di Fisica dell'Universita' - Pad. 19/20 - Mostra d'Oltremare -1-80125 Napoli - Italy
(4) Guest Astronomer at ESO, La SUla, Chile
* Based on Observations collected at the European Southern Observatory, La Silla, Chile

Long slit Halley comet spectra taken at ESO Observatory after the perihelion have been analyzed. Relative intensity
radial profiles along and perpendicular to the sun direction have been obtained for CN (Av=0), Cj (Av=0) and Cj
(4050 A) bands. Interpretation of these profiles with the vectorial model allowed us to trace the variability of the
gas production rate vs. time before the observations. It has been shown that the comet increased its gas production
rate of a factor 3 on 22.9 March 1986, then it decreased to half the 23.1 March 1986.

OBSERVATIONS. spectral trend is obtained by convolving the solar flux

spectrum (A'Hearn et al. 1983) with our measured
As part of a coordinate project of multiwaveiength instrumental profile. The spatial profile of the dust
observations of Halley comet, long slit visible emission was measured, along the slit direction, in some
spectroscopic observations have been made, during the spectral regions with no detectable gas emission. By
post-perihelion, at the European Southern Observatory multiplying the spatial and spectral distributions a matrix
(Chile) from March, 19 to March 23, 1986 when the comet with the 2-D spectrum of the dust was determined. The 2-D
was about 1 and 0.80 A.U. respectively from the sun and spectrum of the gas component has been finally obtained
from the earth. We used the 1.52 m telescope, equipped by subtracting the dust matrix from the total emission
with a Boiler & Chivens spectrograph and a 3 Stage EMI matrix. Since the dust contribution was hifh expedaJly in
tube + photographic plates as detector. The image scale the inner coma region, the gas emission for species wilh
was 19.4 arcsec/mm on the slit plane, corresponding to 87 small scalelength (as e.g. C3) was obtained with a relatively
arcsec/mm on the photographic plate. The entrance slit large error.
height was 8.09 arcmin on the sky and gave a comet Wavelength integrations over the considered spectral
spatial coverage of about 2.8 10^ km. With a grating of bands give the spatial distribution of the relative emission
1200 I/mm (reciprocal dispersion equal to 59 A/mm) the of the selected species.
whole optical range was covered with two exposures
(3650-5350 and 5000-6700 A). With a slit width of 150
micron the FWHM of the instrumental profile was about CN
3,5
4 A, in the whole spectral range. The exposure time ranged 1 1 ! 1 ~1
from 1 min to a maximun of 60 min in order to correctly
expose both weak outer coma and intense inner coma
features. The slit orientation was either parallel and xe - -
perpendicular to the sun direction. As suggested by the
International Halley Watch, also spectra of solar analog
stars (Landolt #102-1081 and #106-1146), and flux •
as -
standard star (HD 117880) where obtained during each -
observational run.

2.8 •
SPECTRA REDUCTION.

All the spectra have been digitized with a PDS

microphotometer using a scanning aperture of 100*25 urn2- I.S
corresponding to 8.7 arcsec along the slit direction (and
equivalent to roughly 5000 km on the comet) and to 1.5 A
in the spectral domain. The spectra have been I.B 1 1 1 1 1
photometrically calibrated (d => I), corrected for the 'S'
distortion (due to the intensifier tube), wavelength
Nucl.Dist. 10E3 km
calibrated and corrected for the atmospheric extinction.
Finally, the spectra have been converted in relative
intensity units by using the instrumental spectral response, Fig. 1 - Spatial distribution of relative band emission of CN
determined with the spectra of the solar analog stars. (Av = 0) on 23.3 March, 1986 along the sun direction. Sun
To obtain the gas emission the contribution of the dust is on the right.
emission had to be subtracted. Since the dust spectral
emission is due to the scattering of the solar radiation, its

79
 C3 The data analisys is under completion and the next step wii!
—r_ be the determination of the temporal (and, possibly the
"T •
spatial) absolute Q(t) values for the various considered
species in order determine the variability of the Halley
comet during the considered period.

CN (Dv=0)

I 1

Nucl.Dist.. 10E3 km

Fig. 2 - Spatial distribution of relative band emission of C?

(4050 A) on 23.3 March, 1986 along the sun direction. Sun
is on the right.
Nucl.Disi. 10E3 km
INTERPRETATION OF THE RESULTS.
Fig. 3 - Spatial distribution of relative band emission of CN
Profiles of the relative emissions as a function of the (Av = 0) corrected for the effect of solar radiation Dressuie
distance from the nucleus for CN (Av=0), C2 (Av=0) and (crosses) and vectorial model calculation (full lint,.
O) (4(150 A) are obtained using spectra wilh different
rxpnsurt: time. I-igg. 1 and 2 represent typical profiles of a
long lifetime (CN) and short lifetime (C^) elements along
the solar direction. In the CN profile is dearly visible the C2
jsymmetry due to the effect 0! the solar radiation pressure.
As for the pre-perihelitim data (Falciani et al..1986,1987),
the einksioii p'ofile:; akirit' the sflor direction have oeen

•'iva! m'.iiji-l
;<:cl profii:-.-. r-:;u :.ti)l ;• r-i-iJ';
Miiiii .sea!-.- i>:,i,:l-, dur. , , -ii .r.ii-
tlit: i\'.r.f •..::',-•!'. i>.- .':>.', i u >,1i:-..-'c'-, IS,,, :•'•. U' '
i i b s c r v e i : ji'ieil'inH app<irii: 0
<:i:ri'.;£> rhi.-". H . ' l i e y <.-'.>:!ici I
; t:
i"i 'jlma;i c\ a!., l
1 lit: need 10 take miii acecuini of a iime dependeni pa.s
pr<Kluct)o:) rah". (Q) introduces a too large amount of
indipendem pari'meters. We thus decided 10 use the
published values for the lifetimes and velocities lor both
the parent and daughter elements (A'Hearn, 1982 . Cochran,
1985;. The model free parameter becomes the time
dependent gas production rates.
Figti 3, 4, 5 snow •>. comparison between the observed data
on March 23.30, 1986 (crosses) and the vectorial modei Nucl.Dist. li3E3 km
calculation (full line), for the ^antisolar profiles of CN
(Av=0), Co (Av=0) and C3(4O5O A). The best fit parameters
Fig. 4 - Spatial distribution of relative band emission of Co
are quoled in Tab I. it can be seen that the agreement
between the mesured data and model calculations is fairly (Av = 0) corrected for the e.ffect of solar radial.on pressure
good. For all the three species the gas production rate (crosses) and vecional model calculation (full line).
increases of a factor 3 around 0.4 days before the
observations, and then it decreases of a factor 2 0.2 days
later.

SO
 Tab.]

CN (Av=O) C2(Av=0) C3(4050 A)

3
tp (1AU) 20*10 s 28*10 3 s 3*10 3 s
V
P 1.0 km/s 1.0 km/s 1.0 km/s
CD 30*10 4 s I2*10 4 s 6*10 4 s
0
l\ v
d
Q (At>0.4 days)
1.0 km/s
0.6
1.0 km/s
0.7
1.0 km/s
0.7
I Q (At=0.4 days) 1.8 2.0 2.3
0 (At=0.2 days) 1. 1. 1.

Where: tp.td are the adotted lifetimes for parent and daughter
vp.vd " " velocities " "
Q is the molecule production rate normalized to 1 for
Nuci.Dist. 10t3 km the time of observations.

Fig. 5 - Spatial distribution of relative band emission of C 3

(4050 A) (crosses) and vectorial model calculation 'full
line).

REFERENCES.

A'Hearn, M.F.: 1982, in Comets, L.L. Wilkening Ed., The Falciani, R., Festou, M.C., Smaldone, L.S. and Tozzi,
University of Arizona press, Tucson. AZ, 433. G.P.:1987, to be submitted to Asiron. Astrophys.

A'Hearn, M.F., Olhmacher, J.T. and Schleicher, D.G.: 1983, Feldman, P.D., Festou, M.C., A'Hearn, M.F., Arpigny, C ,
Thee. Rep. AP 83-044, liniversily of Maryland, Dep. of Butterworth, P.S., Cosmovici, C.B., Danks, A.C., Gilmozzi,
Astron. and Astrophys., Cu'lege Park, MD. R., Jackson, W.M. McFadden, L.A., Patriarchi, P.,
Schleicher, D.G., Tozzi, G.P., Wallis. M.K., Weaver, H.A.
Beard, D.B., Whelan, T A. and Gas!, M.A.: 1985, Astrophys. and Woods. T.N.: 1987 Asiron. Astrophys. , in press
J., 295, 668. (Halley's comet issue).

Cochran, A.L.: !98S, •'. >.f;,•,•;../.. <Xi, .:<>!)9. f-cstou. M.C.: 1981 Asiron. Astrophys. ,95,69.

Falciani, R., I-cstou. M ('.. S:nu]Ao:v. I..S. and Tozzi,

G.P.:i986. in 2'Uh !•'.'.' '..' ",.T.'- •.•.•;<;; proceedings on the
exploration o f l u i l L / - • ; '• ••'• '-•" 250 H i . 7?..

81
 THE TAIL LENGTH OF COMET HALLE* PROM HISTORICAL DATA

F.Esin-Yilmaz 1 '
F.Limboz^
and G.A.Tammann 2 '

1) University Observatory, Istanbul

2) Astronomisches Institut der Universitat Basel
European Southern Observatory, Garching.

&telX3££: About 200 observations from AD66 to 1910 of the tail length of Comet Halley have
been used to derive the mean tail length of the comet as visible to the naked eye under
very good observing conditions. The curve, covering an interval of - 4 5 ^ (t-T)4. 80 days is
skewed and peaks at ~55 million km for (t-T) = 1 8 + 8 days. There is no indication f o r a
secular decrease of the tail length.

I. Introduction Hughes, 1985) detectable secular changes

Much discussion has gone into the are indeed not to be expected.
question whether Comet Halley has betrayed An additional test is here presented
any secular decay during its recorded for possible secular changes of Comet
history. Contrary to previous claims no Halley; it is based on historical data on
such decay is revealed by reports on its the observed tail length.
brightness; unexpected reports on
brightness are rather explained by the II. The Data
comet's irregular activity (and perhaps About 200 visual naked-eye estimates
outbursts as in 1066) as well as by of the tail length of Comet Halley have
inaccuracies of the chroniclers, than by a been collected from various sources for the
systematic trend (Broughton, 1979; Tammann apparitions of AD66 to 1910. The Chinese
and Ve'ron, 1985). Also the great success of observations of the tail length were taken
the orbit reconstruction (Yeomans and from Ho (1962). The relevant observations
Kiang, 1981), which is based on Marsden's for Europe were drawn from Pingre (1783,
et al. (1973) model of nongravitational 1784), Holetschek (1896), Vsekhsviatsky
forces, implies a secularly constant (1958), and in a few cases from
outgassing rate (Yeomans, 1985). In view of contemporary sources. For the apparition of
the dynamical age of the comet of much more 1910 the visual tail observations are
than 16000 years (Yeomans, 1985; cf. also compiled in the Memoirs of the British

1 1 1 1 1 1 1 I 1 1 1

.6 - -
o AD 66-989
\
* 1066-1531 •v
/ \
~ .5 - - 1607 / \ X

+ 1682 / \

\
x 1759 \
/
o * 1835 \
\
I .3 • 1910 t- ^^"^ * / \
\
\
o
\
.2 - \
en
c + • «^ . ** • •

01 + * ° ^ ^ * « *•• \
* » *. - - / ' * ' ' v .• x •
xx ^\> "
V x o •%
'— —
* *w t - v
' 1
Xw
X n ^^ %X X

1 1 1 1 1 1 1 1 1 1 1 1 1 1

-40 -20 0 20 40 80
Days from perihelion
Fig.l. The linear tail lengths in astronomical units of Comet Halley from historical
records from AD66 to 1910. The abscissa gives lays before and after perihelion. The full
drawn line is an upper envelope; it is assumed to reflect the mean tail length to the naked
eye under very good observing conditions. The closed triangles (*) are the photographic
1910 observations by Curtis (1910). The dashed line is adapted from Yeomans (1981).

83
 Astronomical Association, volume 19 (1914); other observers, his estimates for May 26
they are augmented by the data of Barnard to June 6 surpass all other simultaneous
(1914) and Curtis (1914). The latter observations by an average factor of 2.7.
observations, but one, were made His maximum tail length of 0.72 a.u. on
photographically; they fit very well into June 6 (t-T = 47 days), for which date the
the visual observations of 1910 and are upper envelope predicts only 0.25 a.u., is
retained. unparallei led. The only explanation we can
The Chinese observations of the offer for this curious situation is that
angular tail length are given in "chi" or Barnard had very exceptional observing
"zhang" units; it was assumed that 1 zhang conditions at Yerkes Observatory around
= 10 chi = 15° (Kians, 1972). This June 1. Because the upper envelope in Fig.l
conversion agrees somewhat better with is supposed to reflect very good, but not
European observations than Clark and exceptional observing conditions Barnard's
Stephenson's (1977) relation 1 chi = 1°. In estimates are not plotted.
the latter case there would be a hint that The upper envelope in Fig.l is clearly
Comet Halley's tail has secularly increased skeued. While the visual tail observations
in length which we take as improbable. Some begin at (t-T) = -46 days (in 1378 from Far
European estimates of the tail use German Eastern sources) they extend to (t-T) - 76
miles. Here it is to be remembered that days in 1759 and to even 77 days in 1910.
this unit was originally defined as the arc The maximum tail length of ~0.35 a.u. is
of 1/15 degree at the surface of the Earth. reached at (t-T) - 1 8 + 8 days.
It became hence customary to express angles A naked-eye tail length function has
in units of miles, where 15 miles = 1° been given previously (Yeomans, 1981). It
(Ve'ron, 1985). is also shown in Fig.l. There is no
Using the osculating orbital elements agreement between this curve and the
of Comet Halley by Yeonsans and Kiang (1981) presently adopted curve. There are a number
we have calculated the linear tail lengths of reasons for this disagreement. The line
from every visual estimate. The unrealistic by Yeomans is defined as the mean curve
assumption of straight tails has little through the observations; it thus
effect on the result except in special corresponds to "average" observing
situations. The tail curvature becomes conditions, whereas our upper envelope
important only when the Earth is near to supposedly reflects very good conditions.
the ascending or descending node of the Yeomans' curve considers only the
comet at the time of observation. This apparitions of 1759, 1835, and 1910, and
situation arose during the observations of for the latter apparition high weight has
April 9-14, 837, and May 1-5, 1759; they been given to the observations by Barnard,
are hence omitted in the following which we believe to be incomparable for the
discussion. time after May 25, 1910, for the reasons
stated above. We have instead used here an
III. E<?suit? extensive body of observations for 1910.
The linear tail lengths are plotted in Finally Yeomans has used the long tail
Fig.l. For a given time (t-T), where T is observed by de la Nux on May 1, 1759 (t-T »
the time of perihelion, the data scatter 49 days), when the Earth was near the
widely. The reason is obvious: the visible comet's descending node; as discussed in
tail length depends sensitively on the Section II this observation is excluded
observing conditions. The comet's angle here.
from the Sun, moon light, clouds and haze,
zodiacal light and atmospheric extinction IV. Conclusions
may reduce arbitrarily the apparent size of From angular tail length estimates of
the tail. Recorded tail lengths are hence Comet Halley, spanning almost 2000 years,
always miriinium values. In addition, night- linear tail lengths were derived. A plot of
to-night variatic is of the comet's a.ctivity the linear lengths against time before and
and of the magnetic polarity of the Solar after perihelion define reasonably well an
wind may cause strong fluctuations of the upper envelope (Fig.l). This curve is
intrinsic length of the tail. interpreted to give the average tail length
For these reasons a mean line through as visible to the unaided eye under very
the observed points is difficult to good observing conditions.
justify. Instead, we have drawn a smooth There is no indication at constant
upper envelope encompassing about 90% of heliocentric distance that Halley's tail
the observations. The significance of this has faded during the last two millennia.
envelope is that it should reflect the me<in The upper envelope curve is skewed
linear tail length under very good with respect to the perihelion date. The
observing conditions. tail length peaks about 18 days after
The data in Fig.l agree reasonably perihelion when the tail measures -55
well for different apparitions over the million km. During first sightings about 45
intervals of observations. Some points lie days before perihelion the tail measured
above the envelope; they are assumed to be typically 11 million km, while the
observed under exceptionally favorable historical records end near 80 days after
conditions. Messier's observation of April perihelion, when the tail has shrunk to
1, 1759, (at t-T - 19 days) may be off by a about the same value. - Visual observations
factor of 10 (295 instead of the recorded of ihe apparition of 1985/86 have not been
25°). The very long tail (19° corresponding used here; they will provide an independent
to 0.49 a.u.) reported by de la Nux for May check of the present results.
14, 1759 (t-T - 62 days), remains A more detailed analysis of the
unexplained. historical data on Comet Halley's tail does
A particular problem is posed by the not seem io be Justified. Even if the
1910-observations by E.E.Barnard (1914). observing conditions concerning the
While his observations from Nay 3-24 agree positions of the Sun and the Moon and the
on average very well with the estimates of altitude of the coaet were individually
reconstructed, factors like tail curvature, Hughes, D.W. 1985, Mon.Not.R.Astr.Soc.213,
sir transparency, haze, and cloud coverage 103.
would remain unaccountable. Kiang, T. 1972, Mem.R.Astr.Soc.76, 27.
Acknowledgement: Financial support of Marsden, B.G., Sekanina, Z., and Yeomans,
the Swiss National Science Foundation is D.K. 1973, Astron.J.XS, 211.
gratefully acknowledged. Tamir.ann. G . A . ,a n d Veron, P. 1385, Baileys
Komet. Basel: Birkhauser.
References Ve'ron, P. J985, private communication.
Barnard, E.E. 1914, Astrophys.J.12, 373. Pingre, A.G. 1783, 1784, Cometographie ou
Broughton, R.P. 1979, J.B.Astron.Soc.Canada Traite historique et the'oretique des
72, 24. cometes. Paris, 2 volumes.
Clark, D.H., and Stephenson, F.R. 1977, The Vsekhsvyatskij, S.K. 1958, Fizicheskie
Historical Supernovae. Oxford: Pergainon Kharakteristiki Komet. Moscow.
Press, p.149. Yeomans, D.K. 1981, Xhe_-.Cp_mei Hal ley
Curtis, H.D. 1910, Publ,Astr.Soc.Pacific Handbook. Pasadena, Jet Propulsion
11, 117. Laboratory, p.7.
Ho Peng Yoke. 1962, Vistas in Astronomy J>, Yeomans, D.K. 1985, in: Dynamics of Comets:
127. Their Origin and Bvolution, eds. A.Carusi
Holetschek, J. 1896, and G.B.Valsecchi. Dordrecht: D.ReiSel,
Denkschr.Kais.Akad.d.Wiss. Wien, math.- p.389.
naturviss.Cl.63. Yeomans, D.K., and Kiang, T. 1931,
Mon.Not.R.Astr.Soc .I_97, 633.

85
 THE PLASMA TAIL OF COMET BEMNETT 1970 II
J. Zvolankov^, D. Kubacek, and E. M. Pittich
A..tronoir:i cal In:-,titute, Slovak Academy of Sciences, 842 28 Bratislava, Czechoslovakia

A r.et of fourteen large-scale exposures or comet Bennett 1970 II between 1970

Apt i l 27 one] 30 is evaluated. The solar wind velocity is determined 'or *.hif. j-.eri-
o I f rcr. thr- aberration angle of the plasn>a tail. Its radial component ha^ a aini-
n:,i::: val u • of 70-100 km/s in the comet's environment: 50° off the ecliptic at a
! i . • t3P.ee '-f 1 AU from the Sun. This value is 3-4 times less than the satellite da-
t a rccor•ried at the Earth's orbit. The two plasma kinks, visible on 1970 April 30 in
the n orne t tail, moved from the nucleus at a mear radial velocity of 81 a".d 76 km/s,
r.-r, p . - c t i vfcl.y. No disconnection event appeared in the plasma tail.
Keyword-: Comet Bennett 1970 II, Disconnection event, Plasma tail, SoLar wind.

1. INTRODUCTION
Cornet Bt-nnett 1970 II counts among a few BENNETT
comotr. from the last decades, at which a
Ion,; plasma tail was observed. This period
in ('hor-ae'terized by intense space explora-
tion, and sometimes called the satellite
era. Hence, pecularities and motions of dif-
ferent phenomena in the comet's plasma tail
can be studied in conjunction with the in-
terplanetary magnetic field and solar wind
flow data obtained by the satellites.
Plasma tails of comets have been studied
for many years. In spite of the available
satellite data on the solar wind and inter-
planetary magnetic field, an adequate theory
of th" formation and motion of the kinks and
rays does not yet exist. Unfortunately, the
cowptn usually move far from the Earth's or-
bit, where the space probes for measuring
the interplanetary magnetic field and solar
wind flow mostly operate.
We have used a set of fourteen large-
scale exposures of comet Bennett 1970 II
(Table 1) for the study of the solar wind at
a hitjh ecliptical latitude, and for the de-
termination if the motion of plasma kinks in
tho tail relative to the nucleus. Short time
intervals between the exposures — from 11 to
ft
0 rr.inutf'S in one night, have enaole us to
aer.cribe their kinematic behaviour and in-
teraction with the interplanetary magnetic
field and nolar wind flow.
The plates were exposed between 1970 A-
pr-il 27 and 50 with the 30/150 cm astrograph
•if the Skalnate Pleso Observatory of the As-
trono.'i.i 'al Institute of the Slovak Academy
of Sci'-iver. Their exposure time varied from Figure 1. Relative position of comet Bennett
three to ten minutes. the Sun, and the Earth on 1970 April 28/29
2. COMET ORBIT GEOMETRY in Figure 1. The comet was 49.86°above the
ecliptic at nearly the same heliocentri r.
Cjii.'t Bennett moves in a nearly parabolic distance as the Earth: 1.00 AU and 1.01 AU,
orbit, in a plane almost exactly perpendicu- respectively. The distance between the comet
lar to the ecliptic. The inclination of its and the Earth was 1.il AU. The phase angle
orbit i:-, 90.04°. The comet crossed the e- Sun-comet-Earth was 4S°, and the Earth pre-
• •liptie plane at 223.96° of ecliptical lon- ceded the comet by 7° to 4° of ecliptical
gitude. During the investigated time inter- longitude. Therefore, the viewing direction
val the "omet had, therefore, an almost con- from the Earth was almost perpendicular to
stant eoliptical longitude, anproximatel.y e- the comet's orbital plane. The plasma tail
qufU to that of its ascending node. The per- on tie plates is narrow, with rays asymmet-
ihelion of the orbit is 5.85° below the e- rically distributed with respect to the Sun-
eliptic, 0.54 AU from the Sun. The comet -comet direction.
p:a:;sed it on 1970 March 20.05.
The relative positions of the comet, the 3. METHOD 0 .'-/VLYSIS
Gun, ar,.i the Earth on 1970 April 28/29, i.
e. within the investigated period, are shown. For the study of plt»_...c. tail phenomena it

87
is necessary to determine their cometocen- cates that there were no changes of the po-
tric coordinates. For this purpose, the eo- larj ty.
ordinati fra.'n" of the exposures was provided
by 45 refervr:-e stars from the Smithsonian 5. PLASMA TAIL
A:-troph.ysiciL Observatory Star Catalog, with
j corr ction for their pp
proper motions. On the seven exposures between 1970 April
lunriti lie. i
the determination f the
of 27 and 28 (Table 1), i. e. on the night of
ind velocity and plasma kink motions April 27/28, the plasma tail was apparently
— .•r.iatoriul --oordinatt-r, of the Sun and the separated into two parts occupying opposite
••"•,:i,n, '•••ciiptieal lon.iitudi" and cometocen- sides of the tail axis. The length of the
ti'i: joordiritT.e - of the Eorth, the coiet 's tail on these plates is 1.74°-2.69°. The
orbitnl v.-'lo'.-it.y component? and equatorial differences are due to the exposure time,
spherical coordinates, and the tabulated which varied from three to ten minutes. The
valuer, - .vere calculated by means of our own plasma tail on the exposures of April
•o:::puti-r programs on Hewlett-Packard 9830. 27.983, 27.9y2 and 28.000 extends out of the
I'he •.•oordinatos of the conet were calcu- field of the plates. Therefore, the tail
lated u::.insT the orbital elements as deter- must have been longer than 2.7°. On the pic-
mined by Marsden (1986). The radial direc- tures it is possible to see the formation of
tion f:'o::i the Sun to the comet nucleus was plasma rays asymmetric to the tail axis.
fixed by the /"reat circle crossing the Sun They are clearly visible on the side of the
•jnd the cose t' nucleus (Dobrovoi'ski j , 1966). tail preceding the apparent motion of the
comet. There are moderate but bright kinks
4. SATELLITE DATA and disturbances.
On the three exposures of April 29 (Ta-
T,»).> satellite data on the solar wind ve- ble 1) the composite structure of the plasma
locity and on the interplanetary magnetic tail is not so clear as on the preceding
field between 1970 April 24 and May 4 are night. The asymmetric formation of the plas-
plotted on Figure 2. The data on the solar ma rays is less expressive, too. A weak
wind velocity are from the VELA 2-6 and plasma cloud is visible in the tail on all
OGO y satellites (King, 1977). The former of these plates. The length of the plasma
operatic! at the distance of 16 Earth radii tail is about 1.90° and the tail is rather
from the Earth's surface, and latter at wide. On the plate of April 29.890 the end
0.04-23 radii, respectively. Between 1970 A- of the tail appears to be ruffleded into
pril 27 and 30 the solar wind velocity was several plasma rays.
;"o ind to vary from 320 to 450 km/s. Unfortu- On the last four exposures of April 30
naooly, during this period ion density and (Table 1) the plasma tail is clearly divided
temperature were not measured. into two parts, symmetrical with respect to
The magnetic field parameters are from the tail axis. These may be due to symmetric
the Explorer 41 (IMP-5) satellite (King, plasma rays. There are asymmetric plasma
1975), which operated at the distance of rays, too. One of them becomes gradually de-
0.06-28 Earth radii from the Earth's sur- formed within this period, and assumes the
face. During the investigated time interval form of a tail disturbance. However, this
the .satellite recorded magnetic field inten- disturbance is not so expressive as on the
sities of 2.8 to 5.5 nT. plates of 1970 March 30 and April 4 investi-
Mo discontinuities in the longitude and gated by Jockers and Lust (1973). The length
latitude angles were recorded. This indi- of the plasma tail on the exposures of April
30 is about 2.2 .

6. PLASMA TAIL AND SOLAR WIND

Sotor wind vplocil
6O0
Due to the interaction of the tail's
plasma with the solar wind flow, there are
400 some deviations of the comet's plasma tail
from the radius vector from the Sun. From
this aberration angle it is possible to de-
termine the velocity of the solar wind in
the comet's region. This problem is discuss-
ed in many papers, e. g. Brandt (1969), Joc-
kers and Liist (1 973), Niedner et al. (1978),
Tarashchuk (1974).
The measured aberration angles between
Longitude angle (dea.1 the projection of the radius vector Sun-
360 -comet and the axes of the comet plasma tail
on the exposures are listed in Table 1. The
270 "•;.. ••-••*. + sign means that the vectors Sun-comet,
comet-Earth, and the tail axis form a right-
-handed vector system.
The velocity components of the solar wind
90 velocity obtained from the aberration angles
are listed in the next columns of Table 1.
They were calculated using the formulae of
LoMwJe angle fdcgt Jockers and Lust (1972). It is essentially
impossible to deduce the solar wind velocity
vector from the measurements of the tail ab-
/ • • .•>•••* erration angle alone. Therefore, we first
assumed that the tangential component of the
-90 solar wind is zero.
24 25 26 27 28 29 3C April / May 1970
The last two columns give the minimum
Figure 2. The satellite solar wind and value of the tangential component of the so-
magnetic field data lar wind speed under the assumption of the .

88
Table 1. Solar wind flow velocity between 1970 April 27 and 30
No Date middle Exposure Aberration Solar wind flow v.:l'oit,v
of exposition time angle minimum radial minimum '_uru-..nt; al
UT tangential - 0 radial - I iw rndinl -
1970 April min deg km/s km/s k::.-'r
1 27.932 10 + 3.2 92 0.3 + 1 J.2 +
2 27-940 10 + 3.0 98 O.U 12. U
3 27.954 9 + 3.0 98 0. 1 + 12.1*
4 27.983 10 + 3.1 94 0.2+ 12.7*
5 27.992 10 + 3.0 97 0. 1 + 12.2 +
6 28.000 9 + 3.2 91 0.4+ 1 5.2*-
7 28.010 3 + 2.9 100 0.0- 11.6 +
3 29.890 10 + 3.0 84 0.6+ 12. 'r
9 29.899 10 + 2.8 91 0.3 + 11.2 +
10 29-909 9 + 3.0 85 0.6 + 12. ;+
11 30.903 10 + 3.3 60 1.7+ 14.4 +
12 30.91) 10 + 3.1 64 1.4+ 1i. ; +
13 30.949 10 + 3.0 65 1.3 + 12.'3 +
14 30.958 10 +2.8 71 1.0+ 11.8 +

Ecliptical latitude +50°. Distance from the Sun 1 AU. F o r sign <- and - see tc-xt.

radial velocity component of 100 km/s and

400 kra/s, respectively. It is the minimum
value only, because the deviation angle of
the solar wind velocity vector from the com-
et's orbital plane is unknown. The tabulated
values of the tangential velocity component
are marked by +, if the aberration angle is Radius
enlarged by a tangential velocity component Vector
of the solar wind, and by - in the opposite April 30
case. The first assumed value of the radial
velocity component is consistent with the
minimum radial -elocity determination, the
second value with the satellite data for a
quiet solar wind flow (Figure 2 ) .
The velocity of the plasma tail inns,
carried alon** b,v the magnetic f'i^ld of the
solar v;ind, does not correspond to the solar 3.2 - -
wind velocity, vilocity o:' tne ions is
reduced by the ki tic crier;--;/ needed for
dust [ = "ti:-lf:: I Tq rash-

P I' \ \\\i; :
On con.put. .":
;e r-ti'MHl :"!.:ir win - Vf.--
• i t y •' • • i-.-l ',, ; v.'.-en ••''•I - ] 'j •'.' k": ' S .
2 8'
/.. e r i ] •. i i l ' ; rai.tr
I ' .i re - liiiii /
whi c\\ i :

rr:?.t,:]y a t thr
ICeJ 111 T.S'.i.

•el i : t i c a l l o u r
rs but 30°
t h e ;;.-] t e l l it.-n were operatir'.),
• helin-
S.'ilii
!
Lhs liort.h, arid ?.p;jroxi-
u
"''I' the ocliptic. V.'hi-:i rn:;ipar..-d with the
satellite n.-rta on the solar wind velocity,
.j20~4'i0 kiii/r: (Figure 2 ) , our value is j-4
times. s:;-.alur than that at zero ecliptical
l a t i t u d e The disproportion is in fact
smaller, because v;e were only able to esti-
mate the lo«- -r limit of th'-- solar wind ve- 054
lo.:i ty .

7. MOTIONS AND VELOCITIES OF THE KINKS

On the four exposures of 1970 April 30
(Table 2) it. was possible to locate reliably
two details. The motion and radial veloci-
ties oi' these plasma kinks were determined Figure 3. The plasma tail of comet ben.nett
from six ti/ae intervals, defined by selected 1970 II. On the left, the aberration r-an/Ues
exposure's. The length of the maximum time between 1970 April 27 and 29. On the ri^-ht,
interval between exposures was 79 minutes, positions of the plasma kinks on ths expo-
that of the minimum time interval 12 rain— sures of 1970 April 30.903, 30.911, iC.vU9
•it.'S. and 30.958, and the aberration an..:l<--s on
During t h e -aaxinium time interval, the 1970 April 30.
 Table 2. Geometrical parameters

Exposure 1970 April (UT) 30.903 30.911 30.949 30.958

Distance comet - Sun (AU) 1.05111 1.05125 1 .05188 1.05202
Distance comet - Earth (AU) 1-36394 1.36413 1.36504 1.36523
Distance Earth - Sun (AU) 1.00756 1.00757 1 .00758 1.00758
Angle Sun - Earth - comet (deg) 49.39 49.89 49.89 49.89
Angle Sun - comet - Earth (deg) 47.15 47.14 47.11 47.10

Table 3. Radial velocities of observed kinks

Interval Kink 1 Kink 2
ax Vr
£ x10° km x105 km km/s x10 5 km xio5 km km/s
0 1 .841 2.920
1 1 080 1.928 0.867 80 2.994 0.745 69
2 4 020 2. 167 3.259 81 3.215 2.954 74
3 4 740 2.224 3.827 81 3.281 3.614 76
0 1 .928 2.994
4 2 940 2. 167 2.392 81 3.215 2.209 75
5 3 660 2.224 2.960 81 3.281 2.869 78
0 2. 167 3.215
6 720 2.224 0.563 79 3.281 0.660 91

first kink receded from the comet nucleus in 8. CONCLUSIONS

the radial direction by mere than 3.82x105
km; from the distance of 1.84x106 km from Between 1970 April 27 and 30 no discon-
the nucleus (exposure of April 30.903) to nection event in the plasma tail of comet
the distance of 2.22x106 km (exposure of A- Bennett 1970 II occured. Th^ l.-ngth of the
prll 30.953). The radial velocity determined plasma tail, as recorded on our ••xpor,ur-r-s,
from the individual time intervals varies was about i.5°.
between 79 km/s and 81 km/s (Table 3 ) . The Between April 27 and 2), the radial com-
:nvan radial velocity of the first kink is ponent of the solar wind velocity, as deter-
80.9 ± 0.8 km/s. mined from the aberration angle of the plas-
The second kink receded during the maxi- ma tail, had a minimum value of 34 /cm/s to
mum time interval from the nucleus by 100 km/s. On April 30 this was a little
j.61x105 km in the radial direction; from smaller, 60 km/s to 71 km/:-. The minimum
the distance of 2.92x106 km from the nucleus value of the tangential component varied be-
(exposure of April 30.903) to the distance tween April 27 and 29 from 0.1 kin/r. to 0.6
of j.281x106 km (exposure of April 30.958). km/s, or from 11 km/s to 1j km/:-, under the
The radial velocity, as determined from the assumption that the radial velocity compo-
individual time intervals, varies between nent was 100 km/s and 400 km/s, respective-
69 km/s and 91 km/s 'Table 3 ) . The mean ra- ly. On April 30 the tangential velocity
dial velocity of this kink is 76.0 ± 6 . 9 component was between 1 km/-, and 2 km/s, or
/
km/;;. I uncertainty larger,, because 12 km/s and 14 km/s, respectively.
thi:', kiuk is not so well defined. On the exposures of April 30 thi posi-
The [."-.itions of the kinks were deter- tions of two plasma kinks were determined.
mined in the cometocentric rectangular coor- They moved from the nucleus at a Sfan radial
dinates x, y in the comet's orbital plane by velocity of 81 km/s and 76 km/?,respectively.
the formulae of Konopleve and Rozenbush
(1974), from the measured equatorial coordi- 9. REFERENCES
nates on the plates. The individual posi-
tiorir. of the kinks in the cornel tail rela- Brandt J. : 1969, Nature et Ori,'in<> d.-r; Cnuie-
tive to the nucleus rare plotted on Figure 3. tes, IAU Coll. 13, Liege, 109-315.
They are removed from the nucleus according Dobrovol'skij 0. V.: 1966, Komety, 31-35.
to the exposures sequence. Jockers K., and Lust R.: 1972, Astr. Astro-
The motion of plasma kinks, as well as phys. 21, 199-207.
the aberration angle of the plasma tail, are Jockers K., and Lust R. : 197 3, Astr. Astro-
due to the interaction of the cometary plas- phys. 26, 113-121.
ma with the solar wind flow. The higher val- King J. H.: 1975, Interplanetary magnetic
ue1 of the mean radial velocity of the kinks, field data book, NSSDC, 75-04, Groenbelt.
76-81 km/s, than tnat determined from the Kink J. H.: 1977, Interplanetary medium data
aberration angle for the solar wind on April book, and Appendix, NSSDC/WDC-A-R+S 77-04
30, 6 0-71 km/s, is due to the different and -04a, Greenbelt.
methods used. In the first case we deter- Konopleva V. P., and Rozenbush V. K.: 1974,
mined velocity of the individual plasma Astrometriya i astrofizika 22, 61-69.
kinks. Their positions in the comet tail re- Marsden B. G.: 1986, 1986 Catalogue of cora-
lative to the nucleus can be determined more etary orbits, Cambridge.
precisely than the aberration angle in the Niedner M. B. Jr., Rothe E. D., and Brandt
second case. Moreover, the solar wind radial J. C : 1978, Ap. J. 221, 1014-1025.
velocity determined from the aberration an- Tarashchuk V. P. : 1.974, Astrometriya i as-
gle is the lower limit only. trofizika 21, 62-69.

90
 PRODUCTION RATES OF GASES AND SOLIDS IN COMET P/HALLEY DURING THE 1986 APPARITION

B . S t e c k l u m a n d '.V. P f a u
Un i v e r s i t 5 1 s -S t e r n w a r t e
Schi I lerga'sschen 2
DDR-6900 Jena
(German D e m o c r a t i c Republic)

From p h o t o e l e c t r i c p h o t o m e t r y a t o u r 9 0 - c m t e I e s c o p e we d e r i v e d c o n t i n u u m a n d e m i s -
s i o n b a n d f l u x e s w i t h i n t h e b a n dp a s s e s o f t h e s t a n d a r d i H W f i l t e r s . T h e s e d a t a we r e
c o n v e r t e d t o g i v e p r o d u c t i o n r a t e s f o r CN, C.,, C , and s o l i d s . The observations
cover the r a n g e o f p r e - p e r i h e I i o n d i s t a n c e s f r o m 2 . 1 AU t o 1 . 1 AU a n d i n c l u d e one
p o s t - p e r i h e I ion measurement a t 1.7 A U . The p r o d u c t i o n r a t e s of t h e g a s e o u s compo-
n e n t s show a s t r o n g d e p e n d e n c e on h e l i o c e n t r i c d i s t a n c e . Ths r e s u l t is compared with
t h e b e h a v i o u r of o t h e r c o m e t s a n d t h e o r e t i c a l c o n s i d e r a t i o n s . The dependence is less
s t e e p f o r t h e so I i d s . T h i s may b e d u e t o r e l a t i v e l y p r o n o u n c e d b a c k s e a t t e r i n g of the
gra ins.
During one p r o - p e r i h e l i o n n i g h t ( r = 1.5 AU) i n t e n s i t y p r o f i l e s a l o n g three sec-
t i o n s t h r o u g h t h e coma of P / H a l l e y w e r e m e a s u r e d . C o m p a r e d w i t h t h e H a s e r rrode I t h e
p r o f i l e s s h o w a g lob a I an i s o t r o p y o f t h e coma a n d p o s s i b l y local structure.

1. Int roduct ion p r o c e d u r e I <_ f . STECKLUM e t a l . , 1 9 8 7 ) using

As a contribution to the IHVV activities the values of A'HEARN ( 1 9 8 6 ) to compute
among others comet P/Hal ley has been ob- c o n t i nuum c o n t r i b u t i o n a n d f l u x v a l u e s . The
served a t t h e ^/O-crn t e l e s c o p e of the Jena fluxes i s r e converted to column densities
University Observatory. This paper presents a c c o r d i n g to the s t a n d a r d formula
the results of the observations together
with an a n a l y s t s of the behaviour of the Ig M(P.)=lg F(R)+27.4497+2lg rd-lg g, (1)
dust and gas components of P/Hal ley. For
various gaseous specieo p r o d u c t ion rates w h e r e M(R) i s t h e number of r r o l e c u l e s within
have been de r i v e d a s w e l l as a relative a c y I i n d e r o f r a d i u s R d e f i n o d by t h e p h o t o -
p r o d u c t ion r a t e f o r sol i d s . The s t r u c t u r e of meter diaphragm and extending entirely
tho coma h a s b e e n i n v o s t i g a t e d by m e a n s of through the coma. F is the e m i s s i o n band
photoelectric sections. Section 2 of the flux i n cgs u n i t s ; r and d a r e t h e h e l i o c e n -
p a p e r g i v e s th'? r e s u l t s o f the photoelectric t r i c a n d g e o c e n t r i c d i s t a n c e s of the comet,
observations. In S e c t i o n 3 t h e e s t i m a t e s for respectively, in AU; and g i s t the floures-
the production rates ind their variation cence e f f i c i e n c y (cgs u n i t s ) p e r m o l e c u l e at
with heliocentric distance aro presented. 1 A(J. V a l u e s o f IT. g o f - 1 2 . G 5 7 f o r C^ and
Section A is concerned w i t h tho r e s u l t s of - 1 2 . 0 0 0 f o r C^ h a v e b e e n u s e d i n accordance
photometric sections through the cometary w i t h MILLIS e l a i . ( 1 9 3 2 ) . Due t o t h e S w i n g s
corna and makes a c o m p a r i s o n w i t h m o d e l s of effect the flourescence efficiency of CN
d u s t an-) g a s p r o p a g a t i o n . varies w i t h the comet's h e l i o c e n t r i c radial
velocity. T h e a p p r o p r i a t e v a l u e s we r e taken
2. P h o t o e l e c t r i c p n o tome t r y from TATUM and +GILLESPIE (1977). Column
The ob s e r / a t ion s we r e ca rr i e d o u t u s i n g s i x densities f o r CO have not + been estimated
standard IH',7 filters with central wave- since vie could d e t e c t CO emission with
l e n g t h s b e t w e e n 3 5 6 nm a n d 5 1 4 n m . The p h o - sufficient accuracy only at two occasions
t o n - c o u n t i n g p h o t ome t e r i s c o m p u t e r - c o n t r o I - (December 5 and December 2 2 ) . The results
led, d e t e c t o r i s a n E M I 6256I3 t y p e p h o t o m u l - for the column d e n s i t i e s for C,i C , a n d CN
tiplier (uncooled). The r e s u l t s for comet are l i s t e d in c o l u m n s 7-9 of T a b l e 1 .
P / H a l ley are published i n STECKLUM e t al. The derivation of the production rates
(1 9 8 7 ) . The measu rement s were t i e d t o the without applying a m o d e l of the comet's
magnitudes adopted by PFAIi and STECKLUM intensity distribution requires a variable
(1986) for IHW s t a n d a r d s t a r s . As recommen- diaphragm s i z e to observe a f i x e d area at
ded by the D i s c i p l i n e S p e c i a l i s t s of the the comet's s u r f a c e . However, t h i s was n o t
IHW P h o t o m e t r y and Pol a r i m e t r y Met t h e z e r o the case w i t h our o b s e r v a t i o n s . Therefore,we
points in a i l f i l t e r b a n d s are arbitrarily applied the H a s e r m o d e l (HASER, 1957) to
def i n e d by t h e V m a g n i t u d e o f the star HD convert the observed column densities to
3 3 7 9 (V = 5 . 8 8 m a g ) . T h e s t a n d a r d deviations p r o d u c t i o n r a t e s . The s c a l e l e n g t h s used f o r
of o u r c o m e t m a g n i t u d e s c a n be e s t i m a t e d to t h e c o m p u t a t i o n of the p r o d u c t i o n r a t e s are
be 0 . 0 5 mag i n a l I b a n d s e x c e p t in the C2 from A'HEARN e t a I . ( 1 9 3 1 ) . The production
filter w h e r e i t may b e a l i t t l e b i t better. rates f o r the gaseous components are given
Owing to the c o n t i n u o u s l y rotating filter in columns 10-12 of T a b l e 1. A relative
wheel in the photometer the c o l o u r -indices production r a t e of t h e so I i d c o m p o n e n t has
are very reliable. been e s t i m a t e d from tho c o n t i n u u m f l u x using
the assumpt ion t h a t the d u s t s c a t t e r s iso-
3 . P r o d u c t i o n r a t e s of comet P / H a l ley t r o p i c a l ly and that the dust outflow is
The d e r i v a t i o n of the p r o d u c t on rates is spherical symmetric. In t h i s case the column
b a s e d on t h e e m i s s i o n b a n d f l u x e s w h i c h have d e n s i t y of cometary d u s t is p r o p o r t i o n a l to
been estimated a c c o r d i n g to the standard the size of t h e coma c o v e r e d by the dia-
 w i l l be reduced to 70%
1 >(>'"<) for
Date Time r d Th R . P*n» l^f Ig Q
(UT) (All) (AU) (deg)TW A GM t h ttNftTlCC£ CN sol ids
19B5
or
f
O c t . 2 2 00.02 2 .06 1.37 155.3 1 W |29.tfe9<-28.7
| 1 29.72 2 5 . 9 2 24.49 25.90 10.89
00.06 29. O 2 9 . 0 7 2 9 . 6 4 2 6 . 0 3 24. .^6 2 5 . 8 2 10.92
01.0? 25.89 24.63 25.70 10.91
01.12 29. !5 2 8 . 9 6 2 9 . 5 9 25.79 2 4 . 7 5 2 5 . 7 6 10.93
23.52 2 05 1.34 155.6 1.39 29. ,!6 2 8 . 0 4 2 9 . 5 5 25.72 23.83 2 5 . 7 3 10.90
Oct.23 00.04 2 9 . 4 3 25.60 24.21 25.62
|29. 4 2 8 . 4 2 10.95
01.01 29.03 7 3 . B5 ZB.S7 25.T9 2 1 . 5 5 2 5 . 6 5 10.88
"bi'.'©9 1-5V6-7
t . 02 fe-9.30 29.08 29.91 25.'94 25.02 26. 29 04
23.22 29. 38 29.05 29.92 26.01 2 4 . 9 9 26. 30 06
Nov. 4 0 1 . 1 0 29.'*©<29.06 29.91 26.04 2 5 . 0 0 2 6 . 2 9 07
01.20 29. A3 29.02 29.94 26.06 2 4 . 9 6 26. 32 05
Nov 29 17.02 1 50 0 . 6 2 150.9 0.64 29.G5 29.00 29.62 26. 18 25.21 26. 37 17
Dec 21. 41 0 . 6 8 •14&.5' 0!.7'029. 29.24 30.02 26.49 2 5 . 3 3 26.60 14
21. 29.76 29. 32 20.05 26.52 25.4 1 23.62 18
O c c . 2 2 17. 1.15 0 . 9 7 1 2 5 . 8 1.01 30.42 29.86 30.80 26.79 2 5 . 7 7 27.09 39
18. 30.52 29.93 30.31 26.03 2 5 . 8 5 27. 15 43
18. 30.56 30.09 30.85 26.9 2 26. 00 27. 20 52
1.T. 30.60 30.00 30.39 2S.96 2 5 . 9 1 27. 24 1 1. 58
13 9G
May 2 0 . 1 6 1.68 0 . 3 9 1 5 0 . 1 1.29 29.57 28.95 29.90 25.97 24.7G 26.09 11.21
2 0 . 26 29.96 29.50 29.72 2 6 . 36 ?5.31 2 5 . 9 1 1 1 . 16
20.30 29.97 29.42 29.84 26.36 25.23 26.04 11.14
20.39 29.92 28.96 29.73 25.?2 24.77 25.97 11.22
20.51 Q 29.53 29.69 30.02 25.93 25.50 2 6 . 21 1 0 . 9 3
scattering angle Th = 180 - solar phase a n g l e
number K of r r o l e c u l s w i t h i n p r o j e c t e d diaphragm
p r o d u c t i o n r a t e 0 i n p a r t i c l e s pe r sec on d

Ph r a g m 1 o f r a d i us p> The e s t i m a t e s a r e b a s e d The v e r y s t r o n g .Hoponclenc: of t h e p r o ' l u c -

o n t h e f 1 u x va 1 ue s a t 4 8 4 . 5 nm o n l y because t t o n r<3 t e s on b-o J i o c e n t r i c d i s t a n c e i s n o t
th r 0 1 iab i 1 i t y o f the data obtained with unusua I amonq come t s , a n d i t h a s boon o b -
tfi f i 1 t or is h i g h e r t h a n f o r t h e IJ f i I - served, e . g . , f o r come 11 P/S t e p h a n - 0 I or ma ,
t c r . Th 0 r e s ul t s f o r the r e l a t i v e production P/Eneke a n d o t h e r s . I t i s u n d o r s t a n d a n I e as
r,i t e f corn a t a ry d u s t a r e l i s t e d i n column thf* resu I t o i a pos i t t v o f e e d b a c k mechan ism
n of T, j b l e 1. proposed by H"J_!_MICH ( 1 9 8 1 ) a n d .'£ iSSfiANTJ
T na j 0 r task o f o u r i n v e s t i g a t i o n ras t o
•-> and \\\ Ef~'.V< ( 1 9'J1 ) w h i c h r e q u i t e f rc>\r-. t h e
•.-, I u '•'/ th cornet 3 v a r i a t i o n at different much \a rnnr cross r.cc t i o n of t h e d u s t h-.i I o
!]••• I i 0 c l i t r i c ,J i r, t . i n c e s .
r> A l t h o u g h t h e obsoi— compa r o d t o t h a i of a p u r e n u c l f u r , , .in j in-?
V I t i0 ^ i nc1u He o n ly t h e i n t e r v a l 1 < r < 2 effects of niu I t i p I o sea t t o r i n q ..i :> I T I ! r^
t h ?r i i) ot r ik i n rj e v i d e n c e f o r p r o n o u n c e d t h e r ma I r a d i a t i o n , 11 o >.ve v e r, i i f forenc")'; in
. ! • :t i vi t y o f :-' /Ha 1 1 ey w i t h i n this distance t h e ^enme t r y o f va r iour. c omo t <"i r y n u c l e i n.iy
r- i0n Tli i i , s hown i n F i g u r e s 1-4 w h o r e inf l u o n c e t h e s t r e n g t h of t h e r;^^nomr-non .
th I T ; ,1 :>ro duct ion r a t e s have been plotted The d i f f e r e n c e be t vje on t h e dene n donee of t h e
• I'' • 1 i n j t h> 1 i 0 cv nt r i c d i s t on ce . The? da s h o d g a s e o u s component s and t h e wooJ-'e r o n - ' of d u ^ t
I in i n : i " !t a
"•j l o a s t s q u a r e f i t of a pov/er may be ex p In i nod by cc-i i t r- r i n-~j e f f e c t s . O u r
I • to t i1'": iit.i The r e s u l t s . i r e g i v e n i n f i r s t o b s e r v a t i o n s •.•JO ro c a r r i e d o u t a t r,c-.i t -
• ) lo taring angles near 100 -in d moy bo i nf I u -
encec! by e n h a n c e J b a c k s a c t t o r i n<], F v i j G n c o
for onhancad b a c k s n e t t o r i n g i n come t o wa s
O>rrt nt low g iven by A* HEARN e t a I . ( 108/,) , fl ILL IS e t
r- ,
1i '• \'~ ± 0. 2! af .(193?) , O-^nOVOLSKy e t ,i I . { 1 9°<0 ) , a n d by
- ! ) . 1o _^ 0 . 7 ' j GIESE et aI .(19H0) f o r cometary c a n d idn t e
-4.72 ± 0.57 pa r t i c I e s . A ma t c h t o t h e der i v o d e x p o n e n t G
-.l.'JG +J.4O of t h e gns p r o d u c t i o n r a t or, r e q u i r e s a d e -
crease of t h e s c a t t e r i n g f u n c t i o n by a f a c -
I I. 1
r..i 11 ' H :.ccn t h a t t h e hohuv i o u r o-j/- t o r ^ of. f. '3t>Gul f o u r i n t h o a r g u m e n t r a n g e f r o m
2
; 7 ! ! - j I l e y w/! s v i ' ry d i f f e r o n t f ^ o n ttHr c j a p s i - t b 1^61^6 . T h i s lead:, t o t h e s u g g e s t i o n
-.: I : m -!e I o f ri i'j i I i h r i urn e v a p o r y t i o r ' o f An thti^ cornet P/ila I l e y s h o a more p r o n o u n i : e d
;
ic M n u c ' i''J:. vn i r h ;"jr e d i c t s a n i p p r o x i Q)a ' e ly bacftrsca t t erM ng t h a n o t h e r comets. However,
r " d.-.-:-j': • r~|f • n c o ' i t t her^e d i s t , i nr e s . S up p o r i from t h e r e s u l t s of t h e ( R - p h o t o m e t r y o f
coinr?-, from r e s u l t s o f 5CHEMI3 e t al.{1936) ROUCHET e t a I . ( 1937) o n e can draw t h e c o n -
•.vl"io ob t a i n o d :i d e p e n r i e n c e o f t h e H-,C - i n d 0 clusion that t h e dependence of t h e du's t
p r o d u c t i o n r a t o 5 o n t h e - 4 . 2 a n d - 4 77 powe r pro-due t i o n r a t e on h e l i o c e n t r i c d i s t a n c e v ^ s
of r, r e s p e c t i v e l y , by means of F a b r y - P e r o t not ve r y d i f f e r e n t f rom t h o s e of gaseous
ground-based spec t r o s e o p y . In t o r e s t i n g i y , species. CATALANO e t a ) . ( ! 9 8 G ) d e r i v e d f r o m
the value o f t h e C^, production rate for their IHVV-na r r o w b a n d pho t ome t r y a nearly
1 H!'o , f J o v e mbo r 3 / h s t a n d s c l e a r l y above t h e cons t a n t dust production rate within the
f ft wh i c h m i g h t b e t h e r e s u i t o f a cornet a r y same h e l i o c e n t r i c d i s t a n c e i n t e r v a I wh i c h i s
outburst at that time. The only one post- in d i s a g r e e m e n t w i t h t h e f o r me r ment i o n e d
pe r i h e I i o n o b s e r v a t i o n f i t s v*e I I into the* f i n d i n g s . T h e e x p o n e n t s o f d e p e n d e n c e of t h e
picture of t h e p r e - p e r i h e l i o n obs erva t i o n s [gas product ion rates of CATALANO et
suggesting that the comet*s behaviour after) p l . ( 1 9 8 6 ) ' a r e smaf f e r t h a n t h e v a I u e s p r e -
the perihelion transit was n o t v e r y diffe- s e n t ed h e r e .
rent f rom the pre-pe r i h e l i o n evolution.

92 lumber i n l i q l i t blue p y n c i l
 0.3 Igr 01 0.2 0.3 Igr

F i g . 1 . R e l a t i v e p r o d u c t i o n r a t e of s o l i d s in r i g . 2 . P r o d u c t i o n r a t e of C , ns a f u n c t i o n
comet P/Halley a s a f u n c t i o n of heliocen- of h e l i o c e n t r i c d i s t a n c e . M o t e t h e o u t s t a n -
tric distance. The f u l l c i r c l e r e f e r s to d i n g v a l u e at Ig r - 0 . 2 7 4 w h i c h m i ^ h t i n -
the p o s t - p e r i h e l i o n o b s e r v a t i o n . d i c a t e enhanced comotary a c t i v i t y .

24.5
255
03 Igr 01 02 0.3 Igr

F i g . 3 . P r o d u c t i o n r a t e of Cj. F i g . 4 . Production rate of CM.

4. Density prof i l e s of comet P/HaI ley shown in F i g u r e s 5 and 6. For the computa-
During the o b s e r v a t i o n at 1985, December tion of the t h e o r e t i c a l p r o f i l e s the scsIo
22/23 the b r i g h t n e s s p r o f i l e of the coma was lengths of A'HEARN e t a l . ( 1 9 T 1 ) have been
measured along three s e c t i o n s , each s m a r t i n g used w i t h the e x c e p t i o n of tho CM parent
from the comet's c e n t e r . The f i r s t ope was sca~1e length which a i d not f i t the data
c a r r i e d out in the d i r e c t i o n of motion ( s u n - v e i l , , A good1 match was o b t a i n e d using the CN
w a r d ) , and the t h i r d in a n t i s o l a r d i r e c t i o n ' . par&t sca-le length of NEWBURN and SPIfP.AD
The p o s i t i o n angle of the v e l o c i t y v e c t o r of (1984).
the comet was 248 and the p o s i t i o n angle of All theoretical prof i l e s qualitatively
the second s e c t i o n 112°. The geometry is agree w f t h the measured p r o f i l e s . However,
shown in the i n s e r t of F i g . 5 . The s t e p s i z e thare are systematic d e v i a t i o n s in the sense
of consecutive measurements nas 21'.'5 a t a that w i t h the e x c e p t i o n of the p r o f i l e for
diaphragm r a d i u s of 14V25. The d e r i v e d emis- the s o l i d s , the measured values f o r the
s i o n band and continuum f l u x e s have been sunward s e c t i o n are sma I l e r than the t h e o r e -
normalized to the maximum values at the coma tical ones, whereas the data f o r the t a i l -
c e n t e r . To compare these r e s u l t s w i t h simple ward s e c t i o n are l a r g e r than the t h e o r e t i c a l
models of dust and gas o u t f l o w the diaphragm Ones. The second s e c t i o n shows an interme-
integration has to be taken into account. diate behaviour. This reflects a global
This has been done using the simple model of • m i s o t r o p y of the coma which is expected due
dust o u t f l o w and the Haser model f o r the ;o the i n t e r a c t i o n with, the s o l a r wind and
gaseous s p e c i e s . The r e s u l t s of the observa- a d i a t i o n . T h i s a n i s b t r o p y is even present
tions In comparison w i t h the models are n the data f o r the s o l i d s . However, the

93
 o 1 1— • I i i i i i i i

1.0 • - 1.0 - -

\
0.9 i - 0.9 \ -

\
0.8 458° 0.8 ' \
-

1 \
0.7 •I 0.7 r \ -

\
0.6 \ • 0.6
\
-
\ \
• \
0.5 0.5 \ •

2.012-lO^km

DL
U.k
\ projected
diaphragm 0.4
° \ »A i 1

•K
diameter \
0.3 v \
0.3 C
e\ • \ 2
o \&
C2 0.2
solids
O ~^»
O.t 8 0.1
O — ~£
o o
, , O1 P i I_ 1
• —1 I • | ' • • i w-
8 10 ollO'-kml 10

;-;,.:.. . V n f i I .-•; of t h od e n s i t y of solids F i n - G . D e n s i t y p r o f i l e s of C , . The t h e o r e t i -

, l.,,r. tf're" .-ct i i . M ' t i i r o i i ' i h t h e c o m a . The ca I p r o f i l e ( d a s h e d l i n o ) is' b a s e d o n t h e
s u n ; « • , i-i t h e d i r e c t i o n o f t h e o p e n c i r c l e . ( l a s e r m o d e l . T h e s y m b o l s ar<^ as i n F i g . 5 .
7>i.> <nri:-t>nt il \.-.tr . - j i v e s t h e p a r t of t h e
; x-;j c j v . - r e d ijy l i v . l i n h r . q m . The dashed
In,,, i •, t h i - t h e o r e t i c a l profile.

•-•i I p r o f i l e f o r t h i s c o m p o n e n t lies rates from narrowband photometry without

. • • , v •r.-'.i s i i r . . i v i h r " , - v h i c h . irny lie- a introducing la n j e s y s t e m a t i c errors. llow-
- T-T-. . l u i ' i i . . - ' - of i i u w r f ' - c l :,K!:'.irrj:in ! c o r r e c - ever, a b e t t o r agreement between observed
| n n and l h e o r o t i c . i l p r o f i Is c a n o n l y be r e a c h e d
1
r .-,.-»* -.»-,, j | » , - i n f i r m t h e s t a t >r.ien t t h a t II" by a p p l y i n g r r n r c e l a b o r a t e d r r c d c l s , e . 9 -o f
Ma-.or --i.'i.-'l f o r t ! , e j a s o o u 5 s p e c i e s t o n c t h e r FESTOII ( 1 9 R 1 a , b ) .
.VI t ,h .i m r , | , , -ro,|,, | o ) Just o u t f l o w n i v i ; a '.'h a r e q r a t e f u l t o O r . AMlEARH, U n i v e r s i t y
-joe ; 5v'.-r.il ! r*.<*zcr i ;•> t i o n of t coma j in- of Maryland, who p u t t h e S t a n d a r d Comet
t..r--,itv ! i sI r i :JU t i o n , i n ! i ., t ' >ere f o<~ •"•, F i l t e r s at o u r d i s p o s a l and t o P r . RCI.'WJH
-u | ; . ) j r I - ! ' d e r i v a t i o n of production f o r h i s l i o l - i '.vi t h t h e o b s e r v a t i o n s .

l
'•'• e e r t ' n r o •:
VI •" 1 , A s t r o n . J . V;,
K , n I L L i " , - : . L . , an ew., O.T. ••
A s t r o n . ' j . !9,c>79.
A' IfAx',' •'.'".: \T)'li, i n :S o l a r fjy s te-n P h o t o m et r y H a r t d b o o ! : , e d . : P.. '•!. G E ' l t T, L M I I m a n - B e l l ,
•~* i c h i n o n i ( ' I'> A ) .
A ' -\- APJJ "\ f : : 19.',.1", IM'.'. : P h o t o m e t r y a n d P o l a r i m e t r y Hot L e t t e r .
: ) , • • : - • « r,' P . , : H A L A ; : A ' : V , A . , !V<rJKS, A . , I I I - J C P ^ M A Z , T . , EpCKTi-lil, N ., and LE HEi"!lRE,T.: 1 9 8 7 ,
A s t r o n ' A s t r o n h y s . 1 7 4 , 2 8 8 .
CATALAN'!, F . A . , RA;-:ATTA, G . A . , L O PP.EST I , C , a n d S TR.AZZULLA , t;... T9PX:, A s t r o n .A s t r o p h y s .

D a r ; 6 v X S ) < y , ().•/., KISELEV, n\H.', tH"E>!)OVA, G.P.y, TUPI-V'A, F . A . , a n d NARIZHIIARA, N . V . :

1930, i n : ' S o l i d ' P a r t i c l e s i n t h eSoJ a r * 5 y s t eirf, ' IA!J S y m p . M o . 9 0 , e ; i s . : I . H A L L IDAY a n d
il.A .Me I 'ITOSH , V< . ; >i d o I P u b I . C o . ' , P o r d r ..-c h t , P.2S9.
I'E.SroU, .''..C: 19:?1a, As t r o n .As t roi.hy s. 9 J , i>9.
FESTO'J, n . C . : 19B1b, A s t r o n . A s t r o p i >ys . 9 G , ~,2 .
GIE3E, P . H . : 1930, i n :S o l i d P a r t i c l e s i n t h eS o U r System, IA l l Syiap.No. 9 0 , e d s . : I . H A L -
LIDAy a n d B . A . M c l UTOSIL ! ) . P.e i d o I P u b I . C o . , D o r d r e c h t , p . l .
HASER, L . : 1957, B u I I . A c a j . 1 . S c i . 3 e I rj i q u o A 3 ,7 A 0 .
HEL1MICH, i i . : 1 9 1 1 , As tron.Ar, t r o p h y s . 3 3 , 34 1 .
MILL IS, <>..L., A'HEAHN, M . F . , and TIIOflPSON, D . T . : 1912, A s t r o n . J . 0 7 , 1310.
NEUOURi'l, R . I . ' , J r . ,a n d SP I M P . A I ) , H . : 1984, A s t n p n . J . B 9 , 7 8 1 .
PFAU, I1/'., and STCCKLUH, i l . : 19.^fi, As t r o n .f l a c h r . 307, 6 A .
STECKI uV-1 R PFAU, I'.1,, and HESSE, M . : 1987, A s t r o n .N a c h r . , i n p r e s s .
SCHERD, F . , ROESLER, F . L . , HAi'.LAIJOER, J . ,a n d REYNOLDS, R . J . : 1086, p a p e r p r e s e n t e d a t
tho 2 6 t h COSPAR Symp. , T o u l o u s e .
TATUM J . i i . and GILLE5P IF, M . J . : 1977, A s t r b p h y s . . 218, 5 G 9 .
r£ISSMAMN, P.P.., and KIEFFER, H . H . : 1 9 8 1 , leprufi 4 7 , 3 0 2 .
 SOLAR CORPUSCULAR RADIATION AND OUTBURSTS OF COMETARY BRIGHTNESS

Andrienko, D.A., Vashchenko, V.N., Mishchishina , I.I., Zosimovich, I.D.

Kiev State University, Kiev, USSR; Centre for Scientific and Technological
Potential and Science - History Studies, Ukrainian Academy of Sciences, USSR

The outbursts of comeiary brightness have To interpret the observed data indicating
been attracting the astronomers attention for the effect of solar wind on comets a mathe-
more than a hundred of years. They play a matical model of an outburst has been deve-
significant role in the study of physical na- loped based on the knowledge of cometary
ture and evolution of comets. An outstanding nucleus as a conglomerate of various ices
Soviet astronomer S.K. Vsekhsvyatsky (j) and refractory impurities ( 5 ) . Surface layer
pointed out the corpuscular fluxes as a plau- of such nucleus, due to thermobarodestruction
sible factor being responsible for the va- (from the experiments carried out by L.A.Kaj-
riation of cometary brightness. He was the makov et al. (6-8))should be destructed pe-
first to suggest that the effect of fragmen- riodically. As a result, icy grains come into
tation of solar corpuscular fluxes on ccmeta- the c o m e t a r y coma a n d form a halo at its p e -
ry ices is one of the causes generating the r i p h e r y . In t h e s o l a r r a d i a t i o n f i e l d t h e
brightness outbursts. halo of icy g r a i n s of a c e n t i m e t e r s i / e m a y
Many authors were studying the relation exist for a s u f f i c i e n t l y long p e r i o d . In c a s e
between outbursts and solar activity, and the comet g e t s into c o r p u s c u l a r flux d u r i n g
revealed the existence of direct correlation, this p e r i o d t h e icy g r a i n s w i t h s t r u c t u r a l
for the majority of comets. It has been sta- i m p e r f e c t i o n s , i n c l u d i n g c r a c k s , w o u l d be
ted that some comets are very sensitive to d e s t r u c t e d by energy p a r t i c l e s of s o l a r w i n d .
corpuscular fluxes (Halley, Schwassmann-Wach- The e n h a n c e m e n t of s o l a r light r e f l e c t i o n
mann, Finsler) and give. 100% correlation, and area due to f r a g m e n t a t i o n w o u l d result in tht
some of them are not affected by solar acti- i n c r e a s e d c o m e t a r y head b r i g h r ME::;1; .
vity. This fact indicates that besides cor- For a q u a n t i t a t i v e e s t i m a t i o n uf .i me d e -
puscular external effect it is necessary, for p e n d e n c e of icy g r a i n halo br l gh I n c;H a f t e r
generating the outbursts, the existence at their d e s t r u c t i o n o n s e t a s y s t e m u! m t e g r o -
present moment of corresponding conditions in d i f f e r e n t i a l e q u a t i o n s w a s set u p :
the comet as well. According to O.V. Dobro-
volsky (2) the interaction between protons of M(t) = ,t) dr
solar origin ard the comet should be displayed
by cometary outbursts with characteristic va-
S(t) = rZf(r,t) dr
riations of the appearance of the head.
At investigating the relation between co-
metary brightness and corrresponding geomag-
netic perturbations there appears a possibi-
lity to estimate the velocity of corpuscular K
rf(r,t) dr
fluxes generating the outbursts. According
to Richter (3) the mean flux velocity comes
up to be 750 km/s. Andrienko et al. (4)
reached a similar conclusion when investiga- w h e r e M ( t ) , S ( t ) is m a s s and area of icy
ting the behaviour of light curves of a number g r a i n h a l o , r e s p e c t i v e l y , N ( t ) the n u m b e r
of comets. High-velocity fluxes of solar wind of icy g r a i n s in a h a l o , f ( r , t ) ?A/e d i s t r i -
appeared to be responsible for cometary ac- b u t i o n f u n c t i o n of icy g r a i n s , / 1 the d e n s i t y
tivity. The evidences of such correlation are of icy g r a i n s , n and TI are s u b l i m a t i o n and
the follows: f r a g m e n t a t i o n c o e f f i c i e n t s rep: risen t i ng , r e -
- a 25-27-day spaced recurrence period of s p e c t i v e l y , the m a t e r i a l m a s s s u b l i m a t i n g or
outbursts for some comets (Schwassmann-Wach- b r e a k i n g away for a unit time irnm a unit
mann, Giacobini-Zinner, Whipple-Fedtke-Tev- area .
tadze 1943 I) corresponding to long-lived The s y s t e m s o l u t i o n at some a s s u m p t i o n s
recurrent solar plasma fluxes; led to the r e s u l t that v a r i a t i o n of icy
- the dependence on heliocentric comet distan- grain halo b r i g h t n e s s is of an o u t b u r s t n a -
ce of mean velocity of material ejections t u r e . It h a s b e e n s h o w n that wiih d u e a c c o u n t
from the nucleus by the law r ~ 2 / 3 w h i c h should of c o n t r i b u t i o n of g a s - d u s t a t m o s p h e r e the
be observed at dominating the ejections due estimated photometric light variation curves
to corpuscular fluxes; are in a good a g r e e m e n t - by s h a p e , a m p l i t u d e
- the existence of correlation between geo- and d u r a t i o n - with the o b s e r v e d b r i g h t n e s s
magnetic perturbations and outburst activity o u t b u r s t c u r v e s . T h i s m o d e l a c c o u n t s for the
of comets; dependenc of c o m e t a r y o u t b u r s t s a m p l i t u d e
- two-peak characteristic of distribution of and d u r a t i o n on their heliocentric; d i s t a n c e
the number of cometary outbursts depending and t h e level of s o l a r c o r p u s c u l a r a c t i v i t y .
on 11-year solar cycle phase with maxima The r e s u l t of s o l u t i o n is g i v e n in F i g . 1.
at phases 0,2-0.3 and 0.7-0,8 coinciding As is s e e n , in the p r o c e s s of icy g r a i n
with distribution of some physical charac- f r a g m e n t a t i o n the h a l o b r i g h t n e s s v a r i a t i o n
teristics of high-velocity fluxes. h a s an o u t b u r s t b e h a v i o u r .

95
 Apart from icy grain halo brightness a vi- and also the existence of wel1-developed
sible cometary brightness includes the bri- plasma structures in heads and tails of
ghtness of gas-dust atmosphere as well. Let comets with outbursts.
us discuss in which manner the visible co-
metary brightness would be affected by the
existence of icy grain halo in cometary
atmosphere and the variation of its area due
to fragmentation and sublimation. Let m
denotes reduced to A = I AU visible brSght-
ness caused by solar radiation reflection of
icy grain halo, and m the dust-gas atmosp-
here brightness, m* and m, the reduced halD
brightness of icy grains and cometary head at
r = I AL), respectively.
Let us introduce A m = m» - m~ and
A m = m, - m and choose, as a zero level,
cometary head brightness at r = 1 AU. The
variation of A m and A m values versus
heliocentric distance for different relations
of m. and m« is given in Fig. 2. The analysis
of trie picture allows to conclude that the
icy grain halo variation due to grains frag-
mentation (Fig. I) in all the cases except
when

d)

m i m +2,5 (n-2) lgr Am

max(rbo'd) IB 0 30 UO
10 10 t
(2)
d'9 rB=Sa .t.
results in the outburst of cometary brightness.
Here r. is the most probable initial size of
O.I
im(t). eft 0,3 Am(th 0,1
3
d
icy grains, n the photometric comet parameter,
"tl<*t ; T the outburst duration.
6
\ 0,6
6
{\ "' . 0.6
The outburst amplitude will denend on m,,
nu, n, r a n d A m (r, >d) values. Provided *l tl
/Y
x
tne condition (?? is satisfied the amplitude
increases with r . The amplitude growth rate
depends on relation of m- to m^ and the out-
burst duration depends on m^, m,, n, r and
Z

H1
\n 20
\ 2
1 \ \
t
'
/A i \ —L-.
10 to
\
'
so
V
uo t
T(r. ,d,r ) values. In case m > m the a. i.
outburst Duration will be longer than the Lime .0.1
im(t
Ifi 0 3 im(i) 0.1
corresponding to given r. ,d> r which is 6 S
0.6
necessary for the icy grafn halo brightness A ^06
to reach the value m ; the outburst duration
being increased at tne expence of increased U
rv\ It

time of brightness decreasing as the total

cometary brightness decreases up to the value
m This results in the increased T 2 /T» rela-
tion as compared to that obtained from Fig. I.
The results of the model proposed are in
Z

. \
zo f 1 \ . n 20
\i A i
40
i \
SO BO t
pood agreement with characteristic parameters
of cometary brightness outbursts. The model
is capable of accounting for the observed
Variation of splinters and granules swarm
outburst amplitudes duration and their vari-
luster in the result of fraction anu subli-
ation at different heliocentric distances
mation for the varied rating r > , at dif-
as well. At large solar distances - both from
ferent heliocentric distances .'"? i me t is
the model data and observational rejults - the
represented in twenty four hour period in
outburst amplitudes and durations are larger
star volume. The ratings are expressed in
than corresponding values at shorter distan-
cm and are printed at each curve.
ces. At short distances cometary head bright-
ness may prevail the icy grain halo brightness,
with the result that cometary brightness out-
burst would not occur.
Within the scope of this model some observed REFERENCES
processes in the cometary heads and tails may
be accounted for. These are an increased te-
mperature in the inner coma, the existence of
short-lived molecules at the head and tail \ .Vsekhsvyatsky, S.K.: 196*, Geomagnetism i
periphery, an intense sweeping out of dust aeronomiya No 4, 329.
in cometary head, radiation polarization, 2 .Dobrovol sky, D.V.: 1961, Nestatsionarnyje
IR-radiation and other spectral peculiarities, protsessy v kometakh i solnechnaya aktiv-
 nost'. Proceedings of the Academy of Science
of Tajik SSR, V. VIII, 183.
3-Richter, N.8.: 1963, The Nature of Comets,
London:Methuen.
4.Andrienko, D.A., Vashchenko, V.N: 1981, "Ko-
mety i korpuskulyarnoje izluchenije Soln-
tsa", M. Nauka, 164.
5.Andrienko, D.A., Mishchishina, I.I.: 1986,
Astronomicheskij zhurnal, V. 63, No 2,
335.
6 .Ka jmakov, E.A., Lizunkova, I.S.: 1982, Komet-
nyj tsirkulyar No 293, 4.
7.Kajmakov, E.A., Li^unkova, I.S.: 1982, Komet-
nyj tsirkulyar No 280, 2.
8.Kajmakov, E.A., Lizunkova, I.S.: 1982, Komet-
nyj tsirkulyar No 283, 3.
9.Adrienko, D., Demenko, A., Demenko, I., Zosi-
•novich, I.: 1971, Comet brightness variation
in outer space conditions. Motion, orbit
evolution and origin of comet. Dordrecht,
Holland.

v<
A S T E R O I D S

ioo
 COLLISIONAL EVOLUTION OF ASTEROIDS AND ASTEROID FAMILIES
P. Paolicchi (1) and V. Zappala (2)

(1) Istituto di Astronomia, Universita rii Pisa, PISA (Italy)

(2) Osservatorio Astronomico di Torino, PINO TORINESE (Italy)

Catastrophic or nearly-catastrophic collisions are the most important ohysical process affecting
the evolution of asteroids following the primordial phases. After a general review of the current ide-
as about col 11 sional evolution, also in the light of laboratory impact experiments, the problems con-
cerning the interpretation of asteroid families as outcomes of catastrophic processes are discussed.
Finally, it is shown how the present, non completely satisfactory, knowledge of collisional processes
can give important indications on the early phases of evolution of the asteroid belt.

1. Introduction 2. Collisional Evolution

On the basis of the most recent dynamical and physi- In their seminal paper, Me Adoo and S u m s (1973)
cal studies, a tentative and preliminary general scena- tried to investigate the collisional evolution of the
rio of the formation and evolution of the asteroidal asteroids, predicted by several dynamical models! We-
belt can be suqgested. The evolutional history of the therill, 1967; Dohnanyi, 1969; Hellyer, 1970 ), by me-
main belt population can be roughly divided in three ans of their observable properties. In particular,
phases : (i) an accretion phase ( - ^ l O 6 yr} leading they analysed the rotational data coming from photome-
to the formation of planetesimals up to the accumula- tric lightcurves, suggesting that the angular momentum
tion of few "small" planets as Ceres and Vesta; (ii) and the shape of the present asteroids could be signi-
a phase (~10 - 10 yr) of strong mass depletion in ficantly affected by evolutionary processes; among
the belt, due to external causes. Probably in the same them mutual catastrophic collisions have played a very
time an increase of the relative velocities of the as- important role. The sample used in the paper was too
teroidal bodies took place, stopping the accretion pro- small \nd biased for giving cl indications, but the
cesses and avoiding the formation of a planet between idea of Me Adoo and Burns was followed by several au-
the orbits of Mars and Jupiter; (iii) a phase (still thors ( Harris and Burns, 1979; Tedesco and Zappala,
active in the present regime) in which disruptive pro- 1980; Farinella et al., 1981a ). The detailed analysis
cesses caused by high-velocity ( -~ 5 km/s ) collisions of a much larger data set and of the major biases,sho-
generated the present asteroid population composed by wed that a simple collisional model could not explain
a variety of different outcomes of catastrophic or ba- in a reliable way all the properties evidenced by ob-
rely catastrophic events. jects of different sizes. In particular, the existence
Even if no direct information on the sequence of of a class of relatively large ( D =; 250 ± 50 km ) a-
primordial events can be achieved with the observations, steroids, showing an elongated shape together with a
a careful investigation of the characteristics of the very fast rotation, was suggested. They were interpre-
present belt has shown how the understanding of the col- ted by Farinella et al. (1981b) as equilibrium triaxi-
lisional phase could be fruitful not only for the study al ellipsoids. It is also plausible to suggest the pre-
of its final outcomes, but even to obtain hints and con- sence of some binary systems (Zappala et al., 1980;
straints on the very early stages of the Solar System Weidenschilling, 1980), originated from a large angu-
and on the involved physical processes. lar momentum transfer during a catastrophic collision.
Starting from these observational evidences and theo-
The present situation will be reviewed in details,
retical predictions, Farinella et al. (1982) presented
showing how statistical and theoretical analyses based
a physical interpretation to be applied to the whole
both on the observational data of physical and rotatio-
population of asteroids, allowing to achieve a semi-
nal properties and on impact laboratory experiments,
quantitative understanding of the observed differen-
allow to understand the various outcomes of break-up
ces within a common general scheme. They derived the
svents among the asteroid population ( rocky fragments,
probability of impacts with a given projectile-to-tar-
" pile-of-rubble" structures, binary systems, families,
get mass ratio for asteroids of different sizes, ta-
etc.). A special attention will be given to the problem
king into account different mass distributions of the
of asteroid dynamical families, which represent a time-
asteroid population at the beginning of the collisio-
honoured but until now puzzling subject. Even if with
nal process. Then, using the results of laboratory
the uncertainties still present both on their identifi-
break-up experiments, they showed that most asteroids
cation and on a reliable three-dimensional description,
were fractured by impacts, at least once during their
the statistical analysis of families can already play
history, as far as one takes into account only the so-
a key role to solve or to clarify many relevant proble-
lid state cohesion. However, they pointed out that the
ms concerning the evolution of the whole asteroidal
influence of self-gravitation and of processes of an-
belt. Finally, it will be shown how some results of the-
gular momentum transfer during catastrophic collisions
se studies can be used to estimate the mass present in
is strongly dependent on the target's size, resulting
the belt at the end of the primordial phases; a funda-
in a variety of possible outcomes, mainly in the in-
mental input to understand the physical processes which
termediate size range ( 100 - 300 km ).
were active in the very early Solar System.

101
 Comparing the theoretical scenario with the availa- the various impact velocities and geometry.
ble observational data on asteroid rotations and sha- The scenario is confirmed by several observational
pes, they confirmed that the proposed interpretation and experimental data, even if important problems re-
can lead to a unified understanding of different and main open.
apparently uncorrelated phenomena. The analysis perfor-
med by Farinella et al.(1982) allowed to state some ge- 3. Break-up Processes: Asteroids and Laboratory
neral conclusions about the role of catastrophic colli- Experiments
sions in determining the evolution of asteroids and
their preseh^otatioral properties. The largest astero- Even if the most immediate confirmation of the col-
ids ( D ^ 300 km ) appear not to have been strongly af- lisional scenario can be found in the observed size-
fected by catastrophic events. Their rotational proper- spin-amplitude correlations, the comparison of stati-
ties confirm that the largest projectile which impacted stical properties of asteroids with those of the frag-
them was not massive enough to overcome their gravita- ments obtained in laboratory catastrophic impact expe-
tional binding, nor to transfer the amount of angular riments is of decisive importance. This approach, ho-
momentum needed for the formation of binaries or of wever, exhibits two important drawbacks: firstly, the
triaxial equilibrium figures. For what concerns ;nter- experiments should cover a wide range of "initial con-
mediate-size objects, the largest probable impacts were ditions"(mass, shape, rotation, composition, relative
close to the limits for disruption and for the transfer velocities of the colliding bodies, and impact geome-
of a quasi-critical amount of angular momentum. In this try), and we are only at the beginning of the phase in
class one can expect formation of binaries, triaxial e- which a statistical analysis of the experimental resu-
quilibrium ellipsoids, and dynamical families. In fact, lts can be useful to find relevant correlations and to
in this case, self-gravitation prevents the complete propose interpretative schemes; secondly, there is a
disruption of the target: most of the mass is reaccumu- difference of 15 to 20 orders of magnitude in mass and
lated by the mutual gravitational attraction of the impact energy between laboratory collisions and those
fragments. The resulting object can be described as a which take place in the asteroidal belt: the possible
"pile-of-rubble" or a megaregolith asteroid (Davis et differences caused by so widely disparate size scales
al., 1979; Fujiwara and Tsukamoto, 1980). Such bodies, are still an open and puzzling problem ( Holsapple and
because of their state of fragmentation, will relax ap- Housen, 1986). Both difficulties entail severe limita-
proximately to the equilibrium shapes consistent with tions to the possibility of an effective comparison.
their spin rates and therefore will have only minor Nevertheless, the available data on mass, velocity,
surface irregularities sustained by the material's shape, and rotation distributions of laboratory frag-
strength. It is also worthwhi le to notice that if the ments ( Fujiwara et al., 1977; Fujiwara and Tsukamoto,
initial velocity distribution of the fragments has a 1980; Fujiwara and Tsukamoto, 1981; Capaccioni et al.,
tail exceeding the escape velocity of the target, few 1986; Fujiwara, 1986; etc.) can be analysed and a com-
fragments may be able to escape, reaching a heliocen- parison can be attempted with the corresponding quan-
tric orbit having orbital elements very close to those tities pertaining to the asteroids. While for mass and
of the most massive remnants : an " asymmetric dynami- velocity distributions the only direct comparison is
cal family " formed by a large primary object accompa- with the outcomes of an individual break-up process
nied by a small tail of few minor asteroids is then (i.e., a family : see Sect. 4 ) , rotations and shapes
formed. can be compared with those of the whole sample of as-
teroids.
Going towards smaller targets, the probability of
obtaining dynamical families increases significantly. For what concerns the rotation rate, the very few
Since a substantial fraction of fragments is not recap- largest asteroids have presumably retained their ori-
tured, in this size range families are no more formed ginal angular momentum through their whole history,
only by the asymmetric tail of high-velocity fragments while objects larger than about 100 km appear to have
escaping close to the impact point, but they are origi- been modified in their rotational properties owing to:
nated from bodies ejected in all the directions. We (i) catastrophic or barely-catastrophic eveits, in
have then the so-called " dispersed families". The pla which, however, the self-gravitation played an impor-
usibility of the collisional hypothesis for the origir tant role producing sometimes peculiar equilibrium fi-
of the most numerous dynamical families was confirmed gures; (ii) loss of angular momentum during large
by Fujiwara (1982), who analysed in details the energy cratering impacts (Dobrovolskis and Burns, 1984).
partition during the collisional formation of the Eos, On the other hand, asteroids smaller than 100 km are
Themis, and Koronis families. The problems concerning probably multi-generation fragments produced by cata-
the asteroid families will be discussed in more detai- strophic break-ups ; consequently the most fruitful
ls in a subsequent section. comparison is between them and the laboratory fragmen-
Finally, tiny asteroids can be considered sinyie ts. Even if with a not complete and biased asteroidal
fragments generated-by catastrophic impacts. Their sample, it turns out that - on the average - the smal-
shape can be irregular since they are dominated by so- lest observed asteroids tend to rotate faster, as re-
lid-state forces and their rotation is connected with sulting from the analysis by Dermott et al.(1984) and
the partitioning of the angular momentum occurred du- also from the most recent data collected by IAU Comm.
ring the catastrophic break-up of their parent body. 15 (see Fig. 13 in Paolicchi et al.,1987). From an ana-
As a general conclusion, one can state that almost lysis of the rotation of laboratory fragments the same
the entire present population of asteroids can be consi- trend results, with an approximate relationship T(pe-
dered as the outcome of a collisional evolution process. riod) vs R(size), supported also by simple theoretical
The observed differentiations are due to the various considerations (Fujiwara and Tsukamoto, 1981).
sizes and physical properties of the targets ( and then For what concerns shapes, Catullo et al.(1984) tri-
to the projectile-to-target mass ratio of the largest ed to compare statistically the shapes of small aste-
collision undergone by different objects), and also to roids with those of the laboratory fragments. They

102
 took into account the fact that lightcurve amplitudes into account by such a simple local model. A lot of
are only a rough indicator of the real shape of the future experimental and theoretical work will be an
objects, and therefore reduced the amplitude of labo- unavoidable prerequisite for a real understanding of
ratory fragments to an aspect angle of 60°, which wou- the fragmentation processes.
ld be theaverage value observed during one opposition,
if it is assumed that rotational axes are distributed 4. Asteroid Families
isotropically on the celestial sphere. In conclusion,
they found that the distribution of the laboratory After the historical papers by Hirayama (1918,1923,
fragments and of the asteroids smaller than 100 km are 1928,1933) the dynamfcal asteroid families, i.e. clus-
very similar indeed, strongly supporting the idea that ters in the space of orbital elements, were studied
small asteroids are fragments generated in impact eve- by many authors and from many points of view.
nts resembling (except for scale) those performed in The transition from the visual identification of some
the laboratory. On the other hand, asteroids larger anomalous clusterings in the a-e-i space to a kind of
than about 200 km show a complete different distribu- analysis allowing quantitative estimates and physical
tion characterized in general by a rather low amplitu- interpretations is not straightforward and requires
de much like that we mignt expect for bodies whose the solution of a few complex problems.
shape roughly fits the spheroidal figures of gravita- The first classification of families was based on
tional equilibrium. Only a limited group! about 15% of the osculating elements. However,these parameters
the sample) presents significantly higher amplitudes, (mainly eccentricity and inclination) are strongly af-
representing probably cases of asteroids relaxed to fected by planetary perturbations and vary sensibly
triaxial equilibrium figures or transformed into near- on time scales much smaller than any reasonable age
ly-contact binary systems. These results are consistent estimates for the families. The linear secular per-
with those concerning spins; more generally, the quali- turbation theory allows to define more significant and
tative fit between the rotation and shape properties constant elements ("proper elements").whose clustering
of laboratory fragments and small asteroids strongly is then much more meaningful, as already suggested by
supports the collisional scenario. On the other hand, the latest Hirayama papers. Nevertheless, the defini-
it follows that a deeper understanding of the catastro- tion of the proper elements themselves is not simple
phic disruption processes is a fundamental tool for at all. In fact, even using high-order theories, dif-
further and decisive investigations on the evolution ferent and often divergent computations were obtained
of the asteroidal belt. However, due to the complexity ( Williams 1969; Kozai, 1979,1983), leading to contro-
of the physics, the theoretical understanding and the versial results. Adding these uncertainties to the am-
ability to predict the final outcomes (i.e., size, sha- biguities arising from various possible definitions
pe, velocity, and rotation distributions for the frag- of a "statistically meaningful clustering," it is not
ments), given the "initial conditions" of the impacti a surprise that the various lists of families reported
is still very poor and mostly qualitative. in the literature ( Brouwer, 1951; Arnold,1969; Lind-
Very recently, Paolicchi et al.(1987) have tried to blad and Southworth,1971; Carusi and Massaro,1977;Wi1-
obtain at least some of the relevant information by liams,1979; Kozai,1979,1983) strongly disagree each
simple semi-empirical approach. Starting from the expe- other (Carusi and Valsecchi, 1982). As a conclusion,
rimental evidence that the fragments are ejected with the only unquestionably real families are the three
an explosion-like velocity field, whose geometry is a1- largest ones (Themis, Eos, and Koronis),already eviden-
most fixed and can be modelled by a few parameters, ced by Hirayama. For what concerns the recent efforts
they have introduced a simple and plausible rupture •for a better and more meaningful definition and compu-
criterion expressed in terms of tiie derivatives of this tation of proper elements, a promising approach can be
field with respect to the position into the target. based on the comparison between analytic computations
Then, they have derived also the average physical pro- and numerical integrations (Carpino et al., 1986; Kne-
perties of the fragments formed in different zones of zevic et al., 1987). In principle, this approach could
the target, and have analysed the correlations among allow to evaluate really "stable" proper elements, de-
these properties for a number of different choices of cisive for coming back to the primordial formation pro-
free parameters of the model. In such a way, they suc- cesses.'
ceeded in performing qualitative and quantitative -om- From a physical point of view, the paper by Gradie
parisons with the evidences coming from laborato •• da- et al.(1979) summarized the studies performed till 1979,
ta as well as from asteroid properties, Several cor- with a particular attention to the distribution of ta-
relations found in the observations and in the experi- xonomic types within the Williams' families. They con-
ments (increasing rotation rates for decreasing sizes, cluded that no naive correlation of the type "same fa-
larger velocities for smaller objects, an almost con- mily - same taxonomic type" was detectable, apart from
stant ratio between translational and rotational ener- the largest ones, which showed unusual and homogeneous
gies, etc.) were confirmed. compositions. Similar results have been derived by Zel-
This kind of approach leads to interesting compari- lner et al.(1985) on the basis of an eight-color survey
sons when kinematical relationships are investigated, of about 600 asteroids. On the other hand, the numerous
so that the introduced velocity field approximation ap- small families defined by Williams did not show any cor-
pears to be quite adequate. On the other hand, the re- relations of this kind. This result could support the
liability of the results is poorer when mass distribu- pessimistic conclusion that only the very few largest
tion and shapes of the fragments are considered. Even families are real, but probably the matter deserves a
from elementary considerations it results that every further scrutiny, and perhaps a new interpretation.
"local" fragmentation model leads to some very appro- The analysis of mass distributions of family memberi
ximate results ; for instance, the geometry of fractu- is another major topic, mainly because it allows a di-
res analysed in the experiments(Fujiwara and Asada, rect comparison with laboratory experiments. In the pa-
1983; Capaccioni et al.,1986) cannot be obviously taken per by Zappala et al. (1984) the data were analysed in

103
 terms of ffle discrete miSS1 distribution .defined by Kre- (v is the escape veloc!ty of the largest remnant, a
sak (1977). The results suggest a power law distribu- reasonable estimate for t/e effective mean velocity
tion for small fragments, with a general agreement with required to leave the parent body (Farinella et al.,
the corresponding behaviour of laboratory outcomes (se« 1987)). The mean ejection velocities were found to be
also Capaccioni et al., 1986). However, for some fami- of the order of 100 m/s. While this is a reasonable
lies there is an evident discrepancy with the experi- value for large bodies, for which escape velocity is
ments, concerning the largest remnant, which results of the same order, it is surprising that even for the
too large when compared with the laboratory outcomes. smallest families mean ejection velocities lower than
The interpretation in terms of gravitational reaccumu- 60 m/s are not allowed. Since this cannot be due dire-
lation of fragments onto the largest remnant is straig- ctly to self-gravitation effects, it seems to indicate
htforward, being also supported by the increase of the a striking discrepancy between asteroidal and labora-
ratio M /M (mass of the largest remnant / mass of the tory break-up processes, where fragment velocities are
parent Body] with the absolute size. The agreement bet- in general lower for the same degree of fragmentation.
ween mass distributions of real families and laboratory This fact is supported by similar results obtained for
experiments can be considered an important support to the Saturn satellite Hyperion, also interpreted as be-
the collision*! theories for the origin of families. ing the largest remnant of a catastrophic process (Fa-
A more difficult and controversial goal of physical rinella et al .,1983).
studies of families is the reconstruction of the dyna- More recently, Davis et al. (1985), after a more detai-
mics of the formation process, i.e., the computation led comparison between families and outcomes of labo-
of the original ejection velocities of fragments with ratory experiments, suggested as a possible solution
respect to the parent body. This could allow a new and of the quoted discrepancies the increase of impact
fruitful comparison between asteroids and experiments. strength due to hydrostatic self-compression. However,
The problem was analysed by Brouwer (1951) and then, the problem is still open, especially for what concerns
adopting Williams1 families, by Zappala et al.(1984). small bodies and small families.
After having fixed the origin in the space of proper Finally,one should remark that the distribution of
elements (the center of mass or the largest remnant of 6a within a family can provide some insights on the
a family) it is easy to define the "position" of each simmetry properties of the ejection velocity field
fragment ( oa, ie , oi ). Then it is possible to cal- (see also Sect. 2). After the pioneering investigation
culate the velocity components v_, v,., and v_ along the by Ip(1979), Zappala et al.(1984) introduced a quanti-
directions ^ (to the Sun), W (normal to the orbital tative simmetry parameter
plane), and T = W x S , by means of the classical Gauss
perturbation equations to zero order in eccentricity c = <vZ>/ <v>2
and for an impulsive velocity change: where the mean velocities are computed with respect to
the largest remnant. It turns out that the most asym-
v. = na( ie /sinT- Sa/a tantr) metric families correspond -on the average- to higher
S o velocities and to larger sizes, in a good agreement
v. * na( 4a/2a) with the prediction of the collisional scenario and
v = na( o W c o s f ) of the related considerations on the gravitational re-
accumulation.
The angles X and vj> are functions of the asteroid true
anomaly and orbit orientation at the very break-up mo- 5. Hissing Mass in the Belt
ment, and therefore they cannot be known; it follows
that the velocities v. and v u can be computed assuming Even if a detailed and quantitative scheme of the
various values of these angles. Even if it is not pos- fragmentation processes occurred during the collisio-
sible to derive the real ejection velocities for each naT «vplution of the asteroid belt is not yet comple-
family, statistically one should expect-on the average- tely available, it is worthwhile to notice that the
an isotropic distribution o^f the three components. preliminary scenario outlined in the previous Sections
Surprisingly, the velocity distribution result^ to be C4n'jjea.d to some basic information about the original
far from the isotropy (even with the most favourable poptfT)!tipn of the asteroids, and the early phases of the
assumption on the unknown angles X and (j> ) since JSolar Sy&Lwn evolution. The overall mass distribution
r.m.s. values of v,. and v,, exceed by a factor four or in t&e~pfotoplanetary circumsolar nebula implies( if
five that of v_. This trend is confirmed also- fey ttare* we assuirte a generally regular behaviour) that the amo-
well established families (Themis, Eos, incT;^6f«)isJ. "Dfft of ^olfd material,within the region presently popu-
Since no physical explanation of this result appears lated-by the asteroids,should have been, at the origin,
to be plausible, at least within the coll1.siona>ltheo- not'Vess than one Earth mass (Weidenschilling,1977): a
ry, one should ascribe it to the above mentioned uncer- value that exceeds by about three orders of magnitude
tainties in the computation of proper element* e and the present total mass of the asteroids (Kresak, 1977).
i . While stressing the need of future works in such In order to explain the removal of the missing mass,
a°direction, this difficulty leads to take into account one can suggest either that it was gradually comminu-
only the velocity component v-, which depends only on ted to dust by the disruptive process caused by repea-
a, the most stable element. Zappala et al.(1984) assu- led collisions at speeds of about 5 km/s and then di-
med as real velocity Voo = (3)* v_, where (3) was In- splaced by non-gravitational forces, or that the mass
serted to account for the other two neglected componen- j*as expelled primordially in the course of the same
ts, under the assumption of an overall isotropy. The process that stirred up asteroid orbits and increased
ejection velocity was then computed by correcting for the relative velocities at impacts. For discriminating
the gravitational slowing-down of fragments escaping between these possibilities, it is decisive to estima-
te at least the order of magnitude of the mass present
from the parent body: . 2
(Voo +
In the belt at the time the accretion was stopped and

104
 the relative velocities increased. A recent study by Carpino.M.,Gonczi,R..Farinella,P..Froeschle,C.and Ch.,
Davis et al.(1985), considering as constraints the pro- Paolicchi.P.,and Zappala.V.: 1986,Icarus 68, 55.
perties of Vesta's basaltic crust and of the Hirayama Carusi.A., and Massaro.E.: 1977, in Comets, Asteroids,
dynamical families, with the new assumptions on the Meteorites: Interrelations,Evolution and Origins,
scaling of impact strength above discussed, concluded (A.H.Delsemme, ed.), p.327, Univ. of Toledo,Toledo.
that the initial population of asteroids was not lar- Carusi.A., and Valsecchi,G.B.: 1982, Astron.Astrophys.
ger than several times the present belt mass. The pre- 115, 327.
vious conclusion supports the hypothesis that most of Catullo.V., Zappala.V., Farinella,P., and Paolicchi,
the mass had to be depleted before the onset of the P.: 1984, Astron.Astrophys. J_38, 464.
present collisional regime. A similar result was rea- Chandrasekhar.S.: 1969, Ellipsoidal Figures of Equi1i-
ched by Farinella et al.(1985) by analysing the influ- oriuin, Yale Univ. Press, New Haven and London.
ence of collisions on the asteroid rotational proper- Davis, D.R., Chapman,C.R., Greenberg,R.,Weidenschil-
ties as derived mainly by photoelectric photometry of ling,S.J., and Harris,A.W.: 1979, in Asteroids,(T.
asteroid lightcurves. As already mentioned, Farinella Gehrels, ed.),p.528,Univ.of Arizona Press, Tucson.
et al.(1981b) have shown that in the range 200-300 km Davis,D.R., Chapman,C.R., Weidenschilling.S.J., and
an unusually large fraction of objects is observed with Greenberg,R.: 1985, Icarus 62_, 30.
rapid spins and large lightcurve amplitudes (i.e., very Dermott.S.F., Harris,A.W., and Murray,CD.: 1984, Ica-
elongated shapes). They interpreted them as collisio- rus 57, 14.
nally-formed "piles-of-rubble", held together by self- Dobrovolskis.A.R., and 8urns, J.A.: 1984, Icarus 5_7,
gravitation and having received a large amount of angu- 464.
lar momentum during the impact. Dohnanyi.J.W.: 1969, J.Geophys.Res. 74, 2531.
If one misures the angular momentum of rotation in Farinella,P., Paolicchi,P., and Zappala.V.: 1981a,
units (GM3R)J, according to the predictions of the Astron.astrophys. 104, 159.
classical theory (Chandrasekhar, 1969), the stable equi Farinella.P., Paolicchi.P., Tedesco.E.F., and Zappala,
librium figures are represented by triaxial shapes for V.: 1981b, Icarus 46, 114.
values of the angular momentum in the range 0.30 to Farinella.P., Paolicchi.P., and Zappala.V.: 1982, Ica-
0.39. Beyond the latter value, binary fission is expec- rus jj2, 409.
ted. Actually, in the range 200-300 km we have about Farinella.P., Hilani.A., Nobili.A.M., Paolicchi.P.,and
1/3 of the asteroids exceeding the critical value 0.3, Zappala.V.: 1983, Icarus 54, 353.
assuming that the density does not exceed 3 g/cnr. Farinella.P., Paolicchi.P., and Zappala,V.: 1985, Mon.
Taking into account that both for the terrestrial pla- Not. R. Astron. Soc. 215_, 565.
nets and the largest asteroid (1 Ceres) the angular mo- Farinella,P.Paolicchi,P., Cellino.A., and Zappala.V.:
mentum is less than 0.1, there is no reason to believe 1987, Bull. Astron. Obs. Belgrade, in press.
that the elongated triaxial bodies had at the end of Fujiwara.A.: 1982, Icarus 52_, 434.
the accretion phase a value larger than 0.1 and thus Fujiwara.A.: 1987, Icarus 70, 536.
one can reliably assume, as an observational constraint Fujiwara.A., Kamimoto.G., and Tsukamoto,A.: 1977, Ica-
of the collisional evolution process, the fact that a- rus 21. 277.
bout 1/3 of the asteroids of quite large size received Fujiwara.A., and Tsukamoto.A.: 1980, Icarus 44, 142.
by the collisions themselves an amount of angular mo- Fujiwara.A., and Tsukamoto.A.: 1981, Icarus 48, 329.
mentum of the order of 0.3. Assuming a power-low dif- Fujiwara.A., and Asada.N.: 1983, Icarus _56, 950.
ferential mass distribution for the bodies colliding a Gradie.J.C, Chapman,C.R., and Williams,J.G.: 1979, in
given target, it is not difficult to derive that the Asteroids, (T.Gehrels,ed.),p.359, Univ.of Arizona
mass of the largest projectile which collided with a Press, Tucson.
250-km target corresponds to a diameter of about 65 km Harris,A.W., and Burns, J.A.: 1979, Icarus 40, 115.
( namely, a projectile able to produce a "rubble-pile" Hellyer.B.: 1970, Mon.Not.R.Astron.Soc. J48, 383.
asteroid). Presently, there are about 450 asteroids Hirayama,K.:1918, Astron.J. 2!» 185.
larger than 65 km and, consequently, every asteroids of Hirayama,K.:1923, Japanese J.Astron.Geopliys. 2>55-
about 250 km had a probability o only 15% of colliding Hirayanja,K.:1928, Japanese J.Astron.Geophys. 5_, 137.
with one of them during 4.5-10 yr. In conclusion, for Hirayama,K.:1933, Proc.Imp.Acad.Japan 9_, 482.
having the actual percentage of high-angular momentum Ip, W.-H.:1979, Icarus 40, 418.
bodies, we need that the "initial" population (at the Knezevic.Z., Carpino.M. .Farine'lla,P. .Froeschle,C. and
end of the accretion phase) was about 5 times more a- Ch.,Gonczi,R.,Jovanovic,B..Paolicchi,P., and Zappa-
bundant than the present one; this result is fully con- la.V. :1987, Astron.Astrophys., in press.
sistent with that of Davis et al.(1985). Consequently, Koza1,Y.:l979, in Asteroids,(T.Gehrels.ed.),p.334,Univ.
the present estimate of the belt mass at the beginning of Arizona Press, Tucson.
of the "3r<^ evolutionary phase"(see Sect.l) can be conr Kozai,Y.:1983, in Dynamical Trapping and Evolution in
sidered quite reliable. The knowledge of this datum is the Solar System,(V.V.Markellos and Y.Kozai,eds.),
extremely valuable for the understanding of the earlier p.117, Reidel, Dordrecht.
phases. Kresak.L.: 1977, Bull.Astron.Inst.Czech. ^ 8 , 65.
Lindblad,B.A.,and Southworth.R.B.:1971, in Physical
REFERENCES Studies of Minor Planets, (T.Gehrels.ed.),p.337,
NASA SP-267, Washington.
Arnold,J.R.:1969, Astron.J. 74, 1235. McAdoo.D.C.and Burns.J.A. :1973, Icarus ^ 8 , 285.
Brouwer.D.: 1951, Astron.J. J56, 9. Paolicchi.P., Cellino.A., Farinella.P., and Zappala.V.;
Capaccioni,F., Cerroni,P..Coradini,M. ,Di Hartino.H.,Fa- 1987, Icarus, submitted.
rinella, P. ,F1 ami ni ,E.,Martelli,G.,Paolicchi,P.,Smith, Tedesco,E.F., and Zappala.V.:1980, Icarus ^ 3 , 33.
P.N., Woodward,A.,and Zappala.V.: 1986,Icarus 66,487. Weidenschilling,S.J.:1977,A:;trophys.Space Sci.5J_, 152.
We1denschilling,S.J.:l980, Icarus 44, 807.

105
Wetherill.G.W.: 1967, J.Geophys.Res. 2?_> 2429.
Williams,J.G.: 1969, Ph.D.Dissertation.Univ. of Cali-
fornia at Los Angeles.
Williams,J.G.: 1979, in Asteroids, (T.Gehrels.ed.),p.
1040, Univ.of Arizona Press, Tucson.
Zappala,V., Scaltriti,F., Farinella.P., and Paolicchi,
P.:1980, Moon Planets 2?, 153.
Zappala.V., Farinella.P.,Knezevic,Z., and Paolicchi,
P.:1984, Icarus 59, 261.
Zellner, B., Tholen, D.J., and Tedesco, E.F.: 1985,
!carus 61, 355.

D I S C U S S I O N

Harris: Dermott has pointed out that the

"IRAS dust bands" account for^/10% of the
total surface area of zodiacal dust. Likewise,
the Eos, Themis, and Koronis families const-
itute /vlO% of the total surface area of all
asteroids in the main belt. Therefore it
appears possible that most of the zodiacal
dust is asteroidal in origin.
Lindblad: We know that meteorite bodies are
expelled from the asteroid belt. Is it pos-
sible that some of the missing mass in the
asteroid population is explained by these
meteorites?.
Zappala: I think that the meteorite bodies
are a product of the collisional evolution
of asteroids. Therefore, they do contain a
not negligible mass, however this cannot
account for' a mass depletion three orders of
magnitude larger than the present one.
Babadzhanov: Is there any special distribut-
ion of the products of fragmentation of aste-
roids according to their sizes and distances
from the main asteroid belt?
Zappala: For what concerns observable bodies,
there is a mixing between the original mass
distribution and the collisional distribut-
ions. I agree that more information can be
obtained from the mass distribution of the
dust, but for the moment no sufficient data
are available.
Ibadov: Can you indicate the rate of generat-
ion of dusty matter during a collisional
evolution of asteroids. I would like to know
the relative role of asteroids and comets in
maintaining the zodiacal dust cloud?
Zappala: Such process we did not consider.
Farinella: As regards the production of dusc
by collisional evolution of asteroids, the
work by R. Greenberg, S. Dermott and others
on the solar sy-tem dust bands discovered by
IRAS has shown that comminution of the present
asteroids by impacts provides the correct
order of magnitude for the dust production
rate .
Harris: In the size range A / 1 0 0 km diameter,
there appears to be a subgroup of very slowly
rotating asteroids. These objects are perhaps
tidally evolved binary systems, which origi-
nated by disruptive collisions such as you
describe.
Knezevic: What are the velocities that you
compare in the first couple of your figures?
Are these the projectile velocities?
Paolicchi: The velocities are those of ejected
fragments, as a function of size. While the
trend is absolutely significant, the numerical
values could be scaled (with rotation and
binding energy) to different values, to fit
the experiments (as in the figure)or the
asteroids.

106
 ASTEROID SHORT-PERIODIC PERTURBATIONS: CRITICAL ECCENTRICITY AND INCLINATION FOR ANALYTICALLY DERIVED MEAN
SEMIMAJOF AXES

Z. Knezevic and B. Jovanovic

Astronomska opservatorija, Volgina 7, 11050 Beograd, Yugoslavia

ABSTRACT: Preliminary results are presented of an attempt to define threshold values of

eccentricity and inclination for which a second order - fourth degree analytical theory of
asteroid motion still provides mean semimajor axes of acceptable accuracy.

It is a notorious fact that any analytical theory using the Everharts program (Everhart, 1985) in the
of asteroid motion, based on the usual development four-body case, with Jupiter and Saturn as
of the disturbing function into a power series perturbing bodies. By fixing some small initial
truncated at some order/degree, can provide results inclination (eccentricity) and varying the initial
of only limited accuracy. The uncertainty of derived eccentricity (inclination), we obtained several
mean and proper elements, frequencies and phases of sets of orbits to which the analytical procedure
free oscillations etc. depends very critically just of elimination of short-periodic perturbations was
on the order (with respect to the perturbing mass) then applied. Table I contains the initial
and degree (power of eccentricity and inclination) osculating elements of the perturbing planets, as
of the terms in the disturbing function where the well as the corresponding initial values of the
truncation takes place. However, although being of asteroid M , W , and JV , being the same for all our
crucial importance for the applicability and experiments. The quantities in parentheses are
reliability of a given theory, these uncertainties those small values of the initial eccentricity and
were so far known only to an order of magnitude at inclination being assigned to one of the elements
best, the amount of the residual error being usually while the other was varied. Fig. 1 shows an example
estimated on Lhe "first neglected term magnitude" of how the total remaining variation of mean
basis. Another important consequence of this semimajor axis increases with the increase of
situation is that one does not explicitly know for initial inclination, while in Fig. 2 the critical
how large eccentricities and/or inclinations the values of eccentricity and inclination are shown
theory still provides a meaningful outcome - i.e. for the nine different values of semimajor axis
results of acceptable accuracy. within the main belt.
In the paper of Knezevic et al. (1987), it has The main conclusion that can be easily drawn
been shown that the second order - fourth degree from this investigation is that in the case of
theory of Yuasa (1973) provides fairly accurate semimajor axis, providing we are far enough from
mean elements (obtained when osculating elements are resonances and at least one of the two signif'.cant
freed from short-periodic perturbations) even for elements - eccentricity and inclination - is small,
asteroids of relatively hi,?h eccentricities and/or Yuasa* s analytical theory removes the short-
inclinations. Here we present some preliminary periodic perturbations to a level accurate enough
results oC an attempt to define more precisely the even for orbits of fairly high eccentricity or
threshold values of eccentricity and inclination inclination (we recall that the median eccentricity
for which this theory still provides mean elements for the numbered asteroid sample is about 0.16,
of acceptable accuracy. The results of this first and median inclination about 8 - see Knezevic,
sta^e of investigation pertain to accuracy of the 1983). The approach to the resonance, as expected,
mean semimajor axis only. The reason for this choice causes the abrupt decrease of the critical values,
is obvious: providing we are far enough from an example being given by the critical eccentricity
resonances, the semimajor axis has no long-periodic value for tt= 3.20 AU (that is rather close to
perturbations, so that its mean value represents 2 : 1 commensurability, located at 3.28 AU). The
the final product of the perturbation analysis, and rapid diminution of the eccentricity and
thus at the same time defines the corresponding inclination critical values with the increasing
proper value. aistance from the Sun is perhaps not entirely
As regards the definition of "acceptable meaningful. It is at least partly due to the simple
accuracy", this is more-or-less an arbitrary choice, criterion that we used to define threshold
depending mainly or the aim of the particular values. Although this, of course, does not affect
study, available computing equipment, etc. We the qualitative validity of our results, some
adopted here as an acceptable accuracy threshold physically better grounded criterion, like, for
one that is usually posed as a requirement for a example, one based on the quantity K(AQ/El), where
reliable classification of asteroids into families. K is a constant, that is connected with a change
Hence, we consider the result as accurate enough if of the orbital velocity (Zappala et al., 198t),
for a certain set oV initial conditions (osculating or some space preserving criterion based, for
elements), the total remaining variation of the example, on Delaunay" s variables, would by all
mean element (defined simply as the difference meant reduce the observed decrease significantly.
between the corresponding maximum and minimum of the Let*s state, finally, that the results presented
derived mean values) in a long-enough time span here are to be completed: first, by increasing the
does not exceed 0.001 (AU for the semimajor axis). number of points for which we have a precise
Note that the Uo. ranges, within which the members determination cf critical values, second, by
of the major well established asteroid families are investigating cases of simultaneous increase of
situated, exttnd typically to several hundredths of eccentricity and inclination, and third, by adding
AU. The "long-tnough" time span for short-periodic to this analysis the results pertaining to other
perturbations elimination is taken to be 500 yr. orbital elements. These three issues, however, are
What we did in practice is to integrate orbits out of the scope of this paper, and are going to
of fictitious bcdies located at various initial be studied in the frame of a future, more
semimajor axes within the main asteroid belt by comprehensive analysis.

107
REFERENCES Knetsevie, Z., Carpi.no, M., Farinella, P., Froeachle
Ch., Froeschle, Cl., Conczi, R., Jovanovie
Dermott, S.F. and Murray, C D . : 1983, Nature 301, B., Paolicchi, P., and Zappala, V.: 1987 j
201. Astron. Astrophya., in press.
Everhart, E.: 1985, in "Dynamica of Comets: Their Yuaaa, M.: 1973, Publ.Astron.Soc.Japan 25, 399.
Origin and Evolution", eda. A.Carusi and G.B. Zappala, V., Farinella, P., Knezevic, Z., and
Valseechi, D.Reidel, Dordrecht, p. 185. Paolicchi, P.: 1981, Icarus 59, 261.
Knezevic, Z.: 1983, Bull.Astron.Obs.Belgrade 133, 16.

i = 38

2.908

•3 .
r 1.4x18

i = 25

'i^fJ^j**^^^
2.988

A = 8.8 x 18

i = 28

2.988
-3
A = 8.4 x 18
3 4
-2
tx!8
Fig. 1 : An example of increase of the total remaining variation of the mean aemimajor axis in the
500 yr time span; case of the small initial eccentricity (e = 0.01) and variable initial
inclination. Scale unit on the y-axia is 0.001 AU, and represents the difference between
the highest and lowest points on the corresponding ploto.

108
 - 30

0.1 - 10

2.3 2.5 2.7 2.9 3.1

Fig. 2: Critical values of the osculating eccentricity (full circles), above which the total remain-
ing variation of the mean semimajor axis exceeds 0.001 AU. Solid lines represent the
libration widths associated with the leading eccentricity term in the expansion of the
disturbing function (as adapted from Dermott and Murray, 1983), and denoting the position
and approximate extent of the Kirkwood gaps in the a - e plane. For the sake of simplicity,
the critical inclinations (open squares) are al30 plotted here, but not the corresponding
libration widths for the a - i plane.

Table I

object I\A £ Q i e . a
Jupiter 311 274 274. 918 100 .046 1. 3064 0.0481 5.2025
Saturn 145 486 338. 635 113.144 2. 4877 0.0515 9.5541
asteroid 80 325 30 (1) (0.01) 2.2-3.2

m
A 110
 PHYSICAL PROPERTIES OF ASTEROIDS

Paolo Farinella

Dipartimento di Matematica, Universita di Pisa, Via Buonarroti 2, Pisa, Ital>

ABSTRACT. In the last few decades new observational techniques have provided a wealth of physical
information on several hundreds of asteroids. These objects are no longer seen as point, i. ike mxiieu
mainly interesting as a 'dynamical zoo', but have become small 'worlds' with known sizes, gross shapes,
surface compositions, rotational properties and collisional histories. The diversity of those 'worl <ls'
is astonishing: they range in size from less than 1 to 10 km, in spin period from ;i j Vw hour:; u nany
days, in sr.ape from nearly spherical to very elongated and/or irregular, in surfat ••• r<-fl*.'(. 11 v, ty from
about 0.02 to 0.4, in composition from metal-rich and silicate rocks to volati le-ri'.ii >:;irtjuti.i'~i-cius
assemblages. Of course there are many peculiar objects: asteroids with surface pHt..l(cs ut different
brightness and colour; bodies which have suffered internal heating and have i]ev*-iopMi ,J r.<re-m.int Ie.-
crust structure; asteroids converted by catastrophic impacts into gravitationalIy b>>un>\ 'pi ley of
rubble 1 ; objects with triaxial equilibrium figures or splitted into binary systems; u^t'jr-b-1'.
asteroids whose spectrophotometric properties are very much alike those of cumelary nuclei. 71., ;
paper reviews some of these recent findings, which are currently being interpreted in the : r..i;v «..f
complex theoretical models for the formation and evolution of orbiting and coll isionai ly irluir.jc!.;ug
bodies.

1.INTRODUCTION into the "Asteroids" book pub! isnr.'d af t.-_-r the 1979
Tucson conference (T. Gehrels, ed. , 'Jmv. of Arizona
Among the known members of the solar system, namely Press, Tucson) and into the next, upda*>:<\ ;uth book
the objects whose heliocentric or planetocentric which is presently in preparation.
orbits have been accurately determined, the asteroids
represent by far the most numerous population. The 2. ASTEROID SIZES AND DENSITIES
number of catalogued bodies is now approaching 4000,
about 97% of which orbit the Sun in moderately Asteroids are generally darker and larger than it was
eccentric and inclined orbits lying in a large thought 20 years ago, when the only available method
toroidal region between 2.1 and 3.6 AU from the Sun, to estimate their size was base-J on (quite
the so-called 'main asteroid b e l t 1 . Their sizes are so arbitrarily) assuming some average albedo value. Most
small (typically, 100 km plus or minus one factor of diameters are now determined by radiometry, i.e. by
10) that even with the best ground-based telescopes deriving the albedo from the compari r.on between the
they are seen as unresolved star-like cbjects (hence brightness at visible wavelengths nnd * h.-it at the
their very n a m e ) . It is then understandable that until infrared wavelengths where the body emi\s thermal
a few decades ago the asteroid population was radiation. This technique was f i rrst applied by using

considered to be interesting mainly as a 'dynamical ground-based telescopes and, more recently, by

1 exploiting space-based observations like those carried
zoo , that is a collection of test particles whose
out by the IRAS satelli to in its systerna* ic survey of
(often peculiar) orbital motions had to be modeled by
the sky at infrared rfaveleiv.'.hs (Matson, 1986). The
the techniques of celestial mechanics. As for their
radiometric technique cars !_>e made -juant i tat i ve only
physical properties, the asteroids were thought to be
by assuming a model for the thermal behaviour of a
just huge 'stones', possibly generated by some
rocky, regolith-covered spinning object, but this
primordial cataclysmic event like in Olbers 1 exploded
model dependence can be catibrated by comparing the
planet hypothesis.
resulting albedos and diameters with those provided by
other methods, like polarimptry (the polari zation vs.
Today, the situation is entirely different. The
solar phase angle relationship has been shown to
asteroidal orbits are still a topic of much current
m
correlate with laboratory measurements of albedo for a
interest f-ir < olestial mechanicians» but a growing
variety of rocky minerals), speckle interferometry,
communi ty '..:' .jt--' ronomers and planetary scientists is
radar and the sporadic observati ons of stellar
now studying t':n; asteroids as a set of small but
occultations. As a result, the radiometrically
diverse 'worlds', with their own physical, chemical
determined diameters are now thought to be generally
and geological characteristics to be understood in the
accurate at the 5% level.
frame of a complex evolutionary scenario. In this
review I shall try to point out some intriguing and
far-reaching results of this recent research effort, The largest asteroid, Ceres, is about 950 km
trying at the same time to emphasize the implications across. There are about 30 asteroids larger than 200
on the processes to which these bodies have been km, 250 larger than 100 km, 700 larger than 50 km. The
subjected in the larger context of the origin and inAS derived size distribution, in the rouge where the
evolution of the solar system. The reader interested observational sample is almost complete, is shown in
in the most technical aspects and in detailed Fig. 1. At sizes between 1 and a few tens of km, we
descriptions of current research is invited to look have enly the very partial (and, possibly, bias-

111
 one (Tor the asteroids, Ceres) allowing alone for a
fraction (2-q)/(q-l) of the total mass. Thus the total
mass in the asteroid belt is not much larger than the
mass of Ceres, a plausible estimate being half a
thousandth of the Earth's mass (or some 5% of the mass
of the Moon). If the original density of solid
material in the solar nebula varied evenly with solar
distance, then the proto-asteroidal material had to be
depleted by a factor of the order of 10 , much more
100 than implied by the resonance-related gaps observed
today. A possibility is that mutual disruptive
collisions gradually comminuted the original
m
planetesimals to dust, subsequently removed by non-
gravitational effects. However, recent investigations
(Davis et al.? 1985; Farinella et al., 1985) have
shown that such an intense collisional depletion is
not consistent with observational constraints inferred,
from the preserved basaltic crust of Vesta, the
abundance of dynamical families and the rotational
10
properties of intermediate size asteroids. Alternative
theories relate the mass depletion to powerful
s resonant interactions occurred in the solar nebula,
possibly sweeping through the primordial asteroid
belt, or to gravitational encounters with large,
planetary-mass planetesimals coming from Jupiter's
accretion zone. The same primordial processes have
probably stirred up the asteroid orbits, increasing
their eccentricities and inclinations and leading to
average relative velocities (about 5 km/s) which allow
50 100 200 disruptive collisions.

DIAMETER (KM)
Direct measurements of individual asteroid masses
and densiti es are still very scarce. For the few
Figure 1
largest asteroids, the analysis of gravitational
perturbations on other asteroids and on Mars (Schubart
affected) sample of the Palomar-Leiden Survey (PLS), and Matson, 1979) has yielded masses affected by large
carried out in the late 60s (Van Houten et al., 1970). error bars, which just allow to conclude that their
These data are usually represented via a power law densities are consistent with typical values for rocks
distribution, where the number dN of bodies in the ("** 3 g/cm^) or for carbonaceous-chondri te meteorit
mass range (m, m+dm) (or, equivalently, in the (•**2 g/cm ). The latter value is close to the Viking-
diameter range (D, D+dD)) is assumed to be measured density of the Martian satellites. For a few
proportional to nT^dm (or to D ^ - ^ ^ d D ) . The PLS objects, nearly equilibrium shapes have been inferred
best-fitting value for the exponent q is 1.65, but at from their rotational properties (Farinella et al-
larger sizes there are 'bumps' and other departures 1981), leading to density estimates which cluster
from a straight line in a double-logarithmic plot of between 2 and 2.5 g/cm . Probably, however, density
the distribution (like that of Fig.l), which appear to data reliable and accurate enough for constraining the
vary with heliocentric distance and taxonomic class composition and internal structure of asteroids must
(Zellner, 1979). From Fig.l we can notice a clear await direct measurements carried out during
excess of asteroids with diameters near 100 km, which spacecraft encounters.
may be related to the fact that at about this size the
self-gravitational binding becomes important with 3. ROTATIONAL PERIODS
respect; to material strengln, changing the response to
disruptive iiapact events. Although a more detailed Most available data on the asteroid rotations and
analysis of the observed size distribu tion is shapes cone from lig.lt (.curve photometry, a traditional
possibly premature, i ts genera J. features compare astronomical techni quo which in the last 15 years has
satisfactorily with simple theoretical models for the been applied by a growing number of observers
evolution of a population of bodies subjected to worldwide. In spite of occasional ambiguities, the
collisional fragmentation, which predict a power-law lightcurve periodicity directly yields the spin period
equilibrium mass distribution with q^ll/6 (Dohnanyi, of the asteroid, and periods for some 400 objects are
1970; Hufner and Mukhopadhyay, 198G). Similar now available. The average period is of about 10 hr,
distri butions have been also observed for the but a significant dispersion is present and periods as
fragments generated in laboratory impact fragmentation short as 3 hr or as long as weeks have been ooserved.
experiments (Fujiwara, 198G). Slal.j GL'LCZXI ;m:\ lyses carried oul. in Lbe l.i.sl. (JPC.-JIJC
(e.g., Farinella et al-, 1981; Dermott et al., 1984)
It is important to notice that, whenever q i s have ev Ldenced r.l i gh t, bu 1. phys ical I y re Lnvan t
less than 2, most of the mass in the distribution is correlations of the spin period with the asteroid size
contained in the few largest bodies, with the largest and taxonomic class. As shown in Fig.2, a running-box
plot of the-average rotation rate vs. diameter (the

112
 bimodal distribution, with several slow rotators which
might just be extinct comet nuclei, for which torques
due to outgassing phenomena could have affected the
initial rotation (although the few available data on
the spins of comet nuclei do not show a clear
overabundance of slow rotators with respect to small
main~belt asteroids).

Modelling the collisional evolution of the

asteroid spins is a very difficult task. A simple
analytical theory proposed by Harris (1979) derives a
differential equation for the evolution of the
1.0 1.3 1.6 1.9 2.2 2.5 rotation rate analogous to that which governs Brow^ian
motion: a positive (spin-up) term is mostly due to the
LOG DIAMETER (KM) rare nearly-catastrophic collisions, and a negative
Figure 2 (spin-down, or 'drag') term is caused by the frequent
small scale impacts. Since the two terms have a
different dependence on the pre-existing spin rate,
the theory implies that an equilibrium spin rate
exists. This equilibrium value depends on several
poorly known parameters , like the mean density of the
asteroid, the characteristic exponent q of the
projectile mass distribution and the fraction f of the
projectile's kinetic energy delivered to fragments
after a catastrophic breakup. If all these parameters
were independent on size, the equilibrium spin rate
would also be independent on size down to diameters
of a few km, while smaller bodies should spin faster
2 4 6 and faster. The equilibrium spin rate is also
ROTATION RATE ( r o t s / d a y ) proportional to the square root of the density, in
agreement with the faster rotation of M-type
Figure 3
(probably metal-rich) asteroids. However, if the
'anelasticity coefficient1 f is at most of the order
upper and lower curve showing the \-C dispersions of of 0.1, as observed in laboratory impact experiments,
the adopted samples), there is a significant drop of the theory predicts equilibrium spin periods shorter
the spin rate at a diameter of about 100 km with by at least a factor 3 than the observed average
respect to iarger bodies, while for smaller asteroids period (Davis et al., 1979). A number of reasons have
there is a much greater dispersion about somewhat been suggested to explain this discrepancy, as well as
shorter mean periods. Moreover, as shown by Fig.3 the size dependence of the spin rate shown in Fig. 2.
(obtained for a sample of about 200 asteroids, chosen First, some of the parameters (for instance, q) are
in order to minimize observational biases), the spin known to vary with size. Second, relaxation to the
rate distribution is not fitted well by a 3- equilibrium spin rate is slow unless the asteroid is
dimensional Maxwellian curve, such as would be able to withstand even the largest collisions without
expected from an isotropic, 'kinetic'-type collisional strong mass loss. This is due to the fact that- the
process, but shows a significant excess of slow theory assumes (for lack of better hypotheses) that
rotators especially at small sizes (less than 100 km). the spin rate is unchanged during a catastrophic
In other words, there are definitely too many fragmentation event. However, it appears more likely
asteroids with long rotational periods than it would that a complex partitioning of angular momentum to
be expected stochastically, and it has been suggested fragments leads to a change in the average spin rate
that in some cases tidal despinning by a satellite in this case, including some definite size dependence
might have occurred, while in others precessional as found in laboratory experiments by Fujiwara and
motions (again forced by a satellite) might cause the Tsukamoto (1981) . Since for most asteroids there is
most prominent brightness variations instead than pure no time for relaxation between two successive
spin. Another intriguing observation is that the breakups, they should reflect the spin rate
metal-rich M-type asteroids have a significantly distribution arising from the breakups rather than the
faster average rotation than the more numerous C and S equilibrium value. Third, the theory assumes that the
classes, possibly implying markedly different bulk asteroids have spherical shapes, but for elongated
properties (like density or impact strength). Similar bodies the higher momentum of inertia could partially
subtle but interesting differentiations have been compensate for a longer spin period. Fourth, as
recently pointed out by Binzel (1987) between two of already mentioned, tidal despinning might have been
the most populous Hirayama's dynamical families, the fairly frequent, and on the other hand for self-
Eos and Koronis families. Families are thought to be gravitating objects the possibility of binary fission
the likely outcomes of the collisional fragmentation implies a lower rotational stability limit at u pcriuil
of sizeable asteroids, and possibly the different of about 4 hr. Fifth, Dobrovolskis and Burns (1984)
distribution of spin rates just 'remembers1 the have pointed out an additional desninning mechanism,
rotation of their parent bodies. Another intriguing baser! on the fact that ejecta from crater-forming
result is that the rotation rates of Earth- and Mars- impacts can preferentially escape in the direction of
crossing asteroids (available for some 25 objects, of the asteroid rotation. This effect only operates in
size of the order of 1 km) have a very flat, possibly

113
 -i
10 -
_j ii
(a) I fragments
15- ~1i fragments r. -

10 -
1 0 I

-
5

oi 10
asteroids
D > 200Km
i
i• •

(b) 5- •
15 -

10 20
asteroids
• \
D -=100Km
15 25 "

20 30 •
(c) A(60°) A(90 o )
' I 'II! I I•| ,I.| . L i •I ' ' • Ii '• I •i '|• i i
02 0.4 06 08 02 04 06 OS
AMPLITUDES (MAG)
Figure 4 Figure 5

the intermediate size range (Fig. 4, case (b)), since observations (Dollfus and Zellner, 1979). However,
for large asteroids most of the ejecta fall back {case when the lightcurve displays a . complex morphology
(a)), while for small bodies nearly all the ejecta (instead than the quasi-sinusoidal form with two
escape (case (c)). This list of problems with Harris' maxima and two minima per cycle caused by an
theory can be seen as just an example of the ellipsoidal shape) and a small amplitude {of the order
complexities and subtleties which have to be accounted of 0.1 mag), albedo patches on the surface may well be
for in order to quantitatively model the evolution of responsible of the observed variations.
the asteroid physical properties.
A statistical comparison between the observed
4. SHAPES AND POLES lightcurve amplitudes of asteroids and those which
would be associated with the irregular shapes of
Additional observational constraints on the fragments from laboratory high-velocity impact
collisional evolution process are provided by the experiments has been carried out by Catullo et al.
knowledge of asteroid poles and gross shapes. The (1984). While for most asteroids larger than 200 km
procedures used for shape and pole studies are closely many lightcurves are available, obtained at different
related, because every shape determination is based on oppositions, this is not the case for many asteroids
some assumption on the orientation of the body. For smaller than 100 km. Thus in the former case the
instance, when the aspect angle (between the polar maximum observed amplitudes can directly be compared
axis and the line of sight) is 90°, if one assumes with the 'equivalent amplitudes' 2.5 log(a/b) computed
that the asteroid albedo is uniform, that the from fragment shapes measured in the laboratory, while
brightness is proportional to the geometric cross in the latter case one has to assume that the
section ('geometric1 scattering of light) and that the amplitudes (both for asteroids and for fragments) are
shape fits well a triaxial ellipsoidal figure of referred to a 60° aspect angle, the average value for
semiaxes a ^ b ^ c , then the lightcurve amplitude A is a set of isotropically oriented polar directions. Fig.
simply given by 2.5 log(a/b); thus this parameter 5 shows the results: the amplitude distributions are
provides an estimate of the equatorial elongation of qualitatively similar for fragments and small main-
the asteroid. On the other hand, for the same shape belt asteroids (among the planet-crossing objects
but at smaller aspect angles the. amplitude is also several bodies have been observed much more elongated
smaller, and of course i't vanishes when the object is than could be predicted from the b/a distribution of
seen pole-on. As a consequence, when the polar axis is the fragments), but a strong difference is found for
unknown, the lightcurve amplitude can be taken only as larger bodies, which show a much narrower peak at low
a statistically meaningful indicator of the shape; amplitudes and just a 'tail' at high amplitudes.
even when the pole is known, the simplifying
assumptions about the ellipsoidal shape, the uniform
These findings are hardly surprising. The
albedo and the geometric scattering law make the shape
collisional evolution models (Karinella ct al., 1982;
determinations just very approximate estimates. For
Davis et al., 1985) predict that most small asteroids
instance, large-scale and strong albedo contrasts are
generally ruled out by the results of polarimetric are just fragments from catastrophic disruption
events. Their escape velocity is lower than the

114
 0.60

1.2-

0.2

0.00
1.50 3.00 4.50 6.00
2 4 6
ROTATION RATE (rots/day) ROTATION RATE (ROTS/DAY)
Figure 6 Figure 7

typical ejecta velocities, so that they could not short periods (this correlation does not exist for
reaccumulate most of the material ejected by impacts, smaller bodies). Finally, nearly-contact equilibrium
and their irregular shape is related to the fact that binary models have been proposed by Weidenschilling
the solid-state material strength allows them to (1980), Leone et al. (1984) and Cellino et al. (1985)
'remember' the features moulded by repeated energetic to explain several cases of very high amplitude
collisions. On the contrary, most large asteroids have lightcurves, like for 624 Hektor (the largest Trojan
probably relaxed to quasi-equilibrium shapes, either asteroid) and 216 Kleopatra. Fig. 7 is a plot derived
because they were primordially melted, or because they by Leone et al., which shows the regions in the
were converted by the collisional process into maximum amplitude vs. spin rate plane were Jacobi
gravitationally bound - 'rubble piles', i.e., ellipsoids and equibrium binaries are possible, the
agglomerations of fragments and debris comminuted by dashed zones correponding to the realistic density
impacts but reaccreted by the target body (because of range between 1.5 and 4.0 g/cm3. The q scale refers to
its relatively high escape velocity - 100 to 150 m/s different values of the mass ratio for the binary
for a 200-km sized asteroid). A 'pile of rubble1 has models. The positions of several asteroids in this
by definition a negligible tensile strength, and if plane are shown by triangles (100 km < D < 150 km),
the individual fragments are small enough and no squares (150 k m < D < 2 0 0 km) and circles (D>200 km);
significant density variation is present, its surface two peculiar objects with D<100 km (43 Ariadne and 44
should roughly fit one of three types of 'liquid' Nysa) are represented by asterisks. Open symbols mean
equilibrium figures, depending on the rotational that the amplitude is probably lower than the maximum
angular momentum L: (i) for 0^L<0.30 (GRM3)1/'2(M and one, because few observations are available. As shown
R are the mass and mean radius of the body, G is the by this plot, were the equilibrium shape of these
asteroids accurately known, a precise estimate of
gravitational constant), an oblate Maclaurin spheroid,
their density would also be possible. For instance,
with a = b ^ c and c/a decreasing for increasing spin
the equilibrium binary modrl for Hektor implies a
rates; (ii) for 0.30 (GRM3)1/2<L <0.39 (GRM 3 ) 1 ' 2 , a
density of about 2.5 g/cm .
triaxial Jacobi ellipsoid with a > b > c and a/b
increasing for increasing angular momenta (but for
decreasing spin rates, due to the rapid change of the Of course, a pile of rubble can relax to an
momentum of inertia); (iii) for L> 0.39 (GRM 3 ) 1 / 2 , a equilibrium figure only if the irregular shape
fission binary system, with nearly-contact components of the largest reaccumulated fragments is smoothed out
and synchronized spin and orbital periods. by a thick regolith layer formed by finer debris. For
the usual power-law mass distribution of fragments, it
Maclaurin spheroids probably account for the is easily shown that the fraction of the total mass
large fraction of small amplitude objects among the contributed by fragments of mean size less than k
large asteroids (including the three largest bodies, times the size of the largest fragment is k'6~3q) ,
Ceres, Pallas and Vesta). Jacobi ellipsoids were first with the exponent q of the differential mass
proposed by Farinella et al. (1981) as an explanation distribution approaching 2 when the shattering
for the observational fact that in the 150 to 300 km mechanism provides significant amounts of energy in
diameter range several large amplitude objects exist excess of the threshold needed for fragmentation (sec
with spin periods in the range from 4 to 6 hr. e.g. Hartmann, 1969). This is probably the case Tor
yielding the appropriate amount of angular momentum asteroids, which have Lo suffer a large number oT
for reasonable densities (~2 g/cm3 ). Fig. 6 is small, subcatastrophic collisions before a disruptive
another running-box plot showing that for bodies larger impact by a massive projectile occurs. The formula
than 150 km high amplitudes are indeed correlated with given above yields, for q=1.8, 10% and 25% of the mass

115
 contributed by fragments of size less than 50 and 10 interpreted as a record of the 'initial' (i.e.,
times that of the largest object, respectively. For accretionary) rotational states not yet randomized by
q=1.9, these percentages are 31% and 50%. Thus it collisions.
seems likely that the amount of small fragments is in
most cases sufficient to prevent the appearance of Is it possible to derive from lightcurve
large-scale irregularities on the surface oi' the observations some different, and more complex 'mixture'
'piles of rubble'. It has been argued that even finely of results about poles, shapes and albedo variations
fragmented bodies should maintain some topographical on the asteroid surfaces ? The traditional negative
features, because a loosely cohesive material can answer is based on Hussell's (1906) study, which
support significant static slopes, just as angles of mathematically proved that lightcurves cannot
repose maintain topography in a sand-box. However, the provide unique solutions for the shape and the albedo
rubble—pile asteroids would be continuously shaked by distribution of planetary bodies; even assuming a
small-scale impacts, causing redistribution of debris known convex shape (and a known polar direction), an
towards depressed areas both by direct production of infinite number of albedo distributions can always
ejecta and by seismic disturbances favouring downslope match the observed lightcurves. There are two reasons
movements of the loose material (indeed, widespread for that: (i) unless the polar axis lies on the
evidence of these phenomena has been observed in the orbital plane, only the brightness difference (and not
Viking images of the Martian moon Deimos). the absolute albedo values) between the two polar
regions can be actually inferred; (ii) even so, the
As concerns poles, several techniques are now lightcurve data do not allow the odd spherical
available which yield reliable results when based on harmonics of the albedo distribution of order > 1 to
sufficient data. The first method to determine from be estimated at all. Therefore, any detailed 'map' of
lightcurve data both shapes and polar directions is an asteroid surface derived from lightcurveswould be
known as 'amplitude-aspect' method (Zappala' et al., totally meaningless. However, Occam's razor can be
1983) and is based on the fact that both the used to constrain a priori the choice of the model to
lightcurve amplitude and the absolute magnitude at be fitted with the data in such a way to obtain some
maximum apparent area are functions of the aspect general information on the average, large-scale
angle. Therefore the latter can be' derived for each distribution of albedo. For instance, Cellino et a ] .
apparition of the asteroid by making some simplifying (1987) have fitted all the available lightcurve data
assumptions on the shape of the body (triaxial for Vesta with a simple model in which the shape was
ellipsoid spinning about the shortest axis), the assumed to be spheroidal (with the flattening treated
scattering law of its surface ('geometric'), the as a solve-for parameter) and only two distinct
influence of nonzero phases and obliquities on the surface regions with two different albedo values and
amplitudes (considered as negligible for observations a geometrically simple border were assumed to represent
at phases "i 10°). Recent work has shown that these the large-scale features of the albedo distribution
assumptions can be relaxed without affecting the final (this latter choice rules out both sources of
solutions for the polar directions by more than 5° or arbitrariness found by Russell). The results of the
10°. A second method, called 'photometric astrometry' fitting procedure represent an almost-unique solution
(Taylor, 1979), assumes that the time of occurrence of for the parameters representing the albedo contrast,
a given feature in a lightcurve (e.g., an extremum) size and position of the 'albedo regions', the polar
corresponds to the time of transit of a specific coordinates and flattening of the asteroid. Fig. 8
meridian or. the asteroid surface on the line of shows a view of the Vesta model leading to this
sight. If lightcurves taken at several apparitions solution; if the derived flattening corresponds to the
well spaced in ecliptic longitude are available, the equilibrium shape of a nearly homogeneous body, a
direction of the polar axis and the sense of rotation density of 2.4±0.3 g/cm can also be inferred. The
are derived by minimizing the residuals of the regular shape and the existence of large-scale albedo
calculated times of transit of a meridian with respect variations are also consistent with spectroscopic
to the actual occurrences of the specific lightcurve studies suggesting that Vesta's surface is covered by
feature. Both these methods clearly work better for extensive lava flows of basaltic composition, as a
objects of very elongated shapes and simple lightcurve consequence of an early partial melting and
morphology, but they are complimentary in that the differentiation of the interior. Vesta is probably a
former one yields better results if the pole lies at 'primordial', unshattered asteroid, whose thin
timet, along the line of sight, while the opposite is basaltic crust displays some mineralogically distinct
true for the latter one. Therefore, when many regions.
observations are available, the final accuracy can be
improved by coupling the two techniques (Magnusson,
1983). Another potentially fruitful technique is 5. TAXONOMY AND COMPOSITIONS
radar. From the observed Doppler bandwidths one gets a
direct measurement of the range of radial velocities The conclusions quoted above about Vesta's composition
on the asteroid surface, and this depends on the size, anc! his'ory are not an isolated case. In the last two
spin period and aspect of the asteroid. So far, these decades an intense observational effort has shed light
methods have been applied only to a few tens of on the problem of asteroid compositions, which have
bodies, and the sample is not yet largo criouj'h for been found to be very diverse and to hold important
meaningful statistical conclusions to be inferred. cluen l.o primord i ni processor; occurred in l.hr; rjolnr
Clearly, the extent to which the polar directions arc ncbuLa and during the early stages of accretion nnd
isotropically distributed on the colesbial sphere di f fcrcril-i ation of planetary embryos. The mniri source
(possibly, as a function of the size of the bodies) is of information is spectral analysis of reflected
potentially an important constraint for collisional sunlight, but other techniques like radiometry,
evolution models, since any anisotropy could be polarimetry and planetary radar have yielded
significant contributions. These data have been often

116
 Figure 8

interpreted via direct comparison with the properties

of mineralogical assemblages found in the Different
meteorite types.

A very apparent difference among diverse types of

asteroid surfaces is evidenced by the distribution of
albedos. When the observational bias against darker
objects is accounted for, some 75% of the asteroid are
found to be very dark, with average albedos of**s 0.04. SEMIMAJOR A X I S
A distinct group of bodies has moderate albedos of
Figure 9
about 0.15, with few asteroids lying in between but a
tail of 'bright' bodies having albedos up 0.4 and
more. A better discrimination is possible if the absorption bands due to silicates like pyroxene and
albedo data are coupled with spectrophotometry data, olivine. It is debated whether their likely meteorite
yielding the behaviour of the reflection spectrum over analogs are the stony-iron meteorites (probably
a wide wavelength interval. Some absorption bands are derived from the core-mantle interface of
unequivocally diagnostic of the presence of silicates, differentiated parent bodies), or the ordinary
water ice and hydrated minerals, but in many cases chondrites, interpreted as assemblages of primitive
these prominent features are lacking and any nebular grains of different compositions, subsequently
inference on the mineralogical composition must be heated and metamorphosed only modestly. The M-type
seen as very conjectural. asteroids have albedos of about 0.10, with slightly
reddish, straight spectra, suggesting a significant
content of nickel-iron metal. It is possible that they
Clustering statistical techniques have been are akin to iron meteorites, hence that they represent
applied to a set of suitably chosen parameters, pieces of the cores of differentiated precursors.
considered a priori as potentially diagnostic of Recent radar observations of the large M-type asteroid
composition, in order to define the so-called 16 Psyche (Ostro et al., 1985) confirm this
taxonomic types. The latest work in this direction interpretation, and suggest that this body is just the
{Barucci et al., 1987) has shown that every collisionally stripped metallic core of a large parent
classification is non-unique, but depends on the asteroid, of about the same size as Vesta. In this
confidence level at which the types are separated. case, it would be difficult to understand why two
However, the principal types coincide in the objects with similar initial structures underwent a
classifications derived by different methods, so that very different evolution as a consequence of the
they can be considered as reliably identified and collisional process (Chapman, 1986).
defined, and correspond very probably to markedly
different mineralogical compositions. For instance, C-
type asteroids have a very low albedo and a fl?t Of great interest is the fact that different
spectrum throughout the visible and the near-IR; they taxonomic types are preferentially located at
are very probably similar in composition to different heliocentric distances. Fig. 9, adapted from
carbonaceous chondritic meteorites, which are very Gradie and Tedesco (1982), shows the distribution of
primitive mineral assemblages subjected to no or very types vs. semimajor axis for about 650 objects, as
little metamorphism after their condensation. D-type compared with the number distribution for a bias-
objects are also dark but have very red spectra, corrected sample of about 1400 asteroids in the same
suggesting the presence of low-temperature organic semimajor axis range (the dashed hisbrograrrt
compounds. These objects are similar to many low- corresponding to taxonomicaily classified objects).
albedo, reddish small bodies found in the outer solar This orderly progression of types is usually
system, including some comets observed at low activity interpreted as reflecting variations in the
and a few small satellites' (e.g., Phoebe). S-types composition of the material which condensed into solid
have relatively high albedos, and their spectra show grains in the solar nebula, variations related in a

117
 predictable way to the temperature decrease with solar Farinella, P.; Paolicchi, P.; Zappala', V.: 1982,
distance. It is also interesting to note that the most Icarus 52, 409.
primitive types (corresponding to least metamorphosed Farinella, P.; Paolicchi, P.; Zappala', V.: 1985,
material) tend to occur in the outer belt, and that Monthly Notices Roy. Astron. Soc. 216, 565.
most asteroids in this outer region resemble in a Fujiwara, A.: 1986, J. Ital. Astron. Soc. 57, 47.
significant way the properties of comet nuclei Fujiwara, A.; Tsukamoto, A.: 1981, Icarus 48, 329.
(Hartmann et al., 1987). Gradie, J.; Tedesco, E.: 1982, Science 216, 1405.
Harris, A.W.: 1979, Icarus 40, 145.
6. FUTURE RESEARCH DIRECTIONS Hartmann, W.K.: 1969, Icarus 10, 201.
Hartmann, W.K.; Tholen, D.J.; Cruikshank, D.P.: 1987,
Many important research programs on asteroid physical Icarus 69, 33.
properties are under way or planned for the near Hiifner, J.; Mukhopadhyay, D. : 1986, Phys. Lett. B 173,
future. These include new spectrophotometry and 373.
lightcurve observations which should extend to small Leone, G.; Farinella, P.; Paolicchi, P.; Zappala', V.:
sizes the presently available data banks; extensive 1984, Astron. Astrophys. 140, 265.
application of relatively new techniques like radar Magnusson, P.: 1983, in: Asteroids, Comets, Meteors
and speckle interferometry; new laboratory simulations (Eds. C.-I. Lagerkvist and II. Rickman: Uppsala
and impact experiments as well as theoretical Univ., Uppsala), p.75.
modelling of the impact events. Space-bound Matson, D.L.: 198G, IRAS Asteroid and Comet Survey,
observations have been recently carried out by IRAS, Preprint Version No. 1 (JPL D-3698, Pasadena).
which has provided an extensive and least-biased Ostro, S.J.; Campbell, D.B.; Shapiro, S.: 1985,
survey on asteroid sizes and albedos, and will be Science 229,442.
carried out by the Hubble space telescope, which has Russell, H.N.: 1906, Astrophys. J. 24, 1.
the potential of obtaining images of asteroid surfaces Schubart, J.; Matson, D.L.: 1979, in: Asteroids (Ed.
at a resolving power corresponding to a few tens of T. Gehrels: Univ. Arizona, Tucson), p.84.
km. However, many basic uncertainties and open Taylor, R.C.: 1979, in: Asteroids (Ed. T. Gehrels:
problems exist whicii ^annot be solved by Earth- and Univ. Arizona, Tucson), p. 480.
near-Earth-bound observations and studies, but need Van Houten, C.J.; Van Mouten-Groeneveld, 1.; Herget,
close—up investigations performed by dedicated space P.; Gehrels, T.: 1970, Astron Astrophys. Suppl. 2,
missions. For instance in situ density and composition 339.
determinations as well as high resolution imaging for Weidenschilling, S.J.: 1980, Icarus 44, 607.
just a few (suitably selected) asteroids would be Zappala', V.; Di Martino, M.; Farinella, P.;
exceedingly valuable. Since space missions have
Paolicchi, P.: 1983, in: Asteroids, Comets, Meteors
explored to date (or will in a few years) all the
(Eds. C.-I. Lagerkvist and H. Rickman: Uppsala
major planets, their satellite and ring systems and
Univ., Uppsala), p. 73.
ev;n some comets, asteroids are the next obvious
Zullner, B.: 1979, in: Asteroids (Ed. T. Gehrels:
target to be considei 5d with a high priority.
Univ. Arizona, Tucson), p.783.

D I S C U S S I O N

REFERENCES
Kristensen: Russell proved in 1906 that we can-
Baruccl, M.;>.. ; Capri a, M.T. ; Coradini, A.; not distinguish between shape and albedo vari-
ations. Is your assumption that the lightcurve
Fulchignoni, M.: 1987, Icarus, in press.
of Vesta is dominated by spottiness supported
Binzel, R.P.: 1987, Icarus, in press. by variations of the color index?
Catullo, V.; Zappala', V.; Farinella, P.; Paolicchi, Farinella: Ihere are polarimetric observations
P . Astron. Astrophys. 138, 464. of Vesta showing a periodicity equal to that
Cellino, A.; Pannunzio, R.; Zappala1, V.; Farinella, of the lightcurve. This strongly suggests a
heterogeneity of the surface. Moreover, Vesta
P.; Paolicchi, P.: 1985, Astron. Astrophys. 144,
is a 500-km sized object , and it is unlikely
355. that its overall shape is irregular (compare,
Cellino, A.; Zappala', V.; Di Martino, M.; Farinella, e.g., with Mimas, Enceladus or Miranda, which
P.; Paolicchi, P.: 1987, Icarus 70, 546. have the same size and show nearly-equilibrium
Chapman, C.R.: 1986, J. Ital. Astron. Soc. 57, 103. s h a p e s ) . On the other hand, Russell's result
is valid for general convex shapes or albedo
Davis, D.R.; Chapman, C.R.; Greenberg, R. ;
distributions on the surface. If one constrains
Weidenschilling, S.J.; Harris, A.W.: 1979, in: the model by choosing an axisymmetric ellipsoi-
Asteroids (Ed. T. Gehrels: Univ. Arizona, Tucson), dal shape and a two-patches albedo distribution,
p. 528. the photometric data can be fitted with no am-
biguity. Of course, this means that only large-
Davis, D.R.; Chapman, C.R.; Weidenschilling, S.J.;
-scale albedo variations can be detected from
Greenberg, R.: 1985, Icarus 62, 30. these data (see Cellino et a l . , 1987 ICARUS
Dermott., S.F.; Harris, A.W. ; Murray, C D . : 1984, 70, 4 4 6 ) .
Icarus 57, 14.
Gr(Jn: I wonder how reliable, i.e. how unequi-
Dobrovolskis, A.R.; Burns, J.A.: 1984, Icarus 57, 464. vocal, is the result you get. The unknown pro-
Dollfus, A.; Zellner, B.: 1979, in: Asteroids (Ed. T. perties for which you have to solve are the
Gehrels: Univ. Arizona, Tucson), p.170. shape, the albedo pattern, and the rotational
Dohnanyi, J.S: 1970, J. Geophys. Res. 75, 3468. state.
Farinella, P.; Paolicchi, P.; Tedesco, E.F.; Zappala',
V.: 1981, Icarus 46, 114.
Farinella, P.; Paolicchi, P.; Zappala', V.: 1981,
Astron. Astrophys.104, 159.

118
 Harris: Russell(1906) demonstrated that cer- it is impossible to deduce the pattern of
tain conclusions can be drawn from a light- albedo variegation frcm the lightcurve. Ke-
curve observed from an equatorial aspect and eping these items in mind, the evidence is
at low phase angle : 1) The presence of any very strong in favor of some pattern of al-
odd harmonic higher than the first indicates bedo variegation on Vesta (i.e., the first
non-geometric scattering; 2) The presence of harmonic is present at all observed aspects
a first harmonic indicates non-geometric scat- nnd phase angles). Beyond a simple statement
tering (unlikely) and/or albedo variegation that it exists, any attempt to derive a map
(almost certainly); and 3) A light curve with or to make physical interpretations based on
no odd harmonics can be due to shape only, a constrained solution for the pattern of
but may also be due to albedo variegation variegation is very dangerous.
non-geometric scattering. He also noted that

11./
13.0
 EFFECTS OF NON-TRIAXIAL SHAPE ON THE DETERMINATION OF THE ASTEROID
SPIN AXIS DIRECTION VIA THE AMPLITUDE-MAGNITUDE METHOD

A. Cellino, V. Zappala, and M. Di Martino

Osservatorio Astronomico di Torino

I- 10025 Pino Torinese(TO), Italy
At present, the Amplitude-Magnitude (AM) method is largely applied for determining the spin axis
direction of asteroids; such a method gives results which are in general in a good agreement with tho
se obtained by means of essentially different methods. However, one of the critical assumptions of
the AM method is that asteroids are modelled as triaxial ellipsoids with semiaxes a > b > c . Although
such an hypothesis appears reasonable for large objects on the basis of physical considerations about
their expected equilibrium shapes, very irregular figures are more plausible for smaller objects, pro
bably dominated by solid-state forces. Therefore, it is worth-while to study the influence that devia
tions from a purely triaxial ellipsoid shape can have on the derived spin axis direction. For this pu
rpose, a numerical program has been developed in order to compute the lightcurves of irregularly sha-
ped objects at given aspect angles. The present paper reports some preliminary results concerning the
uncertainty of the rotation axis direction of asteroids when non-triaxial shapes are considered.

1. INTRODUCTION 2. THE NUMERICAL PROGRAM

During last decade, special efforts have been devo- In order to analyse systematically the influence of
ted to the determination of the spin axis direction of deviations from a regular triaxial ellipsoid shape, it
asteroids. In fact, the knowledge of this parameter is necessary a general model for which the variation
for a large number of objects can provide important in of a few parameters can describe a wide range of irre-
formation about the origin and the evolution of the mi gular but "realistic" shapes. For this purpose, we ado
nor bodies in the Solar System. pted a model formed by merging together eight differe-
The problem of the determination of the spin axis d^ nt octants of ellipsoids having different semiaxes,
rection of asteroids has been solved by different tech provided that adjacent octants have equal semiaxes. As
niques, but mainly using observational parameters ext- "reference" body we have choosen a triaxial ellipsoid
racted from the lightcurves of the objects. Among the having semiaxis ratios b/a = 0.7, c/a = 0.5. These va-
main methods, the so-called Amplitude-Magnitude (AM) lues are in agreement with the results obtained in la-
method (Zappala,1981; Zappala et al.,1983), is based boratory experiments of catastrophic impacts, in which
on the assumption of a triaxial ellipsoid shape for it has been shown that the creation of fragments with
the objects to be studied. Such an assumption has been this mean shape seems a very general rule(e.g., Fuji-
proved to be plausible in the case of large objects wara, 1986); furthermore, this tendency is consistent
(diameter D > 150 km), for which self-gravitation can with statistical approaches on real asteroids (Catullo
play a fundamental role in determining their equilibr- et al., 1984). On the other hand, such a shape gives
ium shapes {Farinella et al., 1981). quite large lightcurve amplitudes for aspect angles ne
On the other hand, deviations from regular triaxial ar 90° ( A ~ 0 . 4 mag).
ellipsoid shapes should be expected for small asteroids, The deformations of the reference object have been
thought to be rocky outcomes of catastrophic events, carried out in the following way: taking a=l as length
whose shape are mainly dominated by solid-state forces. unit, and fixing as constants the sums of the semiaxes
Even if very irregular shapes are in principle recogni 2a = a + a = 2; 2b = b + b = 1.4; 2c = c + c =1,
zable on the basis of the morphology of the observed we have varied, separately ana not, the ratios a 7a,
lightcurves, how they can affect the determination of b /b, c /c from 0.1 to 0.7, obtaining a large set of
the rotation axis is still an almost unknown problem. different shapes.
The aim of the present analysis is to evaluate the The simplest way to compute the corresponding light
errors introduced by applying the AM method to objects curves is to approximate the surface by a polyhedron
which largely differ from regular triaxial ellipsoids. formed by a number of plane facets. Obviously, the ap-
This study assumes a particular importance mainly in proximation is better, increasing the number of facets.
consideration of future applications of this method to As an example, Fig. 1 shows an object having a /a=0.50,
a large set of objects of moderate size, as a larger b /b=0.45, c /c=0.30, seen at 45° aspect angle.
number of photoelectric observations will become avai- The computation of the total apparent area (i.e.,the
lable. "luminosity") is performed adding together the contri-
We should notice that the presence of albedo features butions of all the small plane facets constituting the
on asteroid surfaces can be another source of errors polyhedral surface: each of them can be illuminated or
in the determination of the poles;- we will neglect not, visible or not, and presents a varying cross-sec-
this effect in the present paper, where we concentrate tion to the observer, as the rotation of the object a-
on the shape effect only. The effects of albedo featu- round its axis changes the configuration of the facets.
res have been analysed, for instance, in a paper con- Thus, a lightcurve is obtained repeating the calculati
cerning the asteroid 4 Vesta (Cellino et al., 1987). on at different rotational angles from 0° to 360°.

121
 4. RESULTS AND DISCUSSION

Table I lists the cases we have considered in our sj.

mulations; the columns give: the semiaxis ratios a /a,
b /b, c /c, the coordinates of the computed poles, and
the values of the errors A defined as

&= ((A - A I2-* ( /5 0C - F>o)2)/i

It is easy to see that the computed poles differ mo-
Fig.l: view of an object with a /a=0.50, b /b~0.45,and re from the true pole as the shape becomes more irregi.
c /c=0.30 at 45° aspect angle. lar, as obviously expected. However, the situation is
more complex in the sense that the solutions are sens^
It is well known that the observed lightcurves of re tive in different ways to strong deformations of the
al asteroids depend also on the scattering of the re- object along different axes. For instance, modifying
flected light on the asteroid surface. This effect de- the a /a ratio gives in general smaller errors than mo
pends in a complicated way on parameters like surface difying the b /b ratio.
composition, topography,roughness, etc., and it is mo- Except some cases (discussed later) in which it was
re pronounced as the phase angle increases. On the not possible to find the pole on the basis of the gi-
other hand, when OC =0°, the effect is qi'tte negligible ven lightcurve amplitudes and magnitudes, we see that
especially when low-albedo objects are considered (Lu- in general the errors are not huge, the parameter A
pishko et a.'., 1983; French and Veverka, 1983). In real ranging from a few degrees up to ?0-30° in the worst
cases the observations are never performed at exactly cases. However, in these cases the shape of the objec-
0° phase, but the extrapolation of the observed light- ts is in general so far from a regular triaxial ellip-
curve amplitudes A and magnitudes at maximum V(MAX) to soid that the morphology of the resulting lightcurves
OC =0° is generally possible, provided a certain num- differs sensibly from what has to be expected for a re-
ber of lightcurves at different phases are available. gular ellipsoid; it follows that one can easily know
In this preliminary stage of our study, we have assu- "a priori" that the application of the AM method should
med always (X =0°, and we have neglected the scattering be considered mostly indicative, and comparison with
effect, so that, for a given model, the resulting light different methods for pole determination should be very
curves will depend only on the aspect angle £ . auspicable for a reliable solution.

3. ORBITAL PAHAMETERS AND POLE CALCULATION Table I

List of numerical simulations (see text)

Before to perform the simulations, it has been neces-
sary to determine the relationships connecting the ec-
Pole: \ 45° 0 . 45°
liptic coordinates with the aspect angle £ . To do so,
the i.: .:. MX ii direction of the object' and its orbital a /a b /b c /c Computed Pole
1 1 1
para. .•:'-.; pr.ve been fixed. For what concerns the lat- X (3
ter -• ive choosen values typical of main belt
0.1 1 1 52" 22 24.04
ast-.'. . i.l AU, e*0.1, i=10«, a) = Q =100°); the
0.3 1 1 50 28 17.72
pole •••• •.' 3 were fixed at A = 45°, jj = 45°. 0.5 1 1 48 37 8.54
In L;vj _ oT real observations the pole determina- 1 0.1 1
tion is per: .:rmed on the basis of lightcurvee obtained 1 0.3 1
1 0.5 1 39 56 12.53
at different positions cf the asteroid on the celestial
1 1 0.1 26 67 29.07
sphere. The knowledge of the observed lightcurve ampli- 1 1 0.3 40 53 9.43
tudes and magnitudes at maximum, and of the correspon- 1 1 0.5 44 48 3.16
ding coordinates A and |3 of the asteroid allows to 1 1 0.7 45 46 1.00
compete the aspect angle £ at each observation, and 0.1 0.1 1 46 41 4.12
thus to derive the pole coordinates A and ft 0.1 1 0.1
OC " OC 1 0.1 0.1
0.3 0.3 1 47 38 7.28
In ort'er- to reproduce this situation in our numerical 0.3 1 0.3
simulai.ions fin which, obviously, the aspect angle is 1 0.3 0.3
known "a prv:ri" and allows to compute the lightcurve 0.5 0.5 1 44 46 1.41
of an -,..:j.-<- .jt any position), we have choosen four va 0.5 1 0.5 39 57 13.42
1 0.5 0.5
lues : ' conveniently spread over the celestial as_ 0.5 0.5 0.5
tero: ,'.'• corresponding to aspect angles ranging
from "••.:* t" its minimum value. Then, the corresponding However, even in these caBes the errors of the AM me-
lightcurves vure obtained by the numerical program, thod lie between 20" and 30°, which is an acceptable
and '..he amplitude vs longitude and V(MAX) vs longitude result at least for statistical purposes. Furthermore,
relationships were used as input for the application we have to notice that the ecliptic longitude of the
of the AM method (Zappaia et al.,1983). In such a way computed pole is in general more reliable than the e-
the values of the coordinates of the "computed" pole cliptic latitude, the error of A being about half
(and of the semiaxis ratios) could be compared with the of the error of JJ . oc
"real" assumed values. The discrepancies allow to evalu
Figs.2 and 3 show the results obtained for two extr£
ate the sensitivity of the AM method to the changing of
me cases among those listed in Table I. The figures pre
shape of the model.
sent the Hghtcurves corresponding to the four values
of the choosen longitudes, a view of the object at mi-
nimum and at 90° aspects, the A-V(MAX) plot with the

122
 I. fi SP.= 90*. flflP.« 0?39 UO « 0?7S fll ' O.SO HZ • l.SO
2. fl SP.= 10S. flnp.= 0 . 2 9 UO * O.?2 Bl = 0 . 7 0 82 = 0.70
S. fl SP.= U S . nnp.= D.16 UO • 0.E5 Cl = (i.SO C2 = D.SO
4. R SP.= 123. flnp.= 0 . 1 4 JO » 0.62
PHRSE = 0. OBL. = 0. MO SCATTERING

fl/B = l.«3

8.30

I
0.00 30.00 1B0.0O 270.00 36D.30 w
0.00 0.20 0.10 0.60 0.80 1.00
ROTflTrON flGE Fig. 2 flflPLlTUDE

n
1. fiSP.= 90° finP.= 0. UO = 0" 7 2 fll = 0.10 fl2 = 1.90

2. flSP.= 106. finp.= 0 . 4S UO = 0 . 5 8

Bl = 0.70 B2 = 0.70
3. flSP.= 118. flnp.= 0 . 38 UO = 0 . 4 9
Cl = O.OS C2 = 0 . 9 S
4. flSP.= 123. flnp.= 0 . 34 UO = 0 . 4 5

= 0. OBL. = 0. « 0 SCflTTERIMG

POLE MOT FOUMD

"0.00 90.OD 180.00 J70.00 360*00 0.40 O.&0

ROTRTIOh flG flnPLlTUDE
Fig. 3

123
"observed" points and the best-fit curve (see later). As a conclusion of this preliminary study, we thir.fc
For what concerns the cases for which no solution that realistic errors in the asteroid pole determina-
was found, wo have to notice that they refer to Simula tions could be even lees than 10° in favourable cases,
tions where the b/e ratio could not be computed by mea i.e., when we consider objects for which reliable pho-
ns of the A-V(HAX) relationship. In fact, for a trlaxl- tometric data exist, and the lightcurve morphology and
al ellipsoid with a given a/b ratio, the A-V(HAX) rela the trend of the A-V(MAX) curve are in agreement with
tionship is function of the b/c ratio and belongs to a a triaxial ellipsoid shape. In less favourable cases,
family of curves, some of which are shown in Fig.4. In the reliability of the solutions is lower, but the
our computations the "observed" lightcurve amplitudes presence of significant deviations from a regular tri-
andV(MAX) are fitteci by a curve of this family compu- axial ellipsoid shape should be "a priori" expected
ted by means of least-squares. However, in some ca- both from the lightcurve morphology, and mainly from
ses, it is not possible to find any curve corresponding the A-V(HAX) trend. However, we cannot reach definiti-
to plausible values of b/c ratio, as, for instance, re ve conclusions, at this stage; a larger number of simu-
ported in Fig.3,where tiie trend of the points is evi- lations are needed in order to study the behaviour of
dently not compatible with any curve of the expected the solutions when different "true" pole positions are
kind. This happens mostly when the shapes of the models considered, different laws of scattering and large
largely differ from regular ones. We would like to st- phase observations are taken into account, etc.
ress that in the case of real observations the trend or More complex simulations are planned for the near fu-
the A-V(MAX) relationship is decisive for inferring si- ture, and the corresponding results will be published
gnificant deviations from the triaxlal shape and, con- in forthcoming papers.
sequently, for the application of methods like the AM.
On the other hand, when it is possible to fit the ob- REFERENCES
served amplitudes and magnitudes by means of a "regu-
lar" curvedn the sense of Fig.4), we can be very con- Catullo.V..Zappala.V..Farinella.P..Paolicchi,P.:1984,
fident that the shape is almost triaxial and the pole Astron.Astrophys. 138, 464.
determination is quite accurate. Cellino.A., Zappala.V., Di Martino.M., Farinella.P.,
Paolicchi,P.:1987, Icarus 70, 446.
Farinella,P., Paolicchi,P., Tedesco, E.F., Zappala.V.:
1981, Icarus 46, 114.
French,L.M., Veverka,J.:1983, Icarus 54, 38.
Fujiwara,A.:1986, in "Catastrophic disruption of aste-
roids and satellites", eds. D.R.Davis,P.Farinella.P.
Paolicchi,V.ZappalS. Mem.Soc.Astron.lt. 57, 47.
Lupishko.D.F.,Akimov,L.A., Belskaya.I.N.:1983, in "As-
teroids, Comets, Meteors", eds. C.-I.lagerkvist and
H.Rickman, pp. 65-70. Uppsala Universitet Repocentra
len HSC, Uppsala.
Zappala.V.:1981, Moon Planets 24, 319.
Zappala.V., Di Martino.M., Farinella, P., Paolicchi,P.:
1983, in "Asteroids, Comets, Meteors", eds. C.-I.La-
gerkvist and H.Rickman, pp.73-76. Uppsala Universitet
Repocentralen HSC, Uppsala.

D I S C U S S I O N

Kne2evic: Do you have some recipe to distinguish

between various shapes that all fit the same
observed lightcurve?
We have to notice that the pole solutions found by T e l l i n o : For the moment, we can only say whether
least-squares have in general mean quadratic errors mu or not a given object differs significantly from
a regular triaxial ellipsoid. The exact shape
ch smaller than the corresponding A . This is proba- cannot be derived sasily.
bly due to the fact that with the fixed parameters a
moderate range of aspects (and consequently of ampli-
tudes) is available. It follows that the reliability
of the b/c solution could be quite low. However, in re
al cases the possibility to cover a wide range of aspe
cts is not only due to observational problems, but to
the actual position of the pole itself. In fact, for a
quasi ecliptic orbit and for rotation axes close to the
ecliptic pole, the range of possible aspects decreases
sensibly. Implying less accurate values of the compu-
ted poles. Thi3 fact evidences the necessity to enlarge
the present preliminary analysis to different pole po-
sitions, in order to create an "error map" on the whole
celestial sphere.

124
METEOROID STREAMS ASSOCIATED WITH APOLLO ASTEROIDS : EVIDENCE FROM THE ADELAIDE RADAR
ORBIT SURVEYS.
Duncan Olsson-Steel
Lund Observatory, Box 43, S-22100 Lund, Sweden;
and The University of Adelaide, Australia.

Since the discovery of Phaethon (the 'Geminid asteroid1) in 1983 there has been renewed interest
in the association of meteor showers with Earth-approaching asteroids. In the past the existence
of several streams associated with different asteroids (in particular Adonis, Apollo, Hermes and
Oljato) has been suggested but not proven.
Here the 3759 meteor orbits determined at Adelaide in the 1960's have been compared to the
orbits of all known Aten-Apoilo-Amor asteroids using a new and powerful search technique. Strong
evidence is found for streams associated with Apollo-type asteroids Icarus, Hermes, Adonis, Oljato,
Hephaistos, 5025 P-L, 1982 TA, and 1984 KB; the final five in this list may be members of the
Taurid-Arietid complex, as is Comet P/Encke.
No stream associated with 1862 Apollo was identified, but this may be due to the lack of obser-
vations at the appropriate solar longitude. No streams associated with any Aten or Amor asteroid
were found: this may be due to the limited detectability of their meteors, if they exist, because
of their low geocentric velocities. In general streams were discovered for all asteroids coming
within 0.1 AU of the Earth, having radiants observable from Adelaide and atmospheric velocities
above about 22 km/sec : this suggests that meteoroid streams are a general feature of Earth-
approaching asteroids.

1. Introduction
The dynamical lifetimes of Aten-Apollo-Amor (here- was found in 1983 when the Geminid parent, asteroid
after AAA) and Mars-crossing asteroids are of the 3200 Phaethon, was discovered by the I M S (Davies,
order of 10' - 108 years: this is much shorter than 1986). There is therefore renewed interest in look-
the age of the solar system so that a replenishing ing for meteor activity linked with AAA asteroids,
source is required (e.g. Rickman, 1985). Opik (1963) and this paper describes a search for such links
suggested that these asteroids are at least in part amongst the radar meteor orbits determined from
the moribund cores of defunct comets which no longer Adelaide, South Australia, in the 1960's. A new and
show obvious comet-like activity. Although a mech- powerful search technique is used, which for the
anism whereby such bodies could be dynamically first time allows a stream to be recognized when it
perturbed from the asteroid belt into planet-crossing has similar orbital characteristics as the sporadic
orbits has now been found (Wisdom, 1983; Wetherill, background. It is shown that there are several cases
1985) there are still reasons to believe that an of Apollo-type asteroids possessing meteoroid streams
interlinkage exists. Despite the fact that there and that for all other Apollos the absence of a
are general dynamical differences between comets and detected stream may be explained by the fact that
asteroids (Whipple, 1954; Kresak, 1984), there are they do not pass sufficiently close to the Earth for
asteroids in comet-like orbits (Hahn and Rickman, stream-intercept to occur, their geocentric velocit-
1985) and equally well P/Encke could be said to be on ies (and hence meteor ionizing efficiencies) are too
an asi.eroid-like orbit. In addition, physical low, the radiants are too far north to be detected
studies of comets and AAA's have shown a lack of from Adelaide, or no data were collected near to the
clear distinction in many cases(Davies, 1986; Hart- times when the radiant might be active.
mann et al., 1987): particular examples are 2201
Oljato (McFadden et al., 1984, 1985; Russell et al., 2. The Adelaide Data
1984), and 2101 Adonis (Ostro, 1985). Thus, the
differentiation between asteroids and comets which Two radar meteor orbit surveys have been conducted
has historically been based upon telescopic appear- by the University of Adelaide (35°S), and these are
ance has become blurred and much similarity is now the only surveys yet conducted from the southern hemi-
recognized. sphere although a new program is now commencing in
New Zealand (Steel and Baggaley, 1985). The first
Another feature often associated with comets, at Adelaide survey ran from 1960 December to 1961 Decem-
least those which approach the Earth to within about ber and resulted in 2092 individual orbits to limiting
0.1 AU, is the existence of meteor showers and hence magnitude +6 (Nilsson, 1964). Generally observations
meteoroid streams which follow the heliocentric were made for about one week every month, although
orbit of the comet in question. These streams are there was a special campaign straddling July/August
formed from the larger dust particles ejected by the since in the southern hemisphere the greatest meteor
comet each time it passes perihelion. The assoc- activity Is seen at that time of year (Keay and
iation of such showers with comets has been well- Ellyett, 1969). The second Adelaide survey was con-
known for over a century (e.g. Porter, 1952; ducted at the end of that decade, and meteors to
Drummond, 1981) and generally comets have been reg- limiting magnitude +8 were detected. A total of 1667
arded as being the major source of meteoroids, with orbits of meteors observed in 1968 December and 1969
non-shower or sporadic meteors originating in the January, February, March, June and October were
disruption of streams by planetary close encounters computed and the results published by Gartre11 and
(Olsson-Steel, 1986). Although there had previously Elford (1975). Again the observation periods only ran
been many suggestions of possible associations between for up to a week in each month, so that short showers
meteor showers and Apollo asteroids (for example, occurring in the other three weeks of each month, or
Hoffmeister, 1948; Sekanina, 1973, 1976; Drummond, in the other six months of the year in the case of the
1981; Babadzhanov and Obrubov, 1983), the first later survey, would not have been detected. In addit-
incontrovertable link between an asteroid and a shower ion, due to the southerly observation site few Meteors

£25
with radiants north of 30°N were observed. Thus entering any value for the nodal longitude a, always
there are many showers, and theoretical radiants of about the same number of 'correlated' meteor orbits
possible parent objects, which could have not been would be found.
detected by these surveys. However, if in reality the data set is non-random
Further details of the Adelaide radar meteor orbit and streams exist, then a larger number of correlated
surveys, including radiant and orbital element dist- orbits would be expected near to n = n 0 than at any
ributions, have been given by Olsson-Steel (1987a). other value of n. For example, if (qo,eo,io,ao) are
The individual orbits are now archived at the IAU given the real values for 3200 Phaethon, then many
Meteor Data Center at the Lund Observatory, Sweden. more correlated meteors are found at i! = 240° - 290°,
and n(Phaethon) = 265° (cf. Figure 1). There are
3. The Stream-Search Technique many fewer similar meteor orbits at all other values
of a : these are part of the sporadic background,
When inspecting large data sets such as those prod- the peak being due to the Geminid shower of which
uced by radar meteor orbit surveys for patterns Phaethon is the parent. The plot for this asteroid
which might indicate the existence of a meteoroid might be considered to be the ideal form of result
stream, account must be taken of the gross distrib- from this new form of analysis, since it results
ution of each of the orbital elements in the data from a strong and distinct stream originating from
set; the search is made especially difficult since a parent with orbital characteristics almost
not only is there 'noise1 in the form of sporadic identical to those of the well-studied stream. A
orbits (the 'signal' being the stream orbits), but similar (but perhaps noisier) form would be expected
also the individual orbits are 'noisey' in that the for other objects which are the parents of substant-
imprecision of the radar measurement techniques means ial numbers of meteors detected in the Adelaide
that the individual elements are not well-determined. surveys.
If a stream has one or more elements which are
distinct from the majority of the sporadics then the 4. The Aten-Apolio-Amor Asteroids
recognition of the stream is relatively straight-
forward: a preponderance of orbits with measured As expected, several of the comets known to be
elements i = 160°- 170° and q • 0.5 - 0.7 AU occurs meteor-producers show evidence of streams in the
only in Nay and October each year, and these are the Adelaide data. However the strongest showers,
Halleyid showers; similarly orbits of large semi- judging from the numbers of correlated meteors which
major axis, q a 0.15 - 0.20 AU and i a 35" - 40° are found, appear to originate from some of the
occur only in December and these are from the Mono- Apollo asteroids; in particular the largest number of
cerotid stream. associated meteors Is found for Jupiter-crossing body
However the bulk of the orbits in any survey do 5025 P-L, and this asteroid along with 2201 Oljato,
not have any such unique characteristics: they are 2212 Hephaistos, 1982 TA and 1984 KB may be part of
mainly of low inclination (i < 20°), semi-random the Taurid-Arietid complex (Bailey et al., 1986;
perihelion distance (q), small semi-major axis Olsson-Steel, 1987c). No streams were found for any
(1.5 < a < 3 AU), moderate to large eccentricity of the Aten or Amor asteroids, and this could be due
(0.5 < e < 0.99), and semi-random argument of peri- to their low geocentric velocities at aphelion and
helion (<D): for example see the orbital distributions perihelion respectively, this limiting the meteor
plotted by Olsson-Steel (1987a), or for the Harvard detectability; also for a shower originating from an
surveys by Sekanina (1973, 1976). Any search based Amor to be detectable the stream would have to be
upon a single orbital element, or using the multi- quite diffuse at perihelion so as to allow some met-
element orbital discriminants of Southworth and eoroids to be Earth-crossing, and this would hinder
Hawkins (1963) or Drumnond (1981), may find a large the recognition of a coherent stream.
number of meteor orbits which appear similar to the Considering now only the Apollo asteroids, the
orbit of a particular short-period comet or AAA following process (as outlined in section 3) was
asteroid, but this may be due to a concentration of carried out. All 49 Apolios discovered through to
sporadic orbits of similar gross characteristics. the end of 1987 June (i.e. up to and including the
Thus the mere fact that a test orbit is similar to a re-discovery of 1959 LM = 1987 MB) *iere studied, and
large number of meteor orbits may be misleading: for for each the parameters (qa,ea,i0 ,a0) were used,
example, on the basis of the D-criterion of South- along with values of a running from 0°to 360°in 5°
worth and Hawkins (1963) Comet 1770 I Lexell has more steps; at each longitude n the values of 0 (South-
correlated orbits in the Adelaide data than any other worth and Hawkins, 1963) and 0' (Drummond, 1981) were
comet, but nevertheless it is doubtful whether any calculated using each of the 3759 meteor orbits: thus
stream is genetically associated with it (KresSkova', a total of 49 x 72 x 3759 x 2 a 26 million orbital
1980; Olsson-Steel, 1987b). comparisons were necessary. A meteor was judged to
be associated with the test orbit if D s 0.20 and/or
The new stream-search technique used here over- D' i 0.125. Several of these Apollos do not pass near
comes these drawbacks, as follows. For either D- by the Earth so that even if the asteroid did possess
criterion (Southworth and Hawkins, or Drummond), a meteoroid stream it would not have been detected.
0 * function {q ,e ,i ,u ,0 ,qi,e,,ii,ui,ai) Of the 49 Apollos, 11 have at least N - 10 assoc-
0 0 0 0 O j J J J J iated meteor orbits on the basis of D and/or D' at the
where the subscript '0' denotes the test object (the 'real' value of the nodal longitude, n » a,. These are
asteroid or comet) and the 'j' denotes a particular all shown 1n Fig. 1, along with 1862 Apollo (which has
meteor orbit (I.e. j = 1 to 3759 for the Adelaide often In the past been suggested as a shower parent)
data). Assuming the Earth's orbit to be circular, and also 1986 JK (another possible meteor progenitor:
the closest approach distance by the asteroid or D n M o n d . 1986). In each case N Is plotted against n
comet is: and the value of n» is Indicated. Recalling the comm-
ents In section 3 concerning the archetypical plot
do function (q ,e ,i ,v> ) * function (n ) for 3200 Phaethon and Its Strong, well-known stream
and d. « 0 for the ometeor
• o else
o it would noto have been (the Gen1nids) It is Immediately apparent that
observed. Sine* do does not depend upon the longit- 5025 P-L, 1984 KB and 1566 Icarus possess streams, as
j<ie of the ascending node (Jo , if the data set were shown by the strong peak In N very close to n = St.;
M d e :ia entirely of randOM sporadic orbits then for Icarus has been suggested as a shower parent in the
any particular (? ,eo,io,u.) the number of correlated past (Setanina, 1973, 1976). Additionally 1982 TA,
orbits on the basis of either D would be approximately 2201 Oljato and 1937 UB (Hermes) also show the char-
constant, and hence independent of n, ; thus by acteristic form expected for an associated stream,
although with the peak in N offset slightly from n,.

126
 2201 OLIHT0

(I)
o
a)
-p
0)

0)

o
)

a) 2101 fCONIS
XI

2 2 1 2 HEPHFIISTOS

19B2 Tfl

Longi-buds of flscending Node (degrees)

Figure 1. The number of correlate! Adelaide meteor orbits for various Apollo asteroids. The real orbital
parameters of each asteroid were u,ed, except that the longitude of the ascending node was varied from 0° to
360° to find out whether there is a concentration of meteor orbits with ( q, e, i, a) similar to the elements
of the asteroid at a particular nodal longitude n. The vertical line terminated by crosses shows the real
value of n for each asteroid.

127
 This may be due to the Earth presently passing through Acknowledgements
the edge of the stream rather than the core centered This work was partially supported by ARGS grant num-
on the parent. An alternative explanation, which ber B 8415432. During 1987 the author is European
might also apply to 2101 Adonis and 2212 Hephaistos Space Agency Fellow at the Lund Observatory. Dis-
for which the peak in N is wel1-separated from n 0 , is cussions with Dr.B.A.Lindblad are appreciated.
that the stream meteoroids have orbits which have
shrunken slightly under the Poynting-Robertson effect
and therefore suffer differential secular parturbat- References
ions compared to the parent asteroid on a larger Babadzhanov, P.B.; Obrubov, Yu.V.: 1983, in Asteroids,
orbit (Babadzhanov and Obrubov, 1984). The final four Comets, Meteors (Eds. C.-I.Lagerkvist and H.Rick-
Apollos (1862 Apollo, 1959 U1, 1983 LC and 1986 JK) man; Univ. of Uppsala, Sweden), p.411.
show no evidence of streams, and have elevated values
of H at all n (i.e. high 'noise') since each of the Babadzhanov, P.B.; Obrubov, Yu.V.: 1984, Soviet
four has i < 8°; such a low inclination is typical Astron. J., 61, 1005.
for the sporadic background meteors. Bailey, M.E.; Clube, S.V.M.; Napier, U.M.: 1986,
Victas Astron., 29, 53.
5. Do all Apollo asteroids have meteoroid Davies, J.K.: 1986, Mon. Not. Roy. Ast. S o c , 221,19P.
streams ?
Having discussed above and shown in Fig. 1 those Drwmond, J.D.: 1981, Icarus, 15, 545.
asteroids which appear to have meteoroid streams for Drwmond, J.D.: 1986, IAU Circ. 4220.
which there _ij» evidence in the Adelaide data, next it Gartrell, G.; Elford, W.G.: 1975, Australian J. Phys.,
is necessary tc examine those asteroids for which 28, 591.
evidence is not found. As previously mentioned, no
Amor or Aten asteroids rendered detectable showers in Hahn, G.; Riohnan, H.: 1985, Icarus, 61, 417.
these data, and this may in part be due to their low Hartmann, U.K.; Tholen, D.J.; Cruikshank, D.P.: 1987,
geocentric velocities: the ionizing efficiency is a
strong function of the velocity. A similar comment Icarus, 69, 33.
applies to the Apollo asteroids: if they have low Hoffmeister, C: 1948, in Meteorstrome (Verlag
geocentric velocities then their meteors will have Johann Ambrosius Barth, Leipzig).
low radar-detection probabilities. Denoting the vel- Keay, C.S.L.; Ellyett, CD.: 1969, Memoirs Roy. Ast.
ocity at the top of the atmosphere (i.e. after accel-
eration by the Earth's gravitational field) by Vo, the S o c , 73, 185.
asteroids in Fig. 1 which do seem to have streams have Kresdk, L.: 1984, Space Sci. Rev., 38, 1.
velocities ranging from Vo s 35 km/sec for Phaethon Kresdkovd, M.: 1980, Bull. Astron. Inst. Czechosl.,
down to Vo = 22 km/sec for Hermes, whereas the final 31, 193.
four (1862 Apollo, 1959 LH, 1983 LC and 1986 JK) all
have Vo < 21 km/sec: this suggests that the low values MoFadden, L.A.; Gaffey, M.J.; McCord, T.B.: 1984,
of Vo may have hindered the detection of such streams Icarus, 59, 25.
as may exist. In fact of the original 49 Apollos McFadden, L.A.; A'Hearn, 14.P.; Millis, R.L.;
studied here, 33 come within 0.1 AU of the Earth but Danielson, G.E.: 1985, Science, 229, 160.
do not have streams recognized in the present analysis.
Of these 33, 22 have Vo < 21 km/sec, and a further 3 Nilsson, C.S.: 1964, Australian J. Phys., 17, 205.
have 21 < Vo < 22 km/sec. Of the remaining 8 Apollos
from the 33, the absence of detected streams can be Olsson-Steel, D.: 1986, Mon. Not. Roy. Ast. S o c ,
explained either by the theoretical radiant being too 219, 47.
far north, or else the absence of data collection at
the longitude of closest approach by the asteroid Olsson-Steel, D.: 1987a, Icarus (submitted).
orbit to the Earth (cf. section 2, and Olsson-Steel, Olsson-Steel, D.: 1987b, Astron. Astrophys. (subm.).
1987a): in fact at the times of closest approach by
1862 Apollo (the middle of Hay and prior to the middle Olsson-Steel, D.: 1987c, The Observatory (August).
of November) no data were collected so that this anal- Opik, E.J.: 1963, Adv. Astron. Astrophys., 2, 219.
ysis does not contradict the positive results of Oatvo, S.J.: 1985, Publ. Astron. Soc. Pacific, 97,
previous researchers (e.g. Hoffmeister, 1948; Seka- 877.
nina, 1973, 1976). however, Babadzhanov and Obrubov
(1983) have pointed out that caution must be applied Porter, J.G.: 1952, in Comets and Meteor Streams
when calculating theoretical radiants and times of (Chapman and Hall, London).
activity using osculating orbits of just the present Rickman, H.: 1985, in Dynamics of Comets: Their Ori-
epoch. gin and Evolution (Eds. A.Carusi and G.B.Valsecchi;
The above discussion may be summarized as follows Reidel, Dordrecht, Holland), p.149.
(see Olsson-Steel, 1987a for more details): Russell, C.T.; Aroian, R.; Arghavani, M.; Nock, K.:
Clear- evidence is found here for meteoroid streams 1984, Science, 226, 43.
associated with each of the Apollo asteroids for Sekanina, Z.: 1973, Icarus, 18, 253.
which the data collection times and techniques Sekanina, Z.: 1976, Icarus, 27, 265.
were favourable.
In other words, it appears that: Southuorth, R.B.; Hawkins, G.S.: 1963, Smithson.
Contr. Astrophys., 7, 261.
Meteoroid streams may be a general feature assoc- Steel, D.I.; Baggaley, W.J.: 1985, in Properties and
iated with Apollo asteroids. Interactions of Interplanetary Dust (Eds. R.H.
These streams may be evidence that the Apollos are Giese and P.Lamy; Reidel, Dordrecht, Holland),p.299.
currently-inactive or exhausted cometary nuclei; Wetherill, G.W.: 1985, Meteoritics, 20, 1.
alternatively the meteoroids may be collisional debris
lost by the asteroids in the present stage of their Whipple, F.L.: 1954, Astron. J., 59, 201.
evolution. Clearly there is much of scientific Uiedom, J.: 1983, Icarus, 56, 51.
import still to be gained from the various meteor
orbit surveys conducted over the past few decades,
and a re-analysis of the available data using the new
method described here should yield extremely signif-
icant results.

128
 D I S C U S S I O N

Babadzhanov: Your conclusion on the meteoroid Olsson-Steel : Many of these asteroids appear
streams and Apollo asteroids is correct if to be the parents of recurent annual streams
meteoroids were ejected recently. But mete- (1566 Icarus and the Daytime' Zeta Arietids;
oroids were ejected too long ago and we can- 3200 Phaethon and the Geminids 1982 TA,
not compare meteoroid streams and Apollo 1984 KB, 5025 P-L and the Taurid-Arietid
asteroids according to the D-criterion and complex, the parent of which has hitherto
similarity of their orbits because these been assumed to be comet Encke; 2201 Oljato
orbits differ significantly. So when comparing and the Chi Orionids, which is also part
the orbits of meteor streams and Apollo of that complex). Thus, it appears that the
asteroids it is necessary to take into account streams are complete loops rather than arcs.
variations of orbital elements as influenced The time-scale for loop-formation (due to
by planetary perturbations. radiation pressure and ejection velocities)
Olsson-Steel: The above comment is entirely is only " 1 0 years .
correct and this constraint implies that Napier: On the question of asteroidal (in a
these streams were formed within the past main-belt sense) versus cometary origins
3 4 for the Apollo asteroids examined: quite a
10 - 10 years. It would be interesting to
see what the time-scale is for collisions by few of the bodies are part of the Taurid-
boulders onto Apollo asteroids, and hence the -Arietid system, which has Encke s comet
possible production of such streams if they as a member. If we are to think of a common
were not formed when the "asteroids" were origin for these bodies, then presumably
"comets" . So these results imply either that they are inactive comets.
Apollo asteroids are often struck by large Olsson-Steel: Yes: possibly these asteroids
objects (/^lO m ? ) , or else they are the were once part of a larger body which
result of a recent enhancement in the number included Encke, or perhaps they represent
of comets. separate bodies which are in some other way
geneticaly related. The existence of one
Farinella: If confirmed, the result that all asteroid (5025 P-L) in a Jupiter-crossing
or most Apollos are associated with meteor orbits suggests that they (including Encke)
streams is very interesting. Instead of the were all part of a super-comet which was
usual "dead comet" interpretation, this could fractured in a close approach to Jupiter,
mean that meteors are collisional ejecta from with the bodies which did not quickly attain
real (-rocky) asteroids. The relevant impacts a small aphelion distance (Q<4.5 A0) having
had to occur recently enough (say,3 10 yr been rapidly ejected: 5025 P-L is then one
ago) to avoid strong changes of the orbital body which has so far managed to evade
elements due to planetary perturbations. Do ejection. The ejection time?scales suggest
you agree? that this occuredA/10 - 10 years ago.
Dlsson-Steel: This is a very useful and Kresak: The orbit of 5025 P-L is very poorly
interesting question which encompasses also determined. If you.take into account its
the comment of P.B. Babadzhanov. I agree uncertainty, how sure you are that the stream
with your comment, and the time scale you you have identified is associated with this
mention is appropriate not only for planetary asteroids, and not with P/Encke ?
perturbations, but also the time-scale for Olsson-Steel : You are correct that the orbit
the loss of if 1 mm meteoroids in Apollo-type is not well determined; however it i? better
orbits due to catastrophic collisions with known than the meteor orbits used here, so
zodiacal dust is (-W0 - 10 years) which the inaccuracy I largely discount. It is
puts an additional time-constraint onto the important to note that I do not suggest that
scene. 5025 P-L (or 1982 TA, or 1984 KB) are the
5chool: You said, you observe meteor streams parents of the complex rather than P/Encke:
associated with asteroids. Are you sure that I suggest here that they all appear to be
what you observe are complete streams ? Is related to the meteoroid complex and to each
it possible that these are fragments of other, and it seems likely that they were
streams what you observe? all at one time part of a single, much larger,
body. Other objects derived from this body
may be the Tunguska object and the Brno
fireball. A long-period comet (1967 II Rud-
nicki) may also be related.

/3o
 PRESENT STATUS OF PHOTOMETRIC PARAMETERS OF ASTEROIDS
Leif Kahl Kristensen

Institute of Physics - University of Aarhus

DK - 8000 Aarhus C, Denmark

ABSTRACT. The external accuracy of photometric parameters of asteroids is inves-

tigated by comparison of published lists. Absolute magnitudes are consistent at
the +0.1 mag Level but phase coefficients are still rather uncertain.

1. Introduction units of .001 mag/deg.

Intercomparisons between different cata- The mean values of the phase angles of the
logues are the standard procedure for esti- observations are not reproduced because
mating their random and systematic errors. these essential data are lacking in the com-
For consistent data an investigation of the parison data.
systematic differences between independent The second listing is essentially due
series of observations may result in impro- to E. Tedesco /1986/ and complete for all
ved accuracy by a combination of the data numbered planets. The photometric parameters
to a mean system. This level of development stated are H and G, defined in I.A.U.
and refinement has for a long time been rea- Transactions .19, B/1985/, 184. For 237
ched by catalogues of star positions, magni- objects or abmjt 7% of the total, G is
tudes, parallaxes and so forth. Our aim is based on a real determination but here we
to take a first step in this direction for are mainly interested in the subset of 78
photometric data of asteroids, - if possible objects, which are present in the two other
at all. lists. The distribution of G for 237 objects
The great difficulties in obtaining 1s nearly uniform in the interval 0<6<.35
reliable photometric data for asteroids are but a peculiar discontinuity at G"0~m'ay
well known. A main problem is that a great Indicate an artificial cut-off.
number of observations are needed in order
to eliminate lightcurve and aspect variati- The third list by Lagerkvist and Willi-
ons; if not eliminated, the observations ams /1987/ is based on a well-documented
wilL be degraded by a large, random-like and homogeneous observational material over
component. Another difficulty is due to the large phase intervals. Different oppositions
dependence of brightness on the solar phase with varying aspects are not combined and
angle /B/. The phase curves are assumed to we may expect the phase coefficient to be
depend on a single shape parameter determi- well determined. In 14* of the cases G is
ned by the surface texture. An additive negative. The adopted standard phase func-
constant, the absolute magnitude, depends tions fitted to the observations are clear-
on albedo and diameter. At present, the ly stated.
shape of the phase curves has to be determi- For the comparison it 1s convenient
ned empirically, and this raises two prob- that the quantities are approximately equal
lems: sets of accurate standard phase curves or at least similar. Phase functions are
must be determined and there is an inherent therefore specified by V and V', as defined
indeterminateness in the definition of the in Kristensen /1987/. The approximate nume-
shape parameter because any monotoneous fun- rical relation for the phase functions used
ction of this may be used as shape parameter by Lagerkvist et al. is:
as well. In practice, the first difficulty
reduces the weight of observations at small
phase and the second difficulty gives an V o • H + 0.31 - 0.27G IM
arbitrariness in the scale and ztro point V' = - .0234 + ,0687/(G + T.00) 12/
of the shape parameter.
Similar relations are valid for the phase
2. The data compared functions adopted officially by I.A.U. Comm.
Three recent lists, here denoted by 20. The deviations, mainly in V , are small
roman numerals I, II and III, have been com- and the transformations above mSy be used ir
pared. The first list III is an improvement all cases.
by Gehrels and Tedesco /1979/ of a long term
I.A.U. standard. This list states the classi- 3. Discussion
cal phase coefficients, the definition of Data I and II are consistent and espe-
which takes advantage of the approximate cially higher numbered objects are practi-
linearity of phase curves in tht range 6° p< cally Identical /for Instance nos. 20, 32,
< 20°. The straight line is specified simp- 51, 77, 78, 88, 89, ..../. However, the data
ly by its coefficient and zero phase value. base may partly be the same with a few im-
Apart from convenience in practice and fami- provements /for Instance 129/. In case II
liarity by long term use, this classical and III the data are independent and the
definition has the advantage that zero points absolute magnitudes /v / give the root mean
and scales are fixed within small limits. square difference .13 Mag. Unless the quali-
Tablt 1 gives .the asteroid number and V as ty of the two lists Is very different, this
the stated B/1,0/ corrected by the color suggests that their mean errors are of order
Index B-V, as given by Bowell et al. /1979/. 10.1 mag In V . in some cases /9, 29, 324,
The phase coefficients /V? are given in 451, 471, ..../ differences exist at the

131
 .3-.4 mag level which a r e not significantly 5. Kristensen L.K.: On the definition of
reduced at t h e phase angle o v e r l a p . asteroid magnitudes.
The phase c o e f f i c i e n t s are difficult tc Astron. Nachr. J5O8 /1987/ 135-138.
obtain and have errors of order
Table 1.
Absolute magnitudes V and phase coeffi-
cients V' in units °of .01 mag and .001
mag/deg for the individual planets numbered
in first column and for the data sets I, II,
where crol)s is the mean error of observati- and ill. Phase coefficients not based di-
on /often including a contribution from the rectly on observations are stated in italics
lightcurve/, A0 is the phase angle interval (in case II, possible values 26. 32 or 36).
over which N observations are supposed to be
uniformly distributed. The mean error depends
only on the distribution and quality of the No. nr No.
errors but not on the parameter /V'/ itself, 1 363 53 899 SO 502 35
38 360 3C2 38 40 32 75B 26
which would be the case for 6. Typical valu- 436 38 440 437 36 42 63 776 35 776
565 65 707 27 706 36
es in the well-documented case III are: 25 554 561 29 36
68 712 38 723 25
<r < 346 26 338 356 28 23
obs~ ' 2 /including lightcurve variations/ 743 15 715 713 32 35 69 728 35 737 36
N~30, and A|W20°; this gives * :~+.006 ( 602 28 595 32 77 B83 32 881 31
59B 34 40
577 38 580 593 32 31 78 B40 39 840
/corresponding to .08-.19 in G/. B 673 28 670 28 79 B20 32 809 35
665 34 B92 38
9 662 34 655 6B0 30 2B 86 31 879
The phase coefficients II and III are 10 564 36 88 733 36 731 35 743 38
566 40 6B4 37
6B6 31 89 38 684 690 43
plotted on Fig. 1. The points ought to con- 11 696 30
749
6B6
32
32
103 789 32 787 38
centrate near the line but show little 12 748 30 749 35 B07 35
13 681 45 69B 6B5 36 50 110 32 805
correlation. The correlation coefficient is 671 656 40 115 778 37 783 36
14 23 548 674 34 35 27
129 802 30 726 733 23
.29 and numerically there is no correlation; 15 550 38 535 32
16 620 28 623 33 617 3B 178 985 21 965 32
the picture is dominated by large random 17 804 37 831 30 192 748 42 743 43 746 37
errors. The only relation between the data 18 667 35 674 32 196 680 23 681 33
seems to be a common mean value: .034 in 19 737 39 743 47 200 850 40 849 41
case II and .037 in case III. 20 677 31 676 31 673 36 230 775 24 769 28 751 40
21 785 26 760 36 755 240 924 39 926 37
The error bars were not drawn in the 22 681 31 674 33 324 706 44 710 39 707 59
24 721 50 735 39 349 620 31 620 29 633 31
pLot because they were either not available 26 788 25 781 26 354 660 28 654 29 665 2B
or underestimated. An advantage of plotting 27 731 32 727 37 423 760 36 741 51
V versus v'is that errors on the average 28 742 33 736 32 433 1100 24 1D9B 32
29 616 31 609 33 626 45 451 689 36 691 34 674 B6
are uniform over the diagram^ any non-linear 30 79<\ 471 6B4 30 727 28
25 7B3 39
mapping /as for instance to G/ distorts 31 680 36 699 37 511 647 44 63B 42
this picture. 32 777 38 778 38 532 602 32 599 45
39 656 27 640 628 32 33 554 920 43 916 36
40 737 738 29 38 704 637 44 630 44 647 32
4. Conclusion 41 743 53 761 36 BB7 1409 42 1444 32
At present, comparisons between publis- 42 774 32 764 55 944 1083 50 1102 36
43 815 47 825 32 1566 1675 32 16B9 32
hed catalogues do not show systematic dif- 44 726 19 724 24 709 23 15B0 1429 36 :4B5 44
ferences and can only give an indication of 46 860 42 B66 39 881 29 1620 1591 30 1606 32
their external errors. Absolute magnitudes 51 767 42 765 41 752 51 16B5 1422 37 1426 43
52 656 36 660 31 2062 1743 27 1720 32
are consistent at the +0.1 mag level but for
phase coefficients the~use of individual
values is hardly better than the use of a
mean value /V ~ .035/. Albedo or taxcnomet- Figure 1.
tric considerations related to phase coeffi- Phase c o e f f i c i e n t s by Lagerkvist et a l .
cients may be uncertain. To improve our (Ill) plotted against t h e M . P . C . s t a n d a r d
knowledge about the physical properties of ( I I ) . D o t s mark p o i n t s with t h e smallest e x -
asteroids, it will perhaps be necessary that p e c t e d accuracy (large l i g h t c u r v e a m p l i -
the present great observational effort is t u d e s , small phase i n t e r v a l , few o b s e r v a -
concentrated on fewer objects. t i o n s o r G v a l u e s n o t determined by direct
u s e o f p h o t o m e t r i c d a t a ) . H i g h e r a n d highest
References a c c u r a c i e s a r e marked b y x and o . Even t h e
1. Gehrels T. and Tedesco E.F., Asteroid best data indicate n o c o r r e l a t i o n .
magnitudes and phase relations.
Astron. J. 84_ /1979/ 1079-1087. .050 /

2. Bowell E., Gehre'ls T. and Zellner B.:

cut-off
Magnitudes, Colors, Types and Adopted
Diameters of the Asteroids. In Gehrels T. °
/editor/:
Asteroids, Univ. of Arizona Press 1979 040
p. 1108.
3. Tedesco E., Marsden B.G.: Magnitude Para- »

meters for the Numbered Minor Planets.

Minor Planet Circular 11095-11108,. Minor • • / • K« •
Planet Centre, Cambridge, Massachusetts.
1986 September 18, .030 * -KM
• / O 1
4 . L a g e r k v i s t C~l and Williams I.P.: D e t e r -
m i n a t i o n of slope p a r a m e t e r s and a b s o l u t t •
* /
m a g n i t u d e s for 51 a s t e r o i d s .
Astron. Astrophys. suppl. Ser. 68 /1987/
295-315. — .020
020 .030 040 .050 .060

132
 UNUSUAL MOTION OF AMOR
K. Zioikowaki
Space Research Centre, Bartycka 18 S 00-716 Warsaw, Poland

Precise analysis of the orbit of minor planet (1221) Amor, based on all obser-
vations made in 1932-1980, shows that in 1956 there was an unexplained event in
the motion of the asteroid. Possible interpretations of that fact as well as pe-
culiarities in the long-term motion of Amor in 1650-2170 are discussed. The ephe-
meris of Amor for 1988 ia presented.

1. Tn "fcroduct ion a priori value of the mean residual of ob-

servations made in some oppositions with
The minor planet (1221) Amor belongs to the suitable value of the mean residual ob-
a group of objects which make relatively tained as the result of orbit improvement
close approaches to the Earth but do not based on the same set of observations and
overlap the Earth's orbit. Together with on a model of the asteroid motion can give
Apollo and Aten groups they constitute a uo some information about quality of the
class of the so-called Earth-crossing as- adopted model. When the mean residual com-
teroids, which are interesting due to their puted from the model of motion is closer
origin. For example, many of them appear to to the appropriate a priori value, we can
be extinct cometary nuclei. consider that the model is better.
Amor was discovered in 1932 by E. Del-
porte in Uccle when the minor planet appro- 2. What happened in 1956?
ached the Earth to within 0.108 AU. Its or-
bital period was found to be cloae to 8/3 Attempts to link all observations made
years. It means that after the time inter- in 1932-1980 by one system of orbital ele-
val of 8 years in which Amor makes 3 revo- ments showed that the motion of Amor is
lutions round the Sun, a close approache of. perturbed not only by n."- •• planets but also
the asteroid to the Earth should be repea- by some unknown forces. '-Jse effects are
ted. This fact gave a chance to observe the very small and it is easy to miss them du-
object, which is one of the smallest among ring the orbital computations. While Schu-
known Earth-crossers, every 8 years. bart (1969 J reported a special subterfuge
Up to now Amor was observed in 7 opposi- enabling to link 5 apparitions in 1932-1964,
tions from 1932 till 1980 (although Schu- Landgraf (1984) announced a successful de-
bart (1969) published ephemerides of Amor termination of the Amor's orbit from 261
for prediscovery approaches in 1924 and observations made in 7 oppositions.
1916, no earlier observations were found However, precise and deep analysis of
unfortunately). The observational material the course of residuals shows that in 1956
obtained during those apparitions is cha- the motion of Amor was disturbed by unknown
racterized in Tab. 1. A total number of factor. Namely it appears that a set of 43
279 observations were selected and weighted observations made in this opposition can
be distinctly divided into two parts:
Table 1 I. 24 observations from the period of
Feb 15 - Mar 20,
Observational material II. 19 observations from the period of
Apr 2 - Jun 5.
It is worth pointing out that on March 21
Oppo- Observational Number Mean Amor passed the Earth at the minimal dis-
sition interval of obs. residual tanoe of 0.115 AU, and that its perihelion
passage occurs on April 3.
1932 Mar 12 - Jun 9 89 1?49 The mean residuals of unit weight of ob-
1940 Mar 14 - Apr 11 21 1.6f servations in part I and part II amount to
1948 Feb 29 - Jul 9 38 2.37 0.74 and 1?01, respectively, and they are
1956 Feb 15 - Jun 5 43 1.93 drastically less than the mean residual of
1964 Feb 4 - Jun 9 65 1.70 the whole set of 1956 observations (see
1972 Jan 11 - Jul 13 16 0.81 Tab. 1 ) . This fact can serve as the first
1980 Feb 13 - Jul 8 7 0.74 proof that such a division is not random
and has a physical sense. The second one
may be the diversity of orbits obtained se-
parately from the observations of parts I
according to objective mathematical criter- and II. It appears that the orbit based on
ia (Bielicki 1972, Sitarski 1983) in the the observations from part I represents the
iterative process of differential orbit im- observations from part II with the mean re-
provement applied to each opposition sepa- sidual equal 26i'8 and vice versa, the orbit
rately. The mean residuals thus obtained based on the observations from part II re-
indicate the quality of suitable observa- presents the observations from part I with
tional data. The weighted mean value of the mean residual equal 59'i7. It is neces-
these residuals (amounting 1.49} may be sary to point out that the analogical test,
used as a priori mean residual of the whole for example in the case of 1964 apparition
observational material. A comparison of the

133
 1681 1?I3 1809 • •• 1992 I9M 1956 198* ... 2o?3 2J05 2.13?
Fig. 1 Minimal d i s t a n c e s between Amor and the Karth

of Amor, shows that the suitable values of axis of the Amor's orbit, which may be con-
mean residuals amount to 4i'75 and 2l96, res- sidered as a measure of the nongravitational
pectively. anomaly (Sitarskl 1983}, computed from the
There is another fact confirming the un-
known events in the motion of Amor not only
in 1956 but also during its unobserved re- ble a priori mean residual amounts to 1?21).
volutions between 1948 and 1964. Successful For a comparison, the same "nongravitatio-
(in a sence explained in the end of Intro- nal effect" computed from the observations
duction ) linkages of observations made 3n made1in 1932- 1948 amounts to (-0.04 + 0.05/
1932-1956 and in 1956-1980 just as in 1948- •10~'° AU/day and does not change the~mean
1964 turned out to be impossible. Similarly, rasidual which amounts to 1.69, as was men-
the attempts to link the observations made tioned above. The obtained value of the se-
in 1932, 1940, 1948 and in part I of 1956 cular change of the semi-major axis of the
as well as in part II of 1956, 1964, 1972 Amor* a. orbit is at least two orders of mag-
and 1980 gave unsatisfactory results. 3tar nitude smaller than typical values for short
example, in the case of the period from -period,comets.
1932 till 1956 (part I) the a priori mean
residual amounts to 1.34, while the mean re- 3.. The long—term motion
sidual obtained in the process of orbit im-
provement based on all observations from Numerical Integration of the equations
that period amounts to 2S06. The really suc- of motion cf Amor in a time span of over
cessful linkages were found only for the ap- 500 years backward and forward from the ob-
paritions 1932-1948 (for example the suita- servational interval shows an interesting
ble mean residuals are equal to 1.65 and periodicity In the 8-year cycle of visibi-
1169, respectively) and 1964-1980. lity of the asteroid. Amor can be observed
All those facts can be considered as ihe during its approaches to the Earth only.
proof that the motion of Amor was disturbed But, as we can see from Fig. 1, the minimal
about 1956 by unknown factors. What can we distances between Amor and the Earth change
say about their physical nature? First of drastically with time. It is especially in-
all it is arousing suspicion that Amor, du- teresting that the forthcoming approach may
ring its some successive revolutions round be one of the last oppositions during which
the Sun, passed on the meteoroid stream a we shall be able to see this mysterious ob-
few times. As a consequence of probable col- ject.
lisions the orbit of Amor could be changed.
Prom among the known streams one of the can-
did ites may be the Lyrid meteor shower, for 4. Let us observe Amor
whioh the maximum of activity occurs in mid All curiosities discussed here connected
April. It appears that the minimal distance with the motion of Amor show a great impor-
between orbits of Amor and Lyrids amounts tance of its observations during the coming
to 0.04 AU. appraaob in 1988. The ephemeris for this op-
The next possible interpretation of un- position is given in Tab. 2. The photogra-
known disturbing forces in the motion ol phic brightness was computed according to
Amor about 1956 is connected with the con- th» formula published by Schubart (1969).
jecture that some Earth-crossing asteroids We are waiting for new observations of Amor
are extinct cometary nuclei. Assuming that in order to improve the results we have ob-
Amor is a young death comet it is reasona- tained hitherto and reported in this paper.
ble to suppose that the thin crust on the
surface of Amor was suddenly split up and
volatile constituents from the inside of Acknowledgments
the object were ejected. In a consequence
Amor could become again a very low active The author would like to thank Prof. G.
comet for a short time. Its activity was Sitarski for useful discussions and com-
too small to be observed, but great enough ments concerning the work on Amor.
to change the orbit. This conclusion may be Ihe computations were made with the R-60
supported by the detection of very small computer at the Warsaw University. The pa-
"nongravitational effects" in the motion of per was supported by the Polish Academy of
Amor in the period 1964-1980. It appoars Sciences in CPBP 01.20.
that the secular change of the semi-major

134
 Table 2 References
Ephemeris of Amor for 1988 Bielicki M., 1972, in "The Motion, Evolu-
tion of Orbits and Origin of Comets",
eds. G.A. Chebotarev, E.I. Kazimirchak-
Date Mag. Polonakaya and B.G. Marsden, D. Reidel
'1950 °195O R (Dordrecht), 112-117.
landgraf W., 1984, Minor Planet Circulars,
Jan 20 12h24?2 -17°O1' 0.54 1.24 19.4 No. 9021.
30 13 10.5 -18 52 0.47 1.20 Sohubart J., 1969, Aatron. Astrophys. 2,
Peb 9 H 04.1 -19 34 0.42 1.16 18.8 173-181.
19 15 03.0 -18 36 0.39 1.12
29 16 02.6 -15 50 0.37 1.10 18.6 Sitarski G., 1983, in "Asteroids, Comets,
Mar 10 16 57.8 -11 46 0.37 1.09 Meteors", eds. C.-I. lagerkvist and H.
20 17 45.2 - 7 09 0.38 1.08 18.7 Rickman, Uppsala, 167-170.
30 18 24.1 - 2 38 0.40 -i.09
Apr 9 18 55.2 + 1 26 0.42 1.11 19.0
19 19 19.2 + 4 58 0.44 1.14
29 19 37.0 + 7 55 0.46 1.17 19.1
May 9 19 48.7 +10 17 0.48 1.22
19 19 54.6 +12 00 0.49 U27 19.1
29 19 54.6 +12 58 0.50 1.32
Jun 8 19 49.4 +13 02 0.51 1.37 19.1
18 19 39.6 +12 05 0.52 1.43
28 19 27.3 +10 07 0.55 1.49 19.2
Jul 8 19 14.6 + 7 17 0.59 1.55
18 19 03.6 + 3 55 0.64 1.61 19.5
28 18 55.9 + 0 26 0.71 1.67

/3£
M E T E O R S

I3B
 PROF. DR. JOHANNES HOPPE
DISTINGUISHED METEOR PHYSICIST
DIED.

One of the most significant originators a success of his theory, which Prof. Hoppe was
of meteor physics in thirties, Prof. Dr. Johannes able to foJlow in his last years.
Hoppe passed away in Jena at the age of eighty, After two operations of his leg in 1982,
Aprii 20, 1987. What we can say on meteor physics he send me a letter announcing his intention
at this symposium is devoted to him the natural to compute the Tungu/ska meteoroid trajectory
way: he was at the beginning of it all. In his again. His mood at that time can be best seen
eminent dissertation "Die physikaiischen Vorgange from the letter itself;
beim Eindringen meteorischer Ko'rper in die Erd-
atmosphare", published in Astronomische Nach-
richten 262 in 1937, pages 169 to 198, he set
up the basic equations of meteor physics, refer-
red to for many years as Hoppe ^s theory. After
the first attempts to constitute a theory of
fragmentation of meteoroids during the atmos-
pheric flight in sixties, Hoppe "s theory started iS-t tr cU
to be called "the single-body theory". His equa-
tions (e.g. in Pecina "s paper, thin publication:
drag equation and evaporation equation) became »«**• fc
a classical part of what we know about the inter-
action of a single unbreakable meteoroid with
the atmosphere. In his dissertation for the
first time, Prof. Hoppe found the complete solu-
tion of the drag and ablation equations on assump-
tion of isothermal atmosphere, expressing veloc-
ity and mass as function of height in terms
of the exponential integrals (third and fourth
equation in Pecina s paper "Meteor Physics";
this publication TS-2). Only recently, hi 5 solu-
tion was substantially enriched, when also the
distance along the meteor trajectory was expres-
sed in terms of exponential integrals as function
of time or height and generalized to any depen- Hri-
dence of atmospheric density on height (Pecina,
Ceplecha 1983; 1984; Bull. Astron. Inst. Czech-
osl. iW, p. 102; 35, p. 120). I propose to call
"the single body theory" of meteoroid interaction
with the atmosphere in this most general form
of solution, simply as "Hoppe 's theory" again,
in memory of the decisive contribution of Prof.
Hoppe to the solution of this problem of meteor
physics. The next generations of meteor physicists
and all scientists relying on data derived from
When the systematic photography of fire- atmospheric trajectories of meteoroids will
balls, the bigger and deep penetrating meteoroids for ever remember the work of Prof. Johannes
with enough observed change in velocity, gave Hoppe.
us relevant observational material, Hoppe "s
theory (the single-body theory) proved to be
valid with high precision of few meters in dis-
tance for more than 50% of observed bodies: Zdenek Ceplecha

\HO
 E V O L U T I O N OF M E T E O R O I D STREAMS

P . B . B a b a d z h a n o v a n d Y u . V. Obrubov

I n s t i t u t e of A s t r o p h y s i c s , D u s h a n b e 7 3 4 6 7 0 , U S S R

A B S T R A C T . A m e t e o r o i d s t r e a m g e n e r a l l y c o n s i d e r e d to be an e l l i p t i c a l r i n g of
r e l a t i v e l y s m a I I t h i c k n e s s . S u c h s h a p e is a t t r i b u t a b l e to m e t e o r o i d s t r e a m s in an
e a r l y s t a g e of t h e i r e v o l u t i o n . D i f f e r e n c e s in p l a n e t a r y p e r t u r b a t i o n s i n f l u e n -
c i n g t h e m e t e o r o i d p a r t i c l e s e j e c t e d f r o m t h e p a r e n t b o d y f r o m v a r i o u s p o i n t s in
its o r b i t at d i f f e r e n t v e l o c i t i e s and t i m e can r e s u l t in a s i g n i f i c a n t t h i c k e n i n g
of t h e s t r e a m . O u r s t u d i e s on t h e e v o l u t i o n of t h e s h o r t - p e r i o d m e t e o r o i d s t r e a m s
h a v e s h o w n t h a t t h e s e s t r e a m s can p r o d u c e s e v e r a l c o u p l e s of s h o w e r s a c t i v e in
d i f f e r e n t s e a s o n s of t h e y e a r .

INTRODUCTION It s h o u l d be n o t e d t h a t a l l p r i n c i p a l
Based upon the o b s e r v e d p e c u l a r i t i e s c h a r a c t e r i s t i c s of m e t e o r s h o w e r s o b t a i n e d
od m e t e o r s h o w e r s o n e m a y d i s t i n g u i s h t h e f r o m o b s e r v a t i o n s r e f e r o n l y to t h o s e s t r e -
f o l l o w i n g s t a g e s of m e t e o r o i d s t r e a m e v o - am m e t e o r o i d s w h o s e o r b i t s c r o s s t h e
lution: E a r t h ' s o r b i t , i.e. s a t i s f y i n g t h e f o l l o w -
1. A c o m p a c t c l o u d of m e t e o r o i d s in t h e i ng c o n d i ti o n :
v i c i n i t y of a coroetary n u c l e u s . An e x a m p -
le is t h e D r a c o n i d m e t e c r o i d s t r e a m w h i c h (1) a (1-e2)»1 + e . c o s u>
p r o d u c e d m e t e o r s t o r m s in 1 9 3 3 and 1 9 4 6 .
2. Meteoroids are distributed unevenly w h e r e a is t h e s e m i m a j o r a x i s , e is t h e
a r o u n d t h e p a r e n t b o d y o r b i t . In t h e v i c i - e c c e n t r i c i t y and o> is t h e a r g u m e n t of p e -
n i t y of t h e p a r e n t b o d y t h e r e is a c o m p a c t r i h e l i o n . T h e s e l e c t i v i t y of o b s e r v a t i o n s
c l o u d of p a r t i c l e s , but a r o u n d t h e w h o l e d e f i n e d by t h e e q u a t i o n ( 1 ) d o e s not p r o v i -
o r b i t t h e r e is a less d e n s e s t r e a m c o m p o - d e a n y r e l i a b l e d a t a on t h e w h o l e m a g n i t u d e
n e n t . T h i s has b e e n s e e n to be t h e c a s e of of d i s p e r s i o n of m e t e o r o i d s t r e a m o r b i t s . O n
the L e o n i d s . t h e o t h e r h a n d , if t h e o b s e r v a t i o n s c o n f i r m
3. M e t e o r o i d s a r e d i s t r i b u t e d a l m o s t e v e n - t h e e x i s t e n c e of t w i n s h o w e r s or t h e n o r t -
ly a r o u n d t h e o r b i t , i.e. t h e r e h a v e b e e n h e r n and s o u t h e r n b r a n c h e s of t h e s e s h o w e r s
p r a c t i c a l l y no c h a n g e s in t h e o b s e r v e d m e - we m a y c o n c l u d e t h a t t h e r e a r e m e t e o r o i d s
t e o r r a t e f r o m y o e a r to y e a r . N o n g r a v i t a t i o in the s t r e a m w h o s e o r b i t s do not c r o s s t h e
nal e f f e c t s r e s u l t in a m e t e o r o i d m a s s s e g r E a r t h ' s o r b i t . For e x a m p l e , t h e s o u t h e r n
r e g a t i o n . Under the g r a v i t a t i o n a l and n o n - and n o r t h e r n T a u r i d s h a v e_ t h e a r g u m esnts
n of
gravitational perturbations the meteoroids p e r i h e L i o n e q u a l to 1 1 3 . 2 ° a n d 2 9 2 . 3 r e s p e c -
f i l l out t h e v o l u m e of s p a c e d e f i n e d by s e - t i v e l y . T h e a r g u m e n t of p e r i h e l i o n of t h e
c u l a r v a r i a t i o n s in o r b i t a l e l e m e n t s . T h i s t w i n s h o w e r of its s o u t h e r n b r a n c h / i . e . p
r e s u l t s in an a c t i v i t y of t w i n s h o w e r s c a - T a u r i d s / is e q u a l to 2 4 6 . A l t h o u g h t h e r e
u s e d by t h e p a s s a g e of t h e E a r t h t h r o u g h a a r e o r b i t s with a r g u m e n t s of p e r i h e l i o n
s t r e a m b e f o r e and a f t e r its p e r i h e l i o n as f r o m 1 1 3 ° to 2 4 6 ° a n d f r o m 2 4 6 ° to 2 9 2 ° ,
w e l l as b r i n g s a b o u t t h e f o r m a t i o n of thb h o w e v e r , it is i m p a s s i b l e t o o b t a i n a n y o b -
n o r t h e r n a n d s o u t h e r n b r a n c h e s of a s h o w e r s e r v a t i o n a l d a t a on t h e m b e c a u s e of s e l e c -
/the T a u r i d s , the G e m i n i d s , the Q u a d r a n - tivity.
tids/.
4 . F u r t h e r , t h e d i s p e r s i o n of o r b i t s of E S T I M A T I O N OF T H E M E T E O R O I D S T R E A M AGE
stream particles becomes considerable. The We a s s u m e d i f f e r e n t w a y s to e s t i m a t e
s h o w e r a c t i v i t y has n o l o n g e r c l e a r l y e x p r e s - t h e a g e of each m e t e o r o i d s t r e a m u s i n g t h e
sed m a x i m u m . T h e s h o w e r r a d i a n t b e c o m e s r e s u l t s of o b s e r v a t i o n s . If a m e t e o r o i d
d i f f u s i v e and o c c u p i e s a l a r g e a r e a in t h e s t r e a m 1s at t h e i n i t i a l s t a g e of e v o l u t i o n
sky w h i l e t h e r a t e of v i s u a l m e t e o r s is e x - t h e s t r e a m a g e m a y be d e t e r m i n e d by t h e
t r e m e l y l o w . Such s h o w e r s a r e u s u a l l y c a l l e d l e n g t h of t h e a r c o c c u p i e d by m e t e o r o i d s ,
meteor assotiations. a s s u m i n g t h e i n c r e a s e v e l o c i t y of t h e a r c
5. At t h e last s t a g e of e v o l u t i o n t h e to be k n o w n . D e t e r m i n e d by t h i s m e t h o d t h e
s t r u c t u r e of a s t r e a m s u f f e r s t h e i n f l u e n - a g e of D r a c o n i d s is 3 yr a n d t h e L e o n i d s
ce of c o l l i s i o n s of m e t e o r i d s w i t h t h e a g e is 4 0 0 yr / P l a v e c 1 9 5 7 / .
s p o r a d i c p a r t i c l e s as well as the p r o l o n - T h e s e c o n d w a y is b a s e d o n t h e o p e r a -
ged i n f l u e n c e of p l a n e t a r y p e r t u r b a t i o n s t i o n of t h e P-R e f f e c t . E s t i m a t i n g t h e s t r e -
and t h e P o y n t i n g - R o b e r t s o n e f f e c t / P - R / . am a g e in s u c h a m a n n e r we s u p p o s e t h a t a f -
T h i s c a u s e s t h e f l u x d e n s i t y of a m e t e o r o i d ter the e j e c t i o n from the parent body the
s t r e a m t o d e c r e a s e so m u c h t h a t t h e s h o w e r s m e t e o r o i d s of d i f f e r e n t m a s s e n t o h a v e t h e
b e c o m e i n d i s t i n g u i s h a b l e from t h e s p o r a d i c equal semimajor a x e s . Taking into c o n s i d e r a -
background. tion this assumption Jones /1978/ estimated
S u c h a s e q u e n c e of the m e t e o r o i d s t r e - t h e G e m i n i d ' s a g e t o be 4.7 t h o u s a n d yr a n d
am e v o l u t i o n p r o c e e d s f r o m t h e t h e o r e t i c a l B a b a d z h a n o v and Obrubov /1983,1984V c o n s i -
a n a L y s i s of t h e j o i n t i n f l u e n c e of p l a n e t a - d e r e d t h i s a g e t o b e f r o m 3.6 t o 19 m i l l e n -
ry p e r t u r b a t i o n s and n o n g r a v i t a t i o n a I e f - nia.
f e c t s on m e t e o r o i d m o t i o n s . T h e t h i r d w a y is b a s e d on t h e d e t e r m i -

U1
 nation of a time of most similarity bet- baum 1981J Fox et al. 1983/. When modelling
ween the meteoroid orbits and the orbit the Geminid stream evolution. Fox et al
of the parent body or only between the indi- /1983/ have adopted the radius of a cometa-
vidual meteoroid orbits. The time passed ry nucleus.to be 10 km. The maximum ejecti-
since after this moment may be considered on velocity of small particles /with radius
as the stream age/Whipple, Hamid 1952/. Ho- of 0.1 cm and density of 0.8 gem" / was fo-
wever, this method seems to be not reliable und to be 660 u s " and the semimajor axes
because of the errors of determination of of meteoroid orbits were in the range 1.12
Orbital elements as well as of the inaccuracy AU to 1.77 AU. The ratio of the stream
of investigation methods of evolution of width in the plane of its orbit to its th i•
orbits over a longtime-scale. ckness /i.e. normal to the orbital plane/
The stream formation may begin at the at the distance 1 AU from the Sun is equal
moment when a cometary nucleus gets a suf- to 7:1. It would take the Earth less than
ficiently small perihelion distance. This two days to intersect such a stream whilt
may happen after a close encounter of a co- the radar meteor shower activity lasts mo-
met with any of the large planets. An esti- re than six days.
mation of the moment of a close encounter Hunt et al /1986/ have attempted to
enables to gain some knowledge of the stre- explain the formation of the Geminids as a
am age. This method suggested the Quandran- result of the collision of the Phaethon
tid stream age to be 3000 yr /Hamid, Yous- with other interplanetary object. It is
sef, 1963/. probable that their results are not in ac-
Eventually, all the methods discussed cordance with observations because the
above are highly doubtful because of the authors assumed the collision to have hap-
selectivity and low accuracy of meteor ob- pened recently.
servations. So the reliable estimates of
the stream age should be supported by an Here we have discussed the papers on
explanation of the other observed features the formation of the Geminid meteor stre-
of a stream such as the duration of shower am. For other meteor streams the results
activity and the existence of branches or of modelling will be in principle the same
twin showers. However, the observed structure at a showei
Jones /19S6/ has adopted the stream /for example, the Geminids/ cannot be ex-
age to be the time needed for the formation plained only by the differences of ejecti-
of northern and southern branches of the on velocities of meteoroids from a parent
Taurid shower. The obtained value of 10 yr body and radiation pressure /Obrubov 1980J
is thought to be highly overestimated beca- Jones and Hawkes 1986/ because over the
use the -initial dispersion of the orbital stream lifetime the planetary perturbation:
elements of meteoroii. was ignored by him. and the P-R effect would change strongly
The upper limit of lifetime of any me- the structure of the stream.
teoroid stream may be considered as the sur-
vial time of its large particles. Among THE EFFECT OF PLANETARY AND NONGRAVITAT10-
the processes resulting in the destruction NAL PERTURBATIONS ON THE METEOROID STREAM
of particles or their sweeping away from EVOLUTION
the stream catastrophic collisions with me-
teoroids of the sporadic background are ex- Planetary perturbations generally
pected to be the most effective. Having ta- change all the orbital elements of meteo-
ken into account these collisions Olsson- roids and do not depend on particle m a s -
Steel /1986/, Steel and E Iford /1986/ have ses. When studying meteoroid stream evolu-
estimated the survival time of particles of tion it was often assumed that the orbital
0.1 cm for 28 meteoroid streams. Their re- elements of all the meteoroids change in
sults show that meteoroid streams could the same manner as those of the mean streai
exist for tens and hundred thousands of yr. orbit /Babadzhanov, Obrubov 1980 Fox et
al. 1983/. Such an approach causes the
METEOROID STREAM FORMATION stream shape or the initial dispersion of
meteoroids' orbits not to change with
Meteoroid streams are formed as a re- tine. However, planetary perturbations can
sult of ejection of particles froir the come- considerably increase the dispersion of
tary nuclei. The ejection velocity of par- the orbital elements of meteoroids and,
ticles with radius of s and density of p eventually, change the shape of the stream
/ s , p in CGS units/ at a distance of r AU The P-R effect reduces the semimajor axis
from the Sun may be calculated by Whipple's and the eccentricity of the orbit in a se-
formula /1951/ cular manner. The lower the mass and densi
of particles the larger is the P-R effect
,/s p r 2.25 -1 which causes the segregation of the semima
where R is the radius of a cometary nucle- axes of particles depending on their masse
us in kfi. According to the formula 121 the Recently Olsson-Steel /1987/ has
ejection velocity depends on the radius and considered the influence of the Yarkovskij
the density of a particle. So the orbits of Radzievskij /Ya-R/ effect on the evolution
particles of various masses differ from of the Geminids /s=0.1 cm, p =1.06 g cm /.
each other. The ejection of particles appe- He has found that if the meteoroids rotate
•rs to occur in random directions that cau-
ses the orbit of particles of equal masses at a very high velocity of 10 4 s -1 , then
to differ from each other as well. The ot- over 10000 yr the elements i,(o,fl would
her probable mechanism of the stream for- change by A1 = +0.64°,Ailm +o.11°, a U> •
mation may be the decay of an asteroid at • + 0.12° respectively. However, these chi
the collision with any large body. ges do not account for the scatter in thes
At the initial stage of its evolution elements which has been obtained from photi
the stream is very flat, narrow at perihe- graphic data. T h u s , according to Jacchia ai1
lion and wide at aphelion /Kazantsev, Sher- Uhipple /1961 / the rms scattering of photo

142
 g r a p h i c o r b i t s of t h e G e m i n i d s is A i = + 0 . 9 , If w e a s s u m e , t h e r a d i u s o f t h e c o m e -
a w = + 1 r 8 and A a =+0.5 . F u r t h e r e m o r i , t h e t a r y n u c l e u s t o b e 1 0 km t h a n t h e s m a l l p a r -
Y a - R e f f e c t in a s e c u l a r s c a l e r e q u i r e s a ticles released from t h e cometary nucleus
c o n s t a n c y in t h e d i r e c t i o n o f t h e m e t e o r o - w i l l m o v e in o r b i t s w i t h s e m i m a j o r a x e s
id r o t a t i o n / R a d z i e v s k i j 1 9 7 8 / t h a t s e e m s f r o m 1 t o 1.7 AU a n d e c c e n t r i c i t i e s f r o m
to be h a r d l y p r o b a b l e over a t i m e i n t e r n a l 0.88 to 0 . 9 2 .
Table 2 indicates secular variations
of m o r e t h a n 1 0 y r .
of t h e G e m i n i d s ' o r b i t s with s e m i m a j o r
The i n f l u e n c e of n o n g r a v i t a t i o n a l e f -
a x e s o f 1 a n d 1.7 A U . T a b l e s 1 a n d 2 s h o w
f e c t s is s t r o n g l y d e p e n d e n t o n t h e s i z e s
t h a t s e c u l a r v a r i a t i o n s of t h e o r b i t s a r e
and d e n s i t i e s of m e t e o r o i d s a n d as t i m e
satisfactorily described by the following
p a s s e s t h i s d e p e n d e n c e r e s u l t s in t h e c o r -
i n t e g r a l s of m o t i o n :
r e l a t i o n of t h e o r b i t a l e l e m e n t s o f m e t e o -
r o i d s w i t h t h e i r m a s s e s . T h e P-R e f f e c t /3/ C.. = / 1 - e 2 / ccooss22ii » c o n s t .
C
p r o v i d e s t h e most c o n s i d e r a b l e c o n t r i b u t i - ? 2 2 const.
on to this p r o c e s s . C 2 = e . / 0 . 4 - s i n i . s i n u>
To e x p L a i n t h e o b s e r v e d f e a t u r e s o f
meteoroid streams we have used t h e H a l p h e n -
Goyryachev method to calculate the first-or- 100°
der s e c u l a r p e r t u r b a t i o n s . This m e t h o d a l -
l o w s u s t o f o l l o w t h e c h a n g e s in t h e o r b i t a l
e l e m e n t s of m e t e o r o i d s i n d e p e n d e n t l y o f b)
t h e i r p o s i t i o n in t h e o r b i t o v e r a long t i -
m e - s c a l e , i.e. allows us to distinguish g e -
n e r a l c h a n g e s i n h e r e n t in a l l t h e m e t e o r o i d s 0
in a g i v e n o r b i t .
In t h e p r e s e n t p a p e r w e s h a l l p r o c e e d
from the initial d i s p e r s i o n of t h e orbital 300
e l e m e n t s , r e s u l t i n g f r o m t h e e j e c t i o n o fp a r -
t i c l e s at d i f f e r e n t v e l o c i t i e s a n d f r o m r a -
diation p r e s s u r e . Such an approach enables
us t o e s t i m a t e h o w m u c h t h e p L a n e t a r y p e r - 200
turbations can change the dispersion of t h e a»1.0 AU
o r b i t a l e l e m e n t s of m e t e o r o i d s a n d , h e n c e ,
t h e s t r e a m s h a p e . T h e m a i n a t t e n t i o n is f o -
c u s s e d on t h e G e m i n i d a n a Q u a d r a n t i d m e t e o -
roid streams since we have t h e most a v a i l a b - 100
le i n f o r m a t i o n a b o u t t h e m . T h e c h a r a c t e r i s - -20 -10
tic f e a t u r e s o f t h e s t r u c t u r e a n d e v o l u t i o n T-10"3yr
of s h o r t - p e r i o d m e t e o r o i d s t r e a m s ar-r p e c u -
liar t o t h e s e s t r e a m s .
Fig. 1. Secular variations of perihelion
THE GEMINIDS arguments for different semimajor
axes of the Geminid orbits. T=0
Let u s a s s u m e t h e G e m i n i d s t o b e f o r m e d corresponds to 1950.0
20 m i l l e n n i a a g o a s a result of t h e d e c a y
of a cometary n u c l e u s t h e remnant of which
is t h e a s t e r o i d P h a e t h o n . T h e r e s u l t s o f c a l -
c u l a t i o n s of s e c u l a r p e r t u r b a t i o n s of P h a e - O/aiS-MlHOBIDS
t h o n ' s o r b i t a r e g i v e r in T a b l e 1 .
OBMINIDS
Table 1. S e c u l a r p e r t u r b a t i o n s in t h e o r b i -
tal e l e m e n t s o f t h e a s t e r o i d P h a e -
thon /a=1.271 A U / . T = 0 c o r r e s p o n d s
to 1 9 5 0 . 0

T - 1 0 " : e : q . i° : Q° : u° : C : C
yr AU" 1 2

1 : 2 : 3 : 4 : 5 : 6 : 7 : S : 9
0 .890 . 140 22.0 265.0 321.7 227 .18 .27
-1 .899 .129 16. 1 287.0 300.2 227 .18 .28 SEITAHTIDS
-2 .901 .126 14.0 325.3 262.6 228 .18 .28
-3 .897 .131 18.0 358.7 228 .18 .28 cT-LEOHIDS
229.8
-4 .888 .143 24.5 15.8 213.1 229 .18 .27
-5 .875 .159 30.3 24.7 2 04.1 229 .18 .27
-6 .860 .178 35.1 30.1 198.1 228 .17 .27
-7 .84 5 .197 38.9 33.7 193.5 227 .17 .27 Fig. 2 Spatial shape of t h e Geminid stre-
-8 .831 .215 41.6 36.3 189.5 226 .17 .27 am m o d e l .
-9 .819 .230 43.5 38.3 185.7 224 .17 .27
-10 .812 .2 39 44.6 40.1 181.9 222 .17 .26
-11 .809 .242 45.0 41.8 178.2 220 .17 .26
-12 .811 .240 44.7 43.7 174.4 218 .17 .26
-13 .818 .232 43.7 45.4 170.5 216 .17 .26
-14 .828 .218 42.0 47.6 166.fi 214 .17 .26
-15 .842 .200 39.4 50.5 162.4 213 .17 .26
-16 .857 .182 35.9 54.4 157.5 212 .17 .26
-17 .872 .163 31.5 60.3 151.4 212 .18 . 2 6
-18 .884 .147 26.1 69.2 142.2 211 .18 .26
-19 .894 .135 20.5 85.2 126.7 212 .18 .26
-2 0 .898 .129 16.7 112.7 100.0 213 .18 .26

143
 liable 2 . S e c u l a r v a r i a t i o n s in t h e G e m i n i d s t r e a m o r b i t s with a = 1 AU a n d a = 1.7 A U ,
and t h e values of and C?- T » 0 c o r r e s p o n d s to 1 9 5 0 . 0
1 AU 1.7 AU

T . 1 0 -3 q o q :C
2
yr AU ;n (0 AU

-20 i877 J123 16.7 112.7 100.0 212.7 .21 I 2 5 .926 .125 16.7 112.7 100.0 112.7 .13 .27
-19 .875 .125 18.6 94.0 118.0 212.0 .21 .25 .912 .149 28.5 64.6 146.2 210.9 .13 .27
-18 .870 .130 21.7 80.1 131.3 211.4 .21 .24 .883 . 199 40.5 51.4 159.5 210.9 .13 .27
-17 . .863 .137 25.1 70.4 140.5 210.9 .21 .24 .850 .256 47.6 46.0 166.9 212.9 .13 .27
-16 .854 .146 28.4 63.5 147.1 210.6 .21 .24 .826 .295 43.0 43.0 173.5 216.5 . 13 .27
-15 .845 155 31.4 58.4 152.2 210.6 .21 .24 .822 .302 51.5 40.7 180.0 220.8 . 13 .27
-14 .836 .164 33.8 54.4 156.5 210.9 .21 .24 .839 .274 49.3 38.3 186.5 224.8 . 13 .28
-13 .827 .173 35.8 51.3 160.1 211.3 .21 .25 .870 .221 43.9 34.9 192.8 227.7 . 13 .28
-12 .819 .181 37.6 48.6 163.3 212.0 .21 .25 .903 .165 33.7 27.8 201.1 228.9 .13 .29
-11 .811 .189 39.0 46.4 166.3 212.7 .21 .25 .926 . 127 18.7 4.7 223.7 228.3 . 13 .30
-10 .805 .195 40.0 44.5 169.2 213.7 .21 .25 .928 . 123 15.2 282.2 304.7 226.9 . 13 .30
-9 .801 .199 40.7 42.7 171.9 214.7 .21 .25 .909 . 154 29.6 2 49.1 337.4 226.5 .13 .30
-8 .798 .202 41.1 41.1 174.6 215.8 .21 .25 .880 .2 04 40.2 240.6 347.1 227.7 .13 .29
-7 .797 .203 41.2 39.6 177.3 216.9 .21 .25 .853 .250 46.0 236.9 353.7 230.6 .13 .29
-6 .798 .2 02 41.0 38.1 180.0 218.0 .21 .26 .84 0 .273 48.3 234.4 0.1 234.5 . 13 .28
-5 .800 .200 40.6 36.5 182.6 219.2 .21 .26 .84 6 .262 47.6 2 32.1 6.6 238.6 .13 .28
-4 .805 . 195 39.9 34.9 185.3 220.2 .21 .26 .870 .221 43.7 228.8 13.2 242.0 . 13 .28
-3 .811 .189 38.9 33.1 188.1 221.2 .21 .26 .901 . 168 35.5 222.5 21.2 243.7 .12 .29
-2 .818 .182 37.6 31.2 190.9 2 2£. 1 .21 .26 .927 .125 22.1 2 04.2 39.4 243.6 . 12 .30
-1 .826 .174 35.9 29.0 193.8 222.8 .21 .26 .934 .111 14.7 132.3 109.8 242.1 . 12 .30
0 .835 .165 33.9 26.3 197.1 223.4 .21 .26 .922 .133 28.8 87.9 153.3 241.0 . 12 .30

T h e i n t e g r a l / 3 / w a sf o u n d b y H o i s e e v / 1 9 4 5 / , f e a t u r e of t h e s h a p e o f a s t r e a m g e n e r a t e d
and / 4 / - b y Lidov / 1 9 6 1 / . f r o m o u r m o d e l i s i t sv e r y l a r g e t h i c k n e s s
The difference between t h e longitudes e c u a l t o 1 AU at a d i s t a n c e of t h e E a r t h
of p e r i h e l i o n o f t h e e j e c t e d p a r t i c l e s a n d from t h e S u n / B a b a d z h a n o v , O b r u b o v , 1 9 8 6 / .
those of Phaethon averages 5 - 1 0 over t h e E j e c t i o n s o f p a r t i c l e s from a p a r e n t
period under review. Hence, we may assume b o d y for a long t i m e p e r i o d c a u s e t h e o r -
that s t r e a m t u r n s a s s i g l e u n i t . T h i s fact b i t s with i d e n t i c a l s e m i m a j o r a x e s t o h a v e
may be used t o d e t e r m i n e t h e shape o f t h e d i f f e r e n t a r g u m e n t s of p e r i h e l i o n . M o r e -
s t r e a m w h i c h it c o u L d t a k e d u e t o p l a n e t a r y over, planetary perturbations increase t h e
p e r t u r b a t i o n s . F o r t h i s p u r p o s e in a f i r s t dispersion of orbital elements also due to
a p p r o x i m a t i o n let u s a s s u m e t h e l o n g i t u d e s t h e s c a t t e r in p o s i t i o n s c f p a r t i c l e s a r o -
of p e r i h e l i o n of o r b i t s of a l l t h e m e t e c r o - und t h e o r b i t / J o n e s 1 9 8 5 / . T h e r e s u l t s of
ids t o b e c o n s t a n t : T a b l e 2 a n d F i g . 1 s h o w that t h e d i f f e r e n c e
in a r g u m e n t s of p e r i h e l i o n of o r b i t s with
151 C 3 = = fi + to = c o n s t . a=1 AU a n d a = 1 . 7 AU w a s 3 1 6 o v e r 2 0 0 0 0 yr
As is s e e n from T a b l e s 1 a n d 2 a n a a f t e r t h es t r e s m f o r m a t i o n . H e n c e , t h e
Fig. 1 t h e larger t h e o r b i t a l s e m i m a j o r volume of space defined by the initial d i s -
axis of t h e meteoroid, the faster its orbit p e r s i o n of o r b i t a l e l e m e n t s a n d b y r e l a t i -
changes. ons 13-51 could b e t h o u g h t t o b e a l m o s t
Due t o t h e d i f f e r e n c e s in t h e c h a n g e filled out.
r a t e of i n i t i a l o r b i t a l e l e m e n t s , a s t i m e If w e a d d t h e c o n d i t i o n IM t o r e l a t i -
p r o g r e s s e s , t h e p a r t i c l e s w i l l f i l l out t h e ons / 3 - 5 / t h e n , us''ng t h e k n o w n s e m i m a j o r
t o t a l v o l u m e of s p a c e d e f i n e d b y r e l a t i o n s axis a n dconstants C | , C , , C , we can d e t e r -
/ 3 - 5 / , i . e . by s e c u l a r p e r t u r b a t i o n s . T h e m i n e t h eo r b i t a l e l e m e n t s o f a p c r t i c l e
s t r e a m s h a p e , f o re x a m p l e , m a y b e d e t e r m i n e d c r o s s i n g t h eE a r t h ' s o r b i t . T h e s e e l e m e n t s
in t h e f o l l o w i n g w a y . T h e v a l u e s o f C. = may b e c a l c u l a t e d b y t h e f o l l o w i n g f o r m u -
=0.13 a n dC,=0.29 correspond t o the orbit lae:
with a = 1 , 7 A U . A s s u m i n g t h e a r g u m e n t of p e r i - Ibl me4+ne2+k=0
h e L i o n t o h a v e t h e v a l u e s from 0 t o 3 6 0
and u s i n g r e l a t i o n s 13-51 w e s h a l l d e r i v e t h e HI i=ArccosVc.,/
c o r r e s p o n d i n g v a l u e s of e , i , fl . M a n y of
these orbits will determine an "outer"/with
r e s p e c t to t h e S u n / s u r f a c e r e s t r i c t i n g t h e 0.4 e - C .
meteoroid stream. Using the same method for / 8 / is = A res in
the orbit with a = 1 A U , C . = 0 . 2 0 , C 2 = 0 . 2 ? w e
s h a l l o b t a i n t h e inner r e s c t r i c t i n g s u r f a c e .
To e s t i m a t e t h e s h a p e of t h e s t r e a m r e s -
tricted by these surfaces, w e have constru-
cted c r o s s - s e c t i o n s n o r m a l t o t h e v e l o c i t y
v e c t o r of t h e o r b i t which h a s t h e s a m e e l e - / 1 0 / Q = C - tu
ments a, e, T as the Phaethon's orbit,but
i is e g u a l t o 0. T h e s h a p e of t h e Gerrinid w h e r e m = a ; n = a ^C . —7 2 a - 0 . 6 ; k= (a-1
meteoroid stream determined by these cross- .(1-C^-C^.
- s e c t i o n s is p r e s e n t e d in F i g . 2. Such a
s h a p e d i f f e r e s g r e a t l y from t r a d i t i o n a l n o - If e q u a t i o n Ibl h a s o n e a d m i s s i b l e s o l u t i o n ,
t i o n s of m e t e o r o i d s t r e a m w h i c h w e r e u s u a l l y then it f o l l o w s from t h e e q u a t i o n 191 that
s u p p o s e d t o b e like an e l l i p t i c ring of r e - the i n t e r s e c t i o n of t h e g i v e n o r b i t with
latively small t h i c k n e s s . T h e characteristic the E a r t h ' s orbit o c c u r s at four v a l u e s of

144
 Table 3. Theoretical and observed radiants
of t h e m e t e o r s h o w e r s p r o d u c e d b y t h e
Geminid meteoroid stream.
Geminids Canis-Minorids
Theor. O b s . Theor. Obs.

256-263 261° 256-263° 252-263°

111-112 112" 108-110° 1 0 5 - 1 1 3 *
0
+33-+32 +32* +11-+12" + 9 - +1 5 "
-1
kms 3 1 - 36 34 3 1 - 36 35- 44
0.05-0.04 - 0.05-0.03

Daytime Dayt ime

Sextantids 8-Leonids
Theor. Obs. Theor. Obs.
190-197° 184-195^ 190-197°
161-162° 152-157° 168-170"
+3- -5" 0-8° 17-16°
kms -1 36- 32 32-30 31-36
0.18-0.13

a n d D a y t i m e f> - L e o n i d s / n a m e d a c c o r d i n g t o
the p o s i t i o n o f r a d i a n t / . T h e o r e t i c a l c o o r -
dinates and solar longitudes for a l l the
180 270 u> 360 s h o w e r s a r e g i v e n in T a b l e 3 . O b s e r v a t i o n a l
data s h o w t h a t a m o n g t h e s e f o u r s h o w e r s a t
least t h r e e s h o w e r s a r e a c t i v e , n a m e l y t h e
Geir.inids, t h e Cani s-Mi n o r ids a n d t h e S e x -
r i g . 3 . T h ed e p e n d e n c e o f e c c e n t r i c i t y , i n c -
lination a n dradii-vectors to orbital nodes tantids as well. T h e Canis-Minorids meteor
of P h a e t h o n o r b i t o n p e r i h e l i o n a r g u m e n t . shower w a s detected by HindLey and Holden
/1970/ and was confirmed by Lindblad /1971/
R a n dR , r a d i i - v e c t o r s t o a s c e n d i n g a n d
a d and Kresakova / 1 9 7 4 / according to results
d e s c e n d i n g n o d e s . R =R = 1 A U c o r r e s p o n d t o of p h o t o g r a p h i c a n d v i s u a l o b s e r v a t i o n s .
ad Kresakova was t h e first to suppose t h e C a n i s -
intersection of thePhaethon's a n d Earth's
-flinorids t o b e o b v i o u s l y a s s o c i a t e d w i t h
c f t i 1' s : 1 - '• L •: c r. i d u , 2 -- C a n i s - H i n o r i d s /
the G e m i n i d s . N i l s s o n / 1 9 6 3 / a s s u m e d t h e
"' - D a y t i n e S e x t a n t i d s , 4 - G e m i n i d s .
Geirinids t o b e a s s o c i a t e d w i t h t h e S e x t a n t -
ids. T h e geocentric radiants and velocities
t h e a r i!:.• rr.ent o f p e r i h e l i o n . of t h e o b s e r v e d s h o w e r s , n a m e l y o f t h e Gemi-
;"•;..' i 5 ; t ii c iri v e n s t r e a m c a n p r o d u c e , i n
nids /Cook 1 9 7 3 / , t h e C a n i s - M i n o r i d s / K r e s a -
'-• r "i n '. ~: '• i •'; , I v i j p a i r s o f s h o w e r s . Arguments
kova 1 9 7 4 / , t h e S e x t a n t i d s /Cook 1 9 7 3 %
'-,! ^ .- r . I' •: ' : o •" -; •"-: n d ' c-iici t u c e s o f t h e a s c e n -•
S e k a n i n a 1 9 7 6 / a r e g i v e n in T a b l e 3. T h e
t! -I-- r i i c i ; , ,- - - . c - c J r : i r d i f f e r b y 1 3 0 ° ,
,'•• ' • . •• ! ' • i . e n - : j ; V ; t - c c e n l T i c i t i e s a r o \!3 lues./D-cri t er ion of S o u t h k o r t h a n d H a w k i n s
• • ' • •• : ' ' f' ', I : ' /
/ i / <'• 3 / betwes-r. t h e o r e t i c a l a n d o b s e r v e d
s h 0 s-. 0 r o r b i t s a r e a l s o g i v e n '-ere. As is
• • f- r • : r : * o : L •;: r v a t - i o r s t h f- : : o r ~
s e e r , t h e '.lieoretic; and observed rjdianti
• T •• •• . i o . - a r i j h e s o f s c •>e » e i f r
;
a r e i n n o -.id ogreeirent.
• • ' < 1 ;. • T - i c - • • ' . : • - I . .:•:-: -. r>
'" h 51 r .-..?t*. : ii i -.: k n e s s d e f i n e d b y t h e o b -
• ' . •• : •.- - . : i.'.. ci i f ! r r b y 1 UC"'.
:.::.•• v e J liiffsr. o r b i t s o f t h e C c s ' i n i d i a n d t h e
• • • ' • v r ' r {.• L i o N c n' i p o ' ; t o •- r - -
'-' j "• i i - f') r, 01 • i d s i n a r e g i o n o f i n t e r s e c t i o n
: • ':.,•• r
. : . : t d n t'. - e - n o w n
o f t h e S e x t a n t i d s ' o r b i t s wit-, the- E a r t h i r
• - - • i c r v h a n d "-o-Jth
0 . 7 AU,. Thi; ir.odf-lled s t r e e t i. ; dth a l c n g t h f
. • ' •• ••• u i
e n * '•
t . ' s e a -
' . i - t h ' s u r b i t is a p p r o x i m a t e 1./ 0 . 1 ? • M L It
: , •• •. f t h •• • '• o w e r s
a i tL . a k e t h e E a r t h a b o u t s e v e n d a y s / T a b -
'. 0 3 / t o p a s r. t h r o u g h s u c h a K t r e a in t h a t
••• i'. a g r e e s '.ith t h e d u r a t i o n o f a c t i v i t i e s ' .
•i' t h e Gerrr!' " d s , t h e C a n i s - M i ;ioi"i d s a n d thr-
'. „ ' •. ' 0: •: ..re o c s i r -
:c?xtantids.
• d ; t .'•.. •• '••• ; v; i .. • s s j I L
i t s / . • c .- - o n d 1 " f . 0 / .
According to numerous investigations
' c i h y t-i ( '• sr - t ha t u t
o f t h e G e m i n i d e v o l u t i o n t h e v a r i a t i o n in
-. i. •"! r - 1 i ;• r ,. • • •:• i '. : . • b a t i o n s
longitude of t h e ascending node of t h e
..• d i si-'•!••• ''"• o : ; r c u -
•stream i s a b o u t - - 1 . 6 o v e r a h u n d r e d y r .
,-i-f p a :• r -; r ! • - 1 •' u ; b i t S .
On t h e o t h e r h a n d t h er e g r e s s i o n o f t h e
:• " ' : . ; ; • ' ••• j r i . ' S o u t h
s h o w e r m a x i m u m a c t i v i t y d a t e h a sn o t b e e n
''••',!-• o -.-1
•-•it V 0 1 A -. 1. i -
o b s e r v e d . T h i s o b s e r v . i t io n a I f a c t i s c o r r e c t -
• •/ e 3 S 'i ; / ,J <;' '. t l ' r C :i l i -
ly e x p l a i n e d i n a n u m b e r o f p a p e r s / S a b a d -
•• :• : h - e ' : . : .. , < h i ' e I ij -
z h a n o v , O b r u b o v , "1982, 1 9 8 3 , 1 9 8 4 ) F o x e t
• ' • c L i n E t i c •" : ; , f o r ••.-. • p I. e ,
al 1 9 8 2 ; J o n e s , H a w k e s 1 9 8 6 / . T h e r e a s o n
.i } ~< a f: t z o t v. r. o w t •• • n -
f o r t h i s p h e n o m e n a i s i n t h ef a c t t h a t t h e
s t r e a m c r o s s - s e c t i o n i n t h ee c l i p t i c p l a n e
' r n T. e q ' j a t i o n t /6-iG/' aaa is d i s p l a c e d a l o n g t h e E a r t h ' s o r b i t a t a
f r., - •CJr r a t - e r narrow aroups rate of variation of perihelion longitude.
v
•, r i! e rr i n i d s t r e a m c a o "• i i - It m a y b e c o n c l u d e d t h a t t h e d i s p l a c e m e n t o f
• • -. ' p o r b i ... ! i e i « ••-, rc, u p . p r o - the Geminid activity dates will b e defined
,., ! T S , s i : c h ;, c t >• t ': e i r i n i d s , by t h e turn o f t h e whole stream. T h e velocity
"• * a n t i d s , t h e C a m s - M i n o r i o ' s of such a t u r n is d e t e r m i n e d b y a n a v e r a g e

145
 variation rate of the Longitude of periheli- les desintegrates into separate parts /arcs,
on. Since this velocity /for example, for over a period of 10 yr. These parts move
the Phaethon orbit at present/ is about in orbits which differ in the argument of
-0.05 over a 100 yr, i.e. very small, it perihelion and in longitude of the ascen-
is impossible to detect it from observati- ding node by 180 . Hence, the effect of the
ons. Plavec /1950/ revealed a very fast resonance 2:1 with Jupiter nay result in the
variation in the radius-vector to the des- formation of branches in the Quadrantid
cending node at which the Geminids are ob- shower over a short time. In the range of
served. Proceeding from this fact he con- values of the semimajor axes from 2.72 to
cluded that observations of the Geminids 3.27 AU the fraction of orbits with a > 3 . 2 5
since 1862 have become possible due to the AU is ignorable. Thus the motion of only a
approach of the stream to the Earth's orbit, small fraction of Quadrantid meteoroids may
Assuming a size of the stream along the be determined by the resonance 2:1 with Ju-
piter. The orbits of the main part of the
radius-vector of the descending node to be
Quadrantid meteoroids will evolve in a man-
equal to its width along the Earth's orbit
ner shown by Hamid and Youssef /1963/,
many authors /Plavec 1950J Babedzhanov and
Babadzhanov and Obrubov / 1 9 7 9 , 1 9 8 0 / , Willi-
Obrubov 198o; Hughes et a I 198o; Fox et ams et al /1979/. But the dispersion of
al 1983/ drew a conclusion that the Gemi- meteoroids orbits will be of great importan-
nids could be observed on the Earth during ce in the subsequent evolution of the stream.
200-300 yr. However the models of the G e m i -
nid formation and evolution indicate the d i - Table 4 and Fig. 4 give the results of
mensions of the stream along the radii-vec- calculations of secular perturbation of the ^
tors to orbital nodes to exceed considerably
the width of the stream along the Earth's Table 4. Secular variations of the Quadran-
orbit. Therefore the visibility period for tid meteoroid stream orbital e l e -
the Geminids may also exceed the values d i s - ments. R and R . radii-vectors to
cussed above. Jones and Hawkes /1986/ f o l - ascending and descending orbital
lowed the stream evolution over 10 yr. Ac- nodes. T=0 corresponds to 1950.0.
cording to their results the general v i s i -
bility period of the shower is more than
0 0 R
1000 yr, and a central core could be obser- T 1o"? e : q : i° : a" m
u> sn : rf
R
ved during 100 yr. However, Jones and Haw- AU d AU a
kes do not explane the observed stream width
_yr
and they conclude that it 1s necessary to -50 .967 .101 18.4 246. 9 214.7 102 0 .11 0 .96
investigate the stream evolution over 10 yr. -48 .970 .093 16.2 141. 9 316.6 98 0 .62 0.11
The XI century observations of the 14 -46 .959 .127 36.7 115. 2 340.3 96 2 .59 0 .13
fireballs are obviously in favour of prolon- -44 .934 .203 51.4 108. 7 344.4 93 3 .96 0 .21
ged observable periods of the Geminids / A s - -42 .895 .323 60.8 105. 8 345.3 91 4 .61 0 .33
tapovi£, Terentjeva 1968/. Fox and Williams -40 .842 .483 66.6 104. 0 345.8 90 4 .91 0 .49
/1985/ as well as Hunt et al /1985/ conclu- -38 .782 .670 70.2 102. 8 346.8 89 5 .04 0 .68
ded that the fireballs mentioned above could -36 .722 .855 72,4 101. 8 349.3 91 5 .09 0 .86
not belong to the Geminids. But as the aut- -34 .677 .995 73.5 100. 9 353.6 94 5 .11 1.00
hors assume a possibility of ejection of -32 .659 1.05 73.8 100. 1 359.4 100 5 .11 1.05
meteoroids from Phaethon and observations -30 .673 1.01 73.4 99. 4 5.2 104 5 .10 1.01
of the fireballs just at the same t i n e , na- -28 .715 877 72.4 98.6 9.8 108 5 .07 0 .88
mely in the XI century, their conclusions -26 .775 .694 70.1 97.7 12.6 110 5 .02 0 .70
can not be considered final. In fact the -24 .837 .502 66.7 96.7 13.8 110 4 .89 0 .50
ejection of bodies responsible for fireballs -22 .891 .335 61.3 95. 1 14.2 "09 4 .61 0 .34
could occur thousands years a g o . The orbital -20 .933 .207 52.9 92. 6 15.0 108 4 .00 0 .21
elements of such bodies could change so gre- -18 .960 .123 39.1 87. 0 18.3 105 2 .70 0 .12
ately that their encounter with the Earth -16 .974 .081 18.3 63. 7 38.7 102 0 .66 0 .09
in the XI century may be thought probable. -14 .974 .081 18.4 320. 5 138.5 99 0 .09 0 .59
Finishing a rewiev of papers on the Ge- -12 .962 .118 38.4 296. 5 159.4 96 0 .22 2 .36
•inid stream evolution let's note that our -10 .937 .193 52.0 280. 2 163.2 93 0 .20 3 .69
model is qualitative. The stream age and the -8 .900 .307 60.4 2 8 7 . 3 164.1 92 0 .32 4 .40
radius of the causative comet were chosen -A .852 .457 65.7 285. 6 164.4 90 0 .47 4 .75
to some extent arbitrarily. Furthermore we -4 .794 .634 69.1 2 8 4 .4 165.1 90 0 .65 4 .92
have used a qualitative method to estimate -2 .735 .817 71.3 2 8 3 . 5 166.8 90 0 .83 5 .00
the influence of planetary perturbations. 0 .683 .977 72.5 2 8 2 . 7 170.0 93 0 .98 5 .02
The smaller initial dispersion of meteoroid +2 .642 1.10 73.3 2 8 2 . 2 174.5 97 1.11 5 .01
stream orbits and the consideration of the 44 .625 1.16 73.5 2 8 1 . 4 179.6 101 1.16 5 .00
P-R effect would result in an increase In +6 .642 1.10 73.1 2 8 0 . 8 184.9 106 1,. 10 5,.03
time neededfor filling out the stream s h a - +8 .676 .998 72.4 2 8 0 . 1 189.7 110 1,.01 5,.05
p e . But it could not change our principal + 10 .717 .871 71.5 279. 5 193.1 113 0,.94 5,.03
conclusion on the possibility of the produ-
cing of 4 meteor showers by the Gentnid
mean Quadrantid orbit by the Halphen-Gorya-
stream /Babadzhanov, Obrubov. 1986/.
chev method. Fig. 4 also shows the results
THE QUADRANTIDS of calculations of the orbital evolution for
10 particles having initially the same or-
According to numerous radar measurements
bits using the Runge-Kutta method /Williams
the semi major axis of the Quadrantid orbitt
et al 1979/. As is seen secular perturbations
1s 2.8 All, but precise photographic observa-
describe the changes of the orbits over a
tions provide a value of 3 AU. Murray /1982/
long time period rather well. On the other
has assumed the semimajor axes of the Quad-
hand, one can see the dependence of v a r i a t i -
rantid meteoroids to be within 2.72 AU to
on of 1 and toon the particle position on the
3.27 AU. According to Froeshle and School
orbit. According to the results of Williams
/1986/ the particles with semimajor axes
•t al /1979/ the semimajor axis cf only one
from 3.25 to 3.31 AU move in resonance 2:1
particle of a ten increases to 4.2 AU over
with Jupiter and the stream of such partic-
4000 yr in the consequence of the encounter

146
 with Jupiter. The amplitude of periodic chan-
des of the semimajor axes of other particles
does not exceed 0.2 AU and dkt can be conside-
red on the average to be constant. It can be
said that for 4 millennia 10 percent of the
Quadrant id meteoroids are subjected to strong
Jupiter perturbations. Below we shaLL not
take these meteoroids into account.
In the case of the Quadrantids the valu-
es of c. and C2 are not constant. Therefore
for the construction of Qandrantid stream
shape for values of co from 0 to 360 we
used the respective values of e, i and (X
calculated by HaIphen-Goryachev method.
Then as in the case with Geminids we have
constructed stream normal cross-sections and
the stream cross-section in the ecliptic pla-
ne /Fig.5/ which give the notion on the stre-
am shape /Babadzhanov, Obrubov 1986/. The
distinctive feature of the Quadrantid stream
is a narrow long jut near perihelion. The
Quadrantid shower is observed namely at the
intersection of this jut by the Earth. One
more interesting feature lies in the fact
that the Earth crosses the stream at four 100
points. Two of them are very close to each
other in perihelion. It means in principle
that Quadrantid stream can produce eight me-
teor showers /Fig. 5/. The elements of mete-
oroid orbits intersecting the Earth's orbit
are given in Table 5.
Table 5. The elements of the Quadrantid mete-
oroid orbits which intersect the -Fig. 4. Variations of perihelion arguments
Earth's orbit and corresponding sho- and inclinations of Quadrantid orbit ac-
wers. cording to calculations by Runge-Kutta
/solid lines; Williams et al 1979/ and
Halphen-Goryachev /dots/ methods.
No : : q : : CO Shower
AU
1 . 0.68 1.000 73.3 99.4 5.6 K-VeUds
22.2 71.8 31.2 D.Adrie-
2 . 0.97 0.086 tids
23.7 310.0 148.2 S.S-Aqua- URSIDS S. S-AQUARIDS
3. 0.97 0.087 rids X-VELIDS N. ff-AQUARIDS
72.5 282.7 170.0 Quadran- .=260°
4 . 0 . 6 8 0.977 tids
72.4 280.1 189.7 Ursids
5. 0.68 0.998 18.9 248.0 213.6 L.*-Cetids
6. 0.97 0.102 20.9 130.8 327.0 N./-Aqua-
7. 0.97 0.097 rids
8. 0.68 0.995 73.5 100.9 353.6 Carinids
ARIETIDS
Table 6 gives the theoretical radiants :-CETIDS
of possible showers for the Quadrantid meteo-
roid stream.These radiantsare close to the
observed radiants of meteor showers: Daytime
Arietids /Cook 1973/, a-Cetids /ass. No 78,
Kascheyev et al 1967/, Southern 5-Aquarids
/Cook, 1973/, Northern 5-Aquarids /Kascheyev fig. 5. The cross-section of the Quadrantid
et al 1967/ and Ursids /Sekanina 1970/. The stream model in ecliptic plane. S-the
observed geocentric radiants and velocities Sun.
for these showers also are presented in Tab- the particles.For exampl?,for particles with
le 6, and we can see a satisfactory1 agree- egual orbital semimajor axes the dispersion
ment with theoretical calculations. Fox in o) may reach 150-180 for the period of 2
/1985/ found that in the past the Quadrantid millennia /Fig. 4/. This dispersion can re-
orbit intersected the Earth's orbit. Theore- sutt in vide simultaneous activity of 3-4
tical shower radiant calculated by Fox prac- showers. In addition the rate of dispersion
tically coincides wirh our theoreti cal'and of <>) can be influenced predominantly by
with the observed radiant of the Southern . the Initial dispersion of particle orbits.
£-Aquarids. But that' was not noticed by him.- As the perihelion distance of Quadrantid
Similar the Geminid case all the Quad- orbit vary from 0.08 AU to 1.1 AU the eject-
rantid stream volume will be filled out by ion velocities can be relatively large. A
particles when the dispersion in the argument high Initial dispersion of meteoroids orbits
of perihelion is 360 . Because of closeness follow. Thus under Influence of planetary
to Jupiter the dispersion of to in the Quad- perturbations the Quadrantid stream volume
rantid stream is determined not only by the will be filled out very rapidly - 1n 5-6
semimajor axes but also by the position of millennia.

147
 Table 6. Theoretical and observable radiants longitude of orbital ascending node. The
of meteor showers produced by the Quadran calculated regression of ascending node is
tid meteoroid stream. V in kms" . in the range from 0.37 to 0.49 per centry
/Babadzhanov, Obrubov 1980J Hughes et al
1981; Murray 1982/. This gives evidence to
Dayt i me Daytime the fact that the regression of the maximum
Arietids oe-Cet ids activity date is the result of planetary
Theor. Obs. Theor. Obs. perturbations, mainly by Jupiter.
First observations of the Quadrantid

1
72° 76 68 78 shower were carried out in 1830 /Hindley
40° 44 41 44 1972/. Babadzhanov and Obrubov /1979, 1980/
23° 23 9 12 and Murray et al /1980/ supposed, that the
41 37 40 39 observations of the shower became possible
D 0.07 0.08 due to the approach of the stream to the
Earth's orbit. These authors drew a conclu-
Southern Northern sion that Quadrantid shower may be active
£-Aquarids f-Aquar ds during about 3 centuries. However, Astapo-
vich and Terentjeva /1968/ contend that the
Theor. Obs. Theor. Obs. bolides observed in XI century on 9-th of
A© 130° 125 131 128 January belong to the Quadrantids. Now we
342° 333 336 337 can suppose the possibility of observations
-15° -16 -3 -5 of Quadrantid meteors in the XI century be-
g
42 41 40 40 cause the dimensions of the cross-section
of the stream in the ecliptic plane are
0.07 0.09 much larger than had been thought earlier.
Rich displays of the <T-Aquarids in the
K-Velids Ursids VIII century are indicative of such conclu-
Theor. Obs. Theor. Obs. sion /Astapovic, Terentjeva 1968/.
279° ? 280 281
145° ? 220 223 SHORT-PERIOD METEOROID STREAMS
-56° ? 55 62
41 ? 40 38 We have selected 30 short-period m e t e -
g
? or showers from Cook's list /1973/ and es-
D 0.20 timated the meteoroid stream thickness and
determined the number of meteor showers
Carinids Quadrantids which can result from one stream. To get an
Theor. Obs. Obs. idea about stream shape due to planetary
281° ? 283 perturbations probably it is enough to e s -
152° ? 230 t i m a t e t h e t h i c k n e s s o f t h e s t r e a m in s o m e
-60° ? 48 points. These points m a ybe t h e perihelion,
V 41 aphelion a n dt h eorbital point with r = a .
g The values o f stream thickness in these
D •7
p o i n t s h , h , a n d h a r e p r e s e n t e d in T a b -
m q
le 7 . Q
This table also gives semimajor a x e s , maxi-
At p r e s e n t s i x m e t e o r s h o w e r s p r o d u c e d
mum and minimum of i n c l i n a t i o n s a n d t h e
by t h e Q u a d r a n t i d m e t e o r o i d stream a r e known.
stream width along the Earth's orbit. Table
T h e a r g u m e n t s of peri h e l l o n s of t h e s e s h o -
7 shows that about 3 0 % of showers a r ep r o -
w e r s are f r o m 3 0 / D a y t i m e A r i e t i d s / t o 3 3 0 °
duced by flat streams - / F / , 4 0 % - by thick
/ N o r t h e r n /> - A q u a r i d s /. T h e r e f o r e w e c a n c o n -
s t r e a m s 111 a n d 307. - b y s t r e a m s c f a b o u t
sider that all the Quadrantid stream volume
the same width and thickness / E / .
is almost filled out.It follows that a careful
Let's consider how many meteor showers
study of Southern hemisphere meteor showers
may be produced by one meteoroid stream.
and searches for Carinids and &-Velids are
W h e n t h es t r e a m o r b i t l i e s i n t h e e c l i p t i c
of interest.
p l a n e it m a y p r o d u c e t w o s h o w e r s if q •: 1 A u
Thus the research carried out by us pro-
a n d o n e s h o w e r i f q ; 1 All. A s t h e f o r m u l a s
ves the separate assumptions on interrelations
/ 6 - 1 0 / s h o w if i 4 0 t h e m e t e o r s t r e a m c:n
between Qadrantids and Ursids /Sekanina 1973/,
p r o d u c e 4 or 8 s h o w e r s . T h e n u m b e r s of m e -
between Quadrantids and fi -Aquarids /Hamid,
t e o r s h o w e r s N f o r e a c h s t r e a m a t e y i v e ~ ; .-.
Whiple 1963/ and between £ -Aquarids and Day-
T a b l e 7 . T h e w e l l - k n o w n m e t e o r s t r t o a of
time Arietids /Cook 1973/.
Encke comet p r o d u c e 4 meteor s h o w e r s : t h e
Mass segregation in the Quadraiitid night time Northern and Southern Taoridc and
stream was found by radar observations /Kas- the daytime /3-Taurids and J - P e r s e i d s . The
cheyev,Lebedinets 1960/. This segregation 1 , - A q u a r i d s a n d ")( - O r i o n i d s , w h i c h h a v e t h e
was satisfactory explained by the ejection Northern and Southern branches, are refer-
of meteoroids from the parent body, Light red to t h e s t r e a m s p r o d u c i n g 4 s n o w e r s . T h e
pressure, P-R effect and planetary perturba- p o s s i b i l i t y of t h e p r o d u c i n g of 8 m e t e o r
tions /Hughes et al 1981J Babadzhanov, Obru- s h o w e r s b y o n e st reamiii I l u s t ra t ed b y Q u a d r a n -
bov 1983; Fox 1983/. tids. The £-Draconids and K-Cygnids are
According to visual observations of also referred to this type of s t r e a m s .
Quadrantid shower since 1835 up to the pre-
sent Hindley /1972/ has found the regression Q u a l i t a t i v e i n v e s t i g a t i o n of t h e s h o r t -
of the maximum activity date, which is equal period meteoroid streams show that their
to 0.28 per centry. From radar observations dimensions m a y be large. This fact should
this regression is found equal to 0 . 3 1 + 0 . 1 7 be c o n s i d e r e d w h i l e e s t i m a t i n g t h e s t r e a m
per century /Hughes 1972/. Taking into consi- volumes, space densities and stream masses.
deration a high inclination of Quadrantid M o r e o v e r it is n e c e s s a r y t o t a k e i n t o a c c o -
orbits it can be supposed that the regressi- unt t h e o b s e r v a t i o n s o f a l l p o s s i b l e s h o -
on in date is equal to the regression of the w e r s , which can be produced by the m e t e o r o -
id s t r e a m c o n s i d e r e d .

148
 Table 7. Semimajor a x e s , maximum and minimum of inclinations, thickness and number
of possible meteor showers - N for short-period meteoroid streams

Shower : a 1° ? h Q = h . • «,,: h q j 1 : N
: AU:max. min. I AU
I
£-Cancrids 2.3 0 0 0 0 0 0.1 2 F
Virginids 2.6 10 3 0.5 0.4 0.03 1.2 4 F
S-Leonids 2.6 12 6 1.0 0.7 0.14 0.7 4 E
Cameloparda li s 1.5 8 7 0.5 0.4 0.23 0.4 4 E
tf-Leonids 2.4 2 1 0.1 0.2 0.00 0.9 2 F
«-Scorpi i ds 2.2 10 3 0.4 0.3 0.02 0.5 4 E
jC-Bootids 1.2 20 18 1.0 0.8 0.58 0.4 4 E
* -BOOTIDS 2.6 30 17 2.6 2.0 0.44 0.5 4 T
T -Herculids 2.7 21 13 2.0 1.5 0.41 0.4 4 T
S.Piscids 2.3 7 2 0.4 0.3 4 F
0.04 1.1
N.Piscids 2.1
S.Taurids 1.9
N.Taurids 2.6 16 0 0.8 0.6 0.07 1.3 4 F
0. /3-Taurids 2.2
D. j-Perse ids 1.6
et-Capr icorni ds 2.5 15 7 1.1 0.9 0.14 0.3 4 T
S. i-Aquarids 2.4 19 5 0.6 1. 1 4 F
N. i-Aquarids 1.8 1.1 0.05
S. ^ - O r i o n i d s 2.2 16 2 1.0 0.7 0.12 0.1 4 T
N. j[-Orioni(is 2.2
f-Arietids 2.1 3 2 0.2 0.2 0.05 0.1 4 E
f-Draconi ds 2.8 38 20 3.4 2.6 0.47 0.4 2> T

^-Ophi uch ids 2.9 10 4 0.7 0.6 0.06 0.1 4 T

Dec. Phoeni ci ds 3.0 16 9 1.5 1.2 0.27 1.0 4 E
K-Cygnids 3.1 40 20 3.8 3.0 0.46 1.0 8 T
jf-S corpiids 3.1 12 6 1.1 0.9 0.14 0.4 4 T
/t-Virginids 3.1 24 10 2.0 1.5 0.36 0. 7 4 T
K-Aquarids 3.2 3 1 0.1 0.2 0.01 O..i 4 F
Ann. Andromedids 3.2 22 4 2.1 1.7 0.30 0.8 4 T
Jun. Bootids 3.3 18 10 1.9 1.5 0.31 0.0 4 T

The phenomenon of formation of shower cal Properties of Neteoroids, eds. C.L.

branches may be w i d e l y spread. So it is Hemenway, P.H.Millman, A.F. Cook,
necessary to continue searching relative Washington D.C., pp.183-191.
showers. In conclusion we would like to em- Drummond J.D. 1982, Icarus, 4 9 , 1, pp.135-
phasize the fact that if we know the exis- 142.
tence of the two branches of a shower then Fox K. 1983, In:"DynamicaI Trapping and
the relative showers with intermediate va- Evolution in the Solar System", eds.
lues of perihelion arguments must be acti- V.V. Harkelos, Y.Kozai, Reid.Publ.Comp.
ve. Dord.-Holland, pp.89-95.
Thus, because of the differences in the Fox K. 1986, In: "Asteroids, Comet* Mete-
eiection velocities/ light pressure and ors, I I " , e d s . , C.-I. Lagerkvist et al.,
times of ejection an initial dispersion Uppsala Univ., pp. 521-525.
of meteoroid orbits is formed. Subsequently Fox K., I.p. Williams 1 9 8 5 , Month.Not. R.
under planetary and non-gravitational per- Astron. S o c , 2 1 7 , 2 , pp.407-411.
turbations this dispersion becomes so great Fox K,, Williams I.P., Hughes D.W. 1982,
that a meteoroid stream produces several Month. Not. R. Astron. S o c , 199, 2 ,
relative meteor showers which are active at pp. 313-324.
different times of the year. Fox K., Williams I..P., D.W. Hughes 1983,
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149
 Month. Not. R. Astron. Soc., 195, 2 , Di s c u s s i on:
pp. 625-637.
Hunt J., I.P. Williams, K. Fox 1985, Month. Lindblad: This is a very interesting paper.
Not. R. Soc., 2 1 7 , 2 , pp.533-538. In your computations you use two
Hunt J., K. Fox, I.P. Williams 1986, In: integrals of motion derived by Moiseev
"Asteroids, Comets, M e t e o r s , I I " , eds. /1945/ and Lidov /1963/. Since these papers
C.I. Lagerkvist et a I., Uppsala Univ., are not easily accessible to most meteor
pp. 549-553. workers, it would be desirahle that a review
Jacchia L.G., Whiple F.L. 1961, Smith. of them be given at a future meteor confe-
Contr. Astrophys., 4 , 4, pp. 97-129. rence.
Jones J. 1978, Month. Mot. R. Astron. S o c ,
Babadzhanov: I shall do this in the nearest
183, 2 , pp. 539-546.
^ — ^ — — ^ ^ — future.
Jones J. 1985, Month. Not. R. Astron. S o c ,
0 Isson-SteeI: This is an interesting and
2 1 7 , 2 , pp. 5X3-532.
important paper. For this to
Jones J. 1986, Month. Not. R. Astron. S o c ,
be a complete theory, I believe that there
2 2 1 , 2 , pp. 257-267.
must be a good explanation of how the
Jones J., R.L. Hawkes 1986, Month. Not. R.
required initial dispersion in semimajor
Astron. Soc., 2 2 3 , 3, pp. 479-486.
axes is achieved; do you think that this
Kazantsev A.M., L.M. Sherbaum 1981, Vestnik
has been done?
Kiev. Gosuniv., 2 3 , pp. 105-109.
Kascheyev B . L . , Lebedinets V.N. 1960, S o v i - Sa'jadzhanov: Yes, I think so. However, if
et Astron. J., 3 7 , 1, pp. 119-122. any initial dispersion in
Kascheyev B . L . , V.N. Lebedinets, M.F. Lagutin semimajor axes and other orbital elements
1967, Meteor Phenomena in the Earth's exists, then, under the pLanetary perturba-
atmosphere, Nauka, Moscow, 260 p. tions, this dispersion becomes so large
Kresakova M. 1974, Bull. Astron. Inst. Czech. that each meteoroid stream produces several
2 5 , 1, pp.20-23. meteor showers.
L1dov M.L. 1961, Iskusstvennye sputniki
Simek: Can you compare the physical chara-
Zeroli, 8, pp. 5-45.
"~^~~"~ cteristics of parent shower with
Lindblad B.A. 1971, Space R e s . , It, 2 8 7 .
those of shower branches? I have in mind
Lovell B. 1954, Meteor Astronomy, Oxford,
the mass-distribution index, the density of
Clar. P r . , 488 p.
meteoroids and other parameters resulting
Moiseev N.O. 1945, Trudy 60s. Astron. Inst.
from meteor spectra?
Mosc. Univ., 15, pp.75-79.
Murray C.D. 1982, Icarus, 4 9 , 1, pp. 125- Babadzhanov: We have compared the physical
129. characteri sti cs of different showers produ-
Murray C.D., D.W. H u g h e s , I.P. Williams ced by the same meteoroid streams. For
1980, Month. Not. R. Astron. Soc., 190, example the densities of meteoroids of Qua-
3, pp. 733-741. drantids and delta-Aquarids are very close.
Nilsson C.S. 1984, Australian J. Phys. 1 7 , But we have not compared the mass-distribu-
p. 2 0 5 . tion indices of shower branches of twin
Obrubov Yu.V. 1980, Ookl. AN T a j . SSR, 2 3 , showers so far.
4 , pp. 175-179.
Olsson-Steel 0. 1986, Month. Not. R. Astron. Stoh I: From observations of the Taurid
S o c . , 2 1 9 , 1, pp. 47-73. complex it apears that several
showers forming this complex are smoothly
Olsson-Steel D. 1987, Month. Not. R. Astron.
connected each with the others /S and N
S o c , 2 2 6 , 1, pp. 1-17.
T a u r i d s , N and S chi-Orionids etc./, forming
Plavec M. 1950, Nature, 165, 4 1 9 2 , pp. 3 6 2 -
thus just one very prolonged stream. Can
-363. your calculations explain this feature or do
Plavec M. 1957, Publ. N o . 3 0 , Czech. Acad. you obtain a few separate branches of a
S c 1 . , Astron. Inst., 94 p. stream in each case?
Radzievskij V.V. 1 9 7 8 , Astron. Vestnik, 1 2 ,
3, pp. 160-165. Babadzhanov: Our calculations can explain
Sekanina Z 1970, Icarus, 13, 3, pp. 4 7 5 - all Fhe features of the Taurid com-
493. plex, but it is necessary to know the initi-
Sekanina z 1973, Icarus, 18, 2 , pp. 2 5 3 - al distribution of the meteoroid's semimajor
-284. axes.
Seksnina Z 1976, Icarus, 2 7 , 2 , pp. 2 6 5 -
-322.
Southworth R.B., G.S. Hawkins 1963, Smith.
Contr. Astrophys., 7 , pp. 261-286.
Steel D . I . , V.G. Elford 1986, Montn. Not.
R. Astron. Soc., 2 1 8 , 2 , pp. 185-199.
Whipple F.L. 1951, Astrophys. J., 1 1 3 , 3,
pp. 4 6 4 - 4 7 4 .
Whipple F.L., S.E. HanHd 7952, Harv. Repr.
Ser. II, No. 3 6 1 , 30 p.
Williams I.P., C.D. Murray, D.W. Hughes
1979, Month. Not. R. Astron. Soc.,
189, 2 , pp. 483-492.

150
 R E S O N A N C E I N T E R M I T T A N C E CAUSES T H E
GRAVITATIONAL S P L I T T I N G O F M E T E O R S T R E A M S

C. F R O E S C H L E 1 , H . SCHOLL 2
1. Observatolre de Nice, Nice, France
3. Astronomisches Rechen-Inetitut Heidelberg, FRG

Abstract
The dynamical evolution of meteor stream particles in resonance appear to be affected by the same resonance
mechanisms as resonant asteroids. Crossing of separatrix.like zones appears to be crucial for the formation of arcs
and for the dissolution of streams.
Investigating the orbital evolution of known resonant meteor streams and of model streams, we have found
examples for such a transitory arc formation. The orbital inclination of a meteor stream appears to be a critical
parameter for arc formation.

1. - I N T R O D U C T I O N proposed by Hughes et al (1981) and by Babadzhanov and

The frequency distribution of semi major axes of me- Obrubov (1983).
teor streams shows minima at mean motion resonances Besides all these non-gravitational mechanisms, mean
with Jupiter (see Lindblad, 1972), like, but however less
motion resonance with Jupiter might be responsible for
striking, as iu the case of asteroids. Hence, the long term
splittings of streams.
evolution of meteor stream particles close to resonance
is affected by the same resonance mechanism as the dy- How a meteor stream can split up into separate arcs
namica! evolution of resonant asteroids. Of course, since was demonstrated by Froeschle' and Scholl (1986) in a
meteor streams particles mostly move on orbits with high model calculation. Froeschle and Scholl placed a highly
eccentricities and inclinations tbeir long term evolution inclined (i = 68°) and highly eccentric (e = 0.68°) model
has been investigated very little in celestial mechanics as meteor stream in the 2/1 resonance region with Jupiter.
such orbits can be hardly approximated by classical se- Jupiter perturbations alone without close approaches to
ries expansions. In addition, there are non-gravitational Jupiter set up the splitting of the model meteor stream
forces like the Poynting-Robertson drag and the solar into arcs.
wind which cause the orbits of small particles to slowly The splitting is caused by the particular dynamics
spiral into the sun. On the other hand, the radiation pres- of resonant motion. The important variable which deter-
sure exerts a force consisting in a reduction of the gravita- mines the splitting, is the longitude of ascending node fi
tional force exerted by the sun on the particle. Radiation of a stream particle's orbit.
pressure depends on particle cross-section. Particles with
Outside a resonance region, fi regresses almost uni-
different masses may feel different accelerations towards
formly due to Jupiter perturbations, in particular due to
the Sun.
orbital momentum transfer. The corresponding rate fi de-
Hence, radiation pressure is expected to cause a mass pends mainly on the semimajor axis of a particle's orbit.
segregation within a stream during its formation and af- We like to emphasize that outside of a resonance region, fl
ter that a further mass segregation might result from does not depend on the mean longitude of a particle with
Poynting-Robertson and solar wind drags. Such a mass respect to Jupiter's mean longitude. In other words, the
segregation is observed in the Quadrantid stream (Hughes average momentum transfer to the particle's orbit which
and Taylor, 1977). Explanations for this observation are determines fl is basically the same for all stream particles

151
 independent of the location of a parjicle in its orbit. As a Schubart (1964, 1978) averages the Hamiltamean H over
consequence, the whole stream precesses without splitting the commiT 'irability periode (p+g)2jr of the short period
up. . M :
In a resonance region, on the other hand, the situa-
tion might be different : The average angular momentum H(M,K,S,v,<r)dM
transfer might be strongly dependent on the location of a
particle in the stream. Hence, the nodal lines of particle Hence 8 is independent of time and therefore 8 is
orbits might precess with very different speeds and their an integral of motion in the average sense. If in addition
motion might even become progrn.1. or librate. This is tj = 0 then K is a second integral. Fig. 1 displays the
the basic mechanism for a stream to split into arcs. An well known topology in the plane X = \j2Scoscr and
arc consists of particles with about the same orbital rate
fl which is very il itferent from orbital rates tl of the other Banana shaped orbits and circular orbits appear in
particles of the original stream. Over which timescales the 5, o space. A zero frequency orbit called the separa-
such arcs remain stable is known only within the frame
trix devides the S, a space in three regions where orbits
of the model, of course, which in particular does not in-
behave distinctly.
clude collisions among stream particles and which does
Region I corresponds to the inner portion of the bi-
not include the Poynting-Robertson effect.
furcation curve around the point a, where the apocentric
In section II, we describe the model and some topo- librators occur. Periceutrie librators on banana- shaped
logical features extrapolated from the planar circular res- trajectories occur around p in region II. The outer circu-
onant restricted three body problem. lators fill region III outside of the bifurcation curve.
In section III, spectacular splitting in the 2/1 res- In the circular averaged model ej = 0, orbits remain
onance for Quadrantid like meteor streams is shown. A in their corresponding region. Iu the more geueral model
long term evolution reveals a resonance intermittance due with ej ^ 0 aud without averaging, orbits can cross the
to some crossiug of a separatrix like zone. bifurcation curve aud consequently can chauge their be-
In the last section, results of the orbital evolutions of haviour. In particular, librators can become circulators
7 knowu resonant meteor streams are described. and vice versa.
It is clear that Schubnrt's topology displayed in Fig.
2. - DESCRIPTION OF THE MODEL
1 is only valid for the circular plauar averaged model.
We first restrict our attention to the planar case since
it leads to a fundamental set of orbits which will be used Only in this model, tb> problem of resonant motion is
as a paradigm to explain the various behaviours found in fully integrable. The critical bifurcation point is called
the three dimensional model. For an approximate ratio a homoclinic point in modern dynamics (Arnold, 1978).
(P + <l)/P °f tue
mean motion of an asteroid to that of It is well known that integrable systems are not generic,
Jupiter, Schubart presents the following system of canon- i. e. small perturbations can destroy the integrability,
ical equations for the planar elliptic problem and the separatrix or homoclinic orbit can cause wild re-
gions with chaotic behaviour (Arnold, 1978). This pecu-
dH liar behaviour for Schubart's topology was displayed by
dl dv ' dl Froeschle and Scholl (1977) in the elliptic averaged case.

dv _ _dH_ da__ _d_H_ Besides ellipticity, also non-averaging or nou-coplanarity

dt ~ dK ' dl ~ dS destroys the integrability. For the case of non-coplanarity
with t the time, H the Hamiltomian we will show that Schubart's topology displayed in Fig.
K = Ja{{p + q)jp) - y/acos<j> 1 remains valid to some extent and can be regarded as
S = i/a(l -CO9 0) a good paradigm in order to understand and to describe
u = (l- li)p/q - M,- the behaviour of resonant orbits in the three-dimensional
<r = A f - ( I - l y ) ( ( p + «)/«) elliptic averaged case.
The osculating elements being defined by :a semi ma- For this more general case, Schubart (1978, 1979)
jor axis, e = sin (f> eccentricity, M mean anormaly, / mean extended the planar model. The six variables in his dif-
longitude. The subscribt j denotes Jupiter's elements. ferential equations are :

152
 S. - R E S O N A N C E I N T E R M I T T A N C E A N D
GRAVITATIONAL S P L I T T I N G OF M E T E O R
STREAMS
\
According to Hughes et al (1979), the Quadrantid
stream has the following orbital parameters with respect
to ecliptic and equinox 1950 : (w = 170° 4, n = 292° 6,
i = 71° 4, e = 0.681, a = 3.064). Using the Schubart av-
eraged program, we have integrated five different streams
with about the same initial conditions but situated within
the resonance. We used 12 starting values ft = 30°, 60°,...,
360° in order to represent a stream. We have found three
modes of nodal motion depending of the values of the res-
onance variable jt three modes of nodal motion ; either
nodal regression with jumps of 180° or temporary libra-
Fig. 1 - Trajectories in S - <r space based on "Schubart's tion, or progression occurs. Consequently a stream may
a la Poincare" s model for 2/1 planar circular resonant or- break up into two isolated arcs. Fig. 2 shows schemati-
bits. cally the starting configuration of a stream and the arcs
formed from this stream in a perspective view.

This stream has its ascending node in the lower part

G = v/a(l - e2)
of Fig. 2 outside of Jupiter's orbit. The dashed part of

*s = tan(i/2)cosfi
9t = t a n ( i / 2 ) s i n n

fl is the longitude of the ascending node of the aster-

oid's orbit with inclination i against Jupiter's orbit reck-
oned from Jupiter longitude of perihelion.
The critical argument <r, r and /< are such that JUPITER

<r = -{u + fi p/q)

Froeschle* and Scholl (1986) have investigated the be- Fig. 2 - The initial stream and the orbits of two re-
haviour of orbits starting with different values of a, e, i sulting arcs A and B after about 1000 Jupiter revolutions.
and eight representative geometric configurations for the Dashed parts of an orbit lie below Jupiter's orbital plane.
angles (w,O,/<, r, w) through the computation of 96 orbits Circles on the initial stream refer to the stream's portion
at the 2/1 Kirkwood gap over 17000 years. A classifica- with ft rnging from - 60° to + 90° (regression). Aster-
tion with respect to the behaviour of u and u yields 5 isks reier to the portion with n vanging from 150° to 210°
classes and three major mechanisms determining orbital (progression).
stability : a libration, e — w phase coupling and u libra-
tion. But for the resonant meteor streams the relevant the stream lies below Jupiter's orbital plane. The circles
variable is the critical argument it whose variations may on the initial stream represent the stream between it =
lead to a spectacular breaking. - 60° and /« = 90°. This stream portion will later form
arc B. The asterisks indicate the stream portion in the
range p — 150°... 210°. A stream dispersion is possible
within 10s years and a very slow dispersion rate of arc

153
 B is expected. On the other hand, arc A will dissolve there is also in the 9k - * 2 spare a sf-paratrix-likc zone.
taster since the nodal rates of arc A orbits depend on the Crossing this zone changes the character of orbital evolu-
variable fi. tion. We conjecture therefore that calculating Liapuuov's
To locate the regions of the a, p, u, i phase space maximal characteristic exponent would reveal a chaotic
where streams break up into arcs is difficult since we are orbit (see for instance Froeschle, 1984).
concerned with a system with three degrees of freedom
and therefore Fig. 1 can only be a crude approxima- 4. - R E S O N A N T ORBITAL EVOLUTION
tion for describing the topology of the system. Obviously OF SEVEN KNOWN M E T E O R STREAMS
there exist separatrix-like surfaces where chaotic motion In table ] , the orbital parameters of seven (p + q)/p
is expected. We have found such orbits with temporary resonant streams are given. We have found (Scholl and
progression of Q with intermittent jumps. Froeschle, 1987) the following
It is interesting to note that the jumps ic n and in June Bootius in 2/1 resonance : Arcs may show up af-
eccentricity are not related to a crossing of the separatrix- ter time scales of 10' years. Since thePoynting-Robertson
like zone in Schubart's S - a plane mentioned above. We effect would cause the dispersion of this meteor stream
investigated the orbital evolution in a differnt plane, namely on such time scales, we do not expect to observe arcs of
in the <?! - * 2 plane, defined above. this stream. On the other hand, fast close approaches of
Like in Schubart's S - <r plane, resonant motion repre- stream particles in the range -90° < f < -60° will form
sented in the * ! - $ 2 plane can show three modes : pro-
a hole in the stream. If it is possible to make observations
gression, regression, and libration. Alternators between
in this region of the stream, an age of the stream might
these three modes are also known to occur like in the S
be estimated, since the formation of the hole takes less
- <r plane (e. g. Froeschle and Scholl, 1977). Figure 3
than 200 years.
shows that our orbit is such an alternator.
The Annual Andromedis stream will not split up into
The trajectory starts at A. Circles represent the tra-
arcs due to the resonance mechanism. We think that its
jectory for the first 100,000 yrs while crosses represent the
inclination of 12° is too low to show this effect. This
trajectory for the remaining period. In the beginning, the
will be a dispersion of the portion of the stream between
orbit librates over one cycle on a banana-shaped curve.
30° 5: M < 120° due to the comparatively fast processional
rates for nodal lines of particle orbits. Changing slightly
the semi-major axis of this stream from a = 3.29 AU to a

= 3.25 AU does not yield quantitatively different results.

The low inclination (i = 4°) of the 3/1 resonant Lib-
rids stream does not favour a fast splitting into arcs. This
stream will disperse rather slowly. After some 103 years,
the stream portions between 150° < ix < 180° will disap-
-8 5 . pear because of the comparatively fast rate of fi.
The June Lyris streams has large inclination (i = 44°)
and high eccentricity (e = 0.67). Nevertheless, no fast
I.I
splitting into arcs on timescales of the order of 10s years
like in the case of the Quadrantids- like stream occurs.
Fig. 3 - An orbit with a temporary progression of 0. The nodal lines of all test particles regress with rates for
The starting values are a = 3.28 AU, e = 0.68, i = 71", n ranging between 30 000 and 45 000 years. This stream
f] =0°, u = 170° and fi =2 10°. The orbit starts at point will disperse slowly.
A. The symbol o is used to plot the trajectory during the
The highly inclined July Phoenicids stream at the

After 100,000 yr, the orbit enters the retrograde circula- 3/1 resonance reveals the regression of the nodal lines

tion region. After two circulations, the orbit appears to with jumps which characterizes the splitting into arcs.

leave this region. Nothing can be predicted for the fur- However, unfortunately, all orbits show the jump. Hence,

ther evolution. Obviously, like in Schubart's S - o space, no splitting into arcs can be expected.

154
 Close approaches to Jupiter cause the formation of Froeschle; 61, Scholl, S.: 1986, Astron. Astrophys.
holes in the 7/3 resonant December Phoenicida stream 158, 259.
within 200 years. The remaining portions will also be Etgkei, D.W., Taylor, I.W.: 1977. Monthly Notices
dispersed due to close Jupiter acounters within a few Roy. Astron. Soc. 181, 517.
103 years. Due to the hole {:•,-,« .tion, short arcs of this
Hughes, D.W., Williams, IP., Foz. K.: 1981. Monthly
stream might form. A more detailed examination of the
Notices Roy. Astron. Soc. 195, 625.
dispersion of this stream due to close Jupiter approaches
Lindblad, B.A.: 1972 The distribution in l / a in pho-
and a comparison with observations might yield estima-
tographie meteor orbits. In Evolutionary and Phys-
tions about a lower or an upper limit of the stream's age.
ical Properties of Meteroids. NASA special publica-
Such an estimation seems iu particular possible for
tion.
the 3/2 resonant Pegasids stream. All our model parti-
Schubart, J.: 1964, Smithsonian Astrophys. Obs.
cles had a fast close encounter with Jupiter wit din 200
Special Report No.149.
years. The Pegasids are located outside of the 3/2 libra-
Schubart, J.: 1978, in Dynamics of Planets and Satel-
tion region which protects the Hilda-type asteroids from
lites and Theories of their Motion, ed. V. Szebehely,
close encounters with Jupiter (Schubart, 1968).
Reidel, Dordrechtm p. 173.
Schubart, J.: 1979, in Dynamics of the Solar System,
5. - CONCLUSIONS
ed. R. L. Duncombe, Reidel, Dordrecht, pp. 207-215.
These seven known meteor streams located in mean
motion resonances with Jupiter do not reveal the same
kind of splitting into arcs discovered by Froeschle and
D I C LI S S I 0 N
Srholl (1980) for a Quadrantid-like meteor stream. This
latter model stream splits into arcs solely due to reso-
K re s a k : What is the width of the resonance
nance mechanisms. No close approaches to Jupiter are in- zone in comparison with the mean error in the
semimajor axis as determined from the obser-
volved. In the case of these seven known meteor streams, vations? I mean whether you can identify indi-
ou the other hand, arcs may form in some cases due to vidual librating objects.
Froeschle: The problem of identifying single
Jupiter approaches. These approaches cause the forma- observations with the arcs we predict has
still to be investigated.
tion of holes iu a •»r-<';iin. Hence, the remaining particles Babadzhanov.- According to observations the
of the stream do form arcs. This mechanism to form arcs semimajor axis of Quadrant ids is in the range
2.79 to 3.27 AU. Thus your results and con-
is, of course, Quite different (rum the resonance mecha- clusions on the disintegration of the stream
into separate arcs refer only to a small part
nism causing the splitting of the Quad""antid-like stream, cf the stream meteoroids, which have a i 3.22
which is based on the different motions of nodal lines of AU. But you show that this is one possibility
of shower branch formation.
stream particles. The close approach mechanism discov- Froeschle: Thank you for your comments. Hence
ered for some of the seven known meteor streams can be the effects we discussed might be real.
L i n d b L a d : In your interesting study you have
used to estimate upper limits for ages of meteor streams. investigated the Quacirantiris and seven other
meteoroid streams. With the exception of the
Such an age estimation would be a premiere in the field Andromedids these streams are of low activity,
of meteors streams. and thus unfortunately we have no accurate
photographic orbits ior checking the computa-
tions. My question is, why you have not stud-
ied the Southern Delta Aquarids, which is the
REFERENCES most prominent meteor shower observed in the
southern hemisphere, and which is located
Arnold, V.I.: 1978, Mathematical Methods of clas- exactly at one of the Kirkwood respnances
(Lindblad. B.A., 1952, Observatory).
sical Mei-li.iui.-s, Translation Springerverlag Heidel- Froeschle: According to the Fox, best in
Uppsala 11, it is close, but not within the
berg. T
>/2 Kirkwood gap.
Babadshanov, P.B., Obrubov, Y.V.: 1983 in High-
lights of Astronomy, vol. 6, 411, Reidel Dordrecht.
Froeschle, a., Scholl, E.\ 1977, Astron. Astrophys.
57,
Froeschle, a.: 1984, Celes. Mech. 34, 95.

155
 THE DISPERSAL OF HETEOROID STREAMS BY RADIATIVE EFFECTS
Duncan Olsson-Steel
Lund Observatory, Box 43, S-22100 Lund, Sweden;
and The University of Adelaide, Australia.

A major problem in meteor astronomy is why the orbits of meteoroids within particular streams
are so dispersed. For streams with aphelia well within Jupiter (such as the Geminids) planetary
perturbations cause insignificant dispersion but can accommodate the required motion of the nodal
heliocentric distance to explain why the Geminids were not observed prior to the 1860's. The spread
in the orbits would also require unreasonably large ejection velocities from the parent. Another
dispersal mechanism is therefore required.
By incorporating perturbations due to the Yarkovsky-Radaievskii effect into the model the Geminid
dispersal can be understood; by including also the effects of the radiation pressure and Poynting-
Robertson forces the main observed characteristics of the stream (shower duration variation with
magnitude; skew rate profile; changes in mass distribution and radiant diffuseness as the shower
progresses) are explicable. The necessary spin rates (about 3000 rev/sec for 1 mm and 1000 rev/sec
for 1 cm radius meteoroids) would be attained within a thousand years of release from the parent
body, due to spin-up under solar radiation pressure. It therefore appears that the Yarkovsky-
Radzievskii effect is an important source of stream dispersion which has been hitherto neglected,
but should be included in future models.

Prologue have been able to demonstrate that the nodal helio-

centric distance was not close to 1 AU until just
"There is no question that meteoroids are dispersed over a century ago, and hence explain why the Geminid
in orbital elements much faster than perturbations, shower was not observed until the 1860's: Jones, 1978,
the Poynting-Robertson effect, and collisions can 1982, 1985; Fox et al., 1982, 1983; Babadzhanov and
explain. I have tried for many years to find other Obrubov, 1980, 1984). Since the spreading of the
physical effects that can produce the dispersion. Geminid orbital energies by the planets is so small,
... I suspect it is some phenomenon of light this stream is of considerable interest as regards an
pressure on spinning grains as Opik has suggested." understanding of the dispersal of streams in general:
Whipple, 1972. knowing that the scatter due to gravitational inter-
actions is certainly too small to be of consequence,
1. Factors which may cause stream dispersal the origin of the observed dispersion can be looked
For some years there has been a realization that the for elsewhere.
member meteoroids of particular streams are rather
more dispersed in orbital elements (in particular the The next dispersal agent to be considered is the
semi-major axis) than can ea?ily be explained or effect of ejection velocities from the parent, such
understood in terms of well-established dispersal that the stream is ;':;m,J with a spread in orbital
mechanisms, as follows. Dfspite the fact that zodiac- energies. Using the standard ejection velocity
al dust particles limit V -> physical lifetimes of formula due to whippie (1951) it has been shown that
the calculated velocities are too small to explain the
iiieteoro ids uf radius tOOym - 10cm (Dohnanyi, 1978; observed shower duration by an order of magnitude
Leinert et al., 1983; Steel and Elford, 1986), these (Fox et al., 1983; Jones et al., 1985); however, more
catastrophic impacts occur on a much longer time-scale recently it has been demonstrated by Jones and Hawkes
than the aqe of meteoroid streams so that they are not (1986) that a better (but still inadequate) fit to the
an important source of dispersion; non-catastrophic observations is gained by including the effect of the
collisions also cannot cause significant dispersion initial differences in the orbital elements (due to
since the dust involved is many orders of magnitude the ejection mechanism) upon the subsequent orbital
smaller in mass than the meteoroids (Jones et al., evolution under planetary perturbations. Thus, to
1985; Olsson-Steel, 1987a). Although streams with date models relying upon ejection velocities have been
orbits like short-period comets (aphelia near Jupiter) unable to explain the observed parameters of the
are quickly scattered by planetary close encounters Geminid stream.
and are the major source of the sporadic background
(Olsson-Steel, 1986), there are some streams which Radiative forces have been considered by mary
cross the giant planets and yet have larger dispersions authors in investigating the evolution of meteoroid
than can be explained i;y planetary perturbations. For streams, and in particular orbital decay under the
example, the Halleyid stream would not be dispersed Poynting-Robertson (P-R) effect has been recognized
significantly, in the same way as the orbit of P/Halley as being important in causing meteoroids to gradually
is stable even under planetary close encounters spiral in towards the Sun before they are eventually
(Olsson-Steel, 1987b), although the stream width may be destroyed in collisions with the zodiacal dust. Not
caused by the comet having a librating orbit (Mclntosh so well recognized has been the role of radiation
and Hajduk, 1983); another example is the Perseid pressure (as opposed to.ejection velocities) in caus-
stream, the Earth being the only planet which the ing loop-formation in streams (Carusi et al., 1983).
stream approaches so that the planetary perturbations The linear dust trails discovered in the orbits of
are too small to explain the shower duration (B.A.Lind- various periodic comets by Sykes et al .(1986), which
blad, personal communication). For streams with aphel- consist of submillimetre (but not much smaller)
ia well within Jupiter's orbit, such as the Geminids meteoroids and hence would be observed on the E- -th as
(Q = 2.6 AU), the dispersal in semi-major axis caused faint radar meteors, are strongly asymmetric: the
by planetary perturbations is certainly very small trails extend rather further behind the comets than in
since the terrestrial planets have little effect: it front, and this vividly demonstrates that radiation
has been shown (Jones, 1985; Jones and Wheaton, 1985; pressure (which always causes the dust to lag behind
Hunt et al., 1985) that the dispersion produced is only the comet) is important in promoting loop formation,
about one-fiftieth of that required by the shower and appears to dominate ejection velocities (which can
duration. (However, these exact numerical integrations cause meteoroids to lead or lag the comet).

157
 If the Geminid stream were gradually formed over a as long as (AT / T) is small, as is the usual case.
length of time > 101* years (i.e. meteoroid ejection These three forces have quite different influences.
continues unabated over this entire period) then it is F R acts directly away from the Sun; if the Doppler
just possible that the "I week duration of the radio term is neglected then F R effectively results in a
meteor shower could be explained by the P-R effect constant reduction factor on the solar gravitational
causing spreading in the orbital energies, due to the attraction: the meteoroid continues to move on an
earliest-released having suffered more orbital cont- elliptical orbit. F p acts both radially and trans-
raction than the later-released particles; however, versely, but is restricted to the particle's orbital
then the visual shower should be much shorter than the plane; as is well-krown, it causes a gradual
~3-4 days actually seen, so that the P-R effect cannot inspiralling towards the Sun as the metecroid's
in isolation explain the shower characteristics, orbital energy declines. However, Fy acts in all
although it may aid the fit between planetary- three dimensions and is diffusive in nature: it can
perturbation/ejection velocity models and the observed lead to either an increase or decrease in the orbital
shower (Jones and Hawkes, 1986). energy (depending upon the spin direction) and will
To date, models for meteoroid stream evolution have cause gradual spreading of all of the orbital f-lements
not included the Yarkovsky-Radzievskii (Y-R) effect, of meteoroid streams.
which received its modern introduction from Dpik
(1951) and was also described by Radzievskii (1952). 3. Expected physical and dynamical parameters
It is shown briefly in this paper, and in more detail In order to calculate the magnitudes of the radiative
by Olsson-Steel (1987a), that the Y-R effect can eas- forces, estimates of the meteoroidal physical and
ily explain the observed dispersion in the Geminid dynamical parameters are required.
stream, and by implication in other meteoroid streams,
for plausible physical parameters and spin rates of The density of Geminid meteors of mass ~1g is
the meteoroids; in fact for the Y-R effect not to be rather higher than that of most meteors, having a
an important source of dispersion would require either value of about 1.06 g/cm3 (Hughes, 1978); this value,
very small (u>s < 1 rad/sec) or very large (u > 10 s which may reflect the small perihelion distance of the
rad/sec) spin rates. If the conclusions of tnis paper Geminids, will be used throughout. The specific heats
are correct then the Y-R effect is the predominant of ices, silicates and iron are of the order of 1000,
stream-dispersal agent in the inner <-,lar system, as 1000 and 500 J/kg/K respectively; the exact value used
foreseen by Whipple (1972), and mu<. be included in is unimportant since the thermal conductivity of the
future models of stream evolution if these are to be meteoroidal material is highly uncertain. Terrestrial
realistic. silicates have a conductivity K 2 3.5 W/m/K, but these
are close-packed structures; the above values for p,
2. Radiative forces upon meteoroids C and I would render a thermal inertia (1/Y) - 2000
J/m z /s s /K (these units are used for this parameter
Burns et al. (1979) have reviewed the forces acting throughout). However the thermal conductivity of the
upon solid particles due to the solar radiation field, material making up a cometary nucleus is thought to
and investigated the relative importance of each as a have a much lower value, of the order of 0.1 W/m/K
function of particle size. The expressions for the (Squyres et al., 1985; Wood, 1986) which would then
three radiative forces favoured by the present author give (1/Y) S 300; free meteoroids might have an even
are: lower conductivity, reduci^q the thermal inertia even
Radiation Pressure (RP): further. Ttv , Geminid mettoroids may be expected to
have thermal inertias of the order of 100 - 500.
F R = (S Q IT r 2 / c) (1 - / c) ) (1) Meteoroidal albedoes are uncertain. The nucleus of
P/Halley has A < 0.04 (Keller et al., 1986), whilst
IRAS observations of the zodiacal dust cloud have ren-
Poynting-Robertson (due to the different Doppler dered A s 0.07 (Hauser et al., 1985), and other
shifts, and hence momentum, of forward- and backward- zodiacal light data and theoretical modelling give
emitted photons): similarly small albedoes (Hanner et al., 1981). A
meteoroidal albedo of 0.1 will be adopted as nominal.
F p = (S Q IT r2/ c) (- {Vr Vt) / c ) (2)
The meteoroid spin angular velocity (u ) is now
required. There have been numerous arguments in the
Yarkovsky-Radzievskii (due to the varying amounts of past in favour of high meteoroid spin rates, of the
momentum emitted in different directions by spinning, order of 10 3 - 10 5 rad/sec. These arguments include
and hence non-isothermal, meteoroids): the fragmentation and bursting of visual/photographic
meteors, the initial widths of radar meteor trains
Fy = (8 Tt r2 / 3) (a T 3 AT / c ) cos 5 (3) (Hawkes and Jones, 1978), and theoretical arguments
based upon spin-up in the solar radiation field either
Here S is the solar flux at the position of the tneteor- via a 'windmill' or a 'paddlewheel' effect (e.g. Rad-
oid (S = '.37 kW/m2 at 1 AU), Q is a scattering coeff- zievskii, 1954; Dohnanyi, 1978; Ratcliff et al., 1980).
icient (Q = 1 is assumed throughout), r is the radius It is quite simple to show that it is solar radiation
of the meteoroid (assumed to be spherical), c is the pressure which dominates the torque upon meteoroids
velocity of light, V is the heliocentric radial vel- (rather than the solar wind, or collisions with smaller
ocity of the meteoro'i'd, V the transverse velocity, particles), and the spin-up proceeds at a rate (Olsson-
0 is the Stefan-Boltzmann constant, f, is the meteoroid Steel, 1987a):
obliquity (the angle between its spin axis and the pole
of its orbit), T is the meteoroid mean temperature, and Aw / At = 15 g S Q / 8 IT c p r2 (7)
AT is the temperature difference across its surface,
derived from: where g is a factor describing the efficiency of the
windmill/paddlewheel. It is to be emphasized that g
AT = < {1 - A) S / u» (4) is not well-known and so far only crude estimates have
been made (Paddack and Rhee, 1976); here a value of
where A is the albedo. The thermal inertia ( 1 / Y ) is g s 0.001 will be assumed. Using even such a small
defined as: (K = thermal conductivity; p = density; efficiency factor one f;nds from (7) that at ) AU:
1 C = specific heat)
(1/Y) = ( K p C ) (5) Au>s / At s 100 rad/sec/year (r = 1mm)
The temperature is: s 1 rad/sec/year (r = 1cm)
T = ( { 1 - A ) S / 4 o ) 1/4 (6) so that very high spin rates would be attained within

158
 a few hundred years; of course, the torque upon an and hence from 1.4 AU originally these larger meteor-
individual meteoroid would not continue in the same oids would now have a s 1.39 ± 0.02 AU. The net
sense or with the same magnitude over its lifetime, effect would be that the radar meteor shower (rsimm)
since variations in its surface structure and refrac- would be expected to commence at least three or four
tive index characteristics will occur due to sputter- days before the visual/photographic shower, with the
ing, collisions, etc. In addition, the spin axis will radar peak occurring at about the time of the onset
precess at a rate: of the visual (r s 1cm) shower; the visual peak would
occur one to two days later, and thereafter there
= 15 S Q / 8 C p r 2 (8) would be a concurrent decline in activity of both
radar and visual meteors. This scenario, based upon
which implies that the spin axis will precess about the results of the theoretical investigation of the
the Sun-meteoroid line several times in each orbit, radiative perturbations described above, is in fact
leading to a random-walk type of movement away from as is observed for the Geminid shower. In addition,
the mean stream orbit. other observed characteristics of the shower are also
As briefly mentioned above the Y-R effect is due to explicable by this model: the mean magnitude of the
the fact that the meteoroid will not be isothermal if meteors increases as the shower proceeds each year,
it is spinning sufficiently quickly. This requires a and only the smaller meteoroids are predicted to
spin rate of: arrive in the early stages of the shower; similarly
the earlier meteors are predicted to have a greater
> 4 TI K / r2 (9) spread in orbital elements, and the radiant is in
fact observed to be more diffuse initially, and to
which, with K s 0.1 and C s 1000 (in SI units) implies contract later in the shower.
D C • 1 rad/sec for r = Iran; for 1cm meteoroids the
necessary spin rate is even lower. At the other end The above analysis was based upon a Geminid age of
of the scale tne Y-R effect would be insignificant if 101" years, whereas some -authors believe that the
u r were so large that AT (equation 4) were very small; stream is rather younger (Kramer and Shestafca, 1985).
this would require io > "10° rad/sec, and in any case Most estimates have been of the order of 5,000-10,000
at such a spin rate the meteoroids would be unstable years, and the annual consistency of the shower
against 'rotational bursting' (Ratcliff et al., 1980). requires an age of at least 500 years (Jones, 1982,
1985). For any age below 101* years the necessary
4. Results for the Geminids spreading can be accommodated by assuming that the
spin rate is lower than the rates used above. If the
The procedure followed here was to numerically integ-
true age were only in fact 103 years then the annual
rals a test meteoroid around a single orbit using
perturbation would need to be 10 times larger, and
elements identical to the mean elements of the Geminid
hence (from equations 3 and 4) «j would have to be
stream: for more details see Olsson-Steel (1987a).
(10) 2 = 100 times smaller. It ii also worthwhile to
Small steps in true anomaly were used, and at each
point out that in the early stages of the stream
point the forces due to the radiative effects were
evolution, whilst the spin rates ire still small, the
calculated, and their individual contributions to the
dispersal of the orbits proceeds quite rapidly and
total perturbation of the orbit were summed. This
the total spreading may be dominated by these early
gives the perturbation over a single orbit (period
stages.
"1.6 years); to get the total orbital change over an
assumed age of 10" years the perturbations were simply Since the perturbative cc-j^U-vsnionc (proportional
scaled up, although in reality the orbit gradually to the forces / r3) due to the radiative effects all
evolves. Since the radiative forces are independent depend linearly upon the radius, if one requires the
of t;,.j an-jular elements, precession and rotation of spread due to the Y-R effect to be equal in magnitude
the ! >,6 of apsides over this time-frame are not to the shrinkage unocr RP + P-R then one obtains a
important as regards the changes in the orbital energy. dependence of spin rate upon thermal inertia which is
independent of the meteoroid radius, and independent
It is. sufficient here to quote the effect upon the
of the assumed age of the stream. This means that a
seini-major axis of the test meteoroid; the changes in simple plot of u against \!/v), as in Figure 1, can
all the other elements are given by Olsson-Steel be used to estimate the necessary spin rate for any
(1987a). Using r = 1mm, A = 0.1, (1/Y) = 300, particular thermal inertia, if the relative values of
p = 1.06 g/cm'.oi = lOVad/sec, and obliquity £ = 45° the shrinkage and the spread can be estimated. As an
or 135°, the change in semi-major axis is: example, consider eqjal -.^irinkage and spread with
A = 0.1 and ( 1 / Y ) -• ,r:/j. -;->r, r•--.-.••. Tig. 1 one reads
Aa = - 0 . 0 2 2 AU in 10" years (RP) off u = 1 . 8 :< 101" ray/sec; huivo/er if the spread
-o.ogy (P-R) were three times the ;.'ir!(.kage tr.en a. would need to
(3) : times lower, o; -c •• 2,000 rad/sic.
±0.13 " " (Y-R)

Thus the total orbital shrinkage (due to RP + P-R) 5. Summary

would be 0.12 AU, with a spread (due to Y-R) of 0.13
AU; prograde spin ({; = 45") results in a plus sign It appears that the Ydrkovsky-Radziev;kii effect is
above, in which case the decay of the orbit under RP able to accommodate the observed characteristics of
the Geminid shower (reviewed by Porubcan, 1978), and
and P-R is opposed by the Y-R effect; retrograde spin
is the major agent causing gradual dispersal (as opp-
U = 135°) gives the negative sign. From the above
osed to gross scattering in close planetary encount-
parameters one finds that a batch of 1mm meteoroids,
ers) of meteoroid streams: its influence should be
all released 10'' years ago with a = 1.4 AU, would now included in future models of stream evolution.
have a = 1.28 ± 0.13 AU (i.e. their semi-major axes
would range from 1.15 to 1.41 AU). These radiative The present model is computationally very simplis-
forces do not affect the perihelion distance apprec- tic and must be refined in order to investigate in
iably, so that the stream of such particles would more detail how the physical and rotational parameters
appear to have a range of aphelion distances, and of the meteoroids affect the evolution of their
would intercept the Earth at slightly different times. orbital energies: little of consequence is presently
known about thermal conductivities/inertias and spin
Using the same physical parameters for a 1cm rates (or spin-up efficiency factors) of such bodies.
meteoroid but with 6000 rad/sec one derives: Particular refinements which need to be included in
the radiative perturbation model include:
Aa = -0.012 AU in 10* years (RP + P-R)
±0.017 " " (Y-R) (i) The effect of gradual spin-up after meteoroid
release from the parent body;

159
 (ii) Precession of the spin axis due to
the solar radiation-imposed torque;
(iii) Integration of the test meteoroids
over many orbits so that the effects
of orbital evolution are incorporated;
(iv) The effect of the finite formation-
time of the stream: the present model
assumes all meteoroids to have been
released by the parent at the same
time.
In order to realistically follow the stream
evolution over centuries and millenia the
radiative perturbation model would need to
be interfaced with models which consider
ejection velocities from the parent, secular
perturbations of the orbits, and possibly
also the differential gravitational perturb-
ations which depend upon the starting posit-
ion in the orbit, such as the models devel-
oped by Fox et al. (1983), Jones (1985), 0-5-1
and Jones and Hawkes (1986). 2-2 2-4 2-6 2-6 3 3-2 3-4 3-6 3-8
LOGjO THERMflL INERTIfl CSI UNITS:
Acknowledgements
This work was largely carried out under Fig. 1. Geminid meteoroid spin rates required in order to get a
ARGS grant number B 8415432. The author spread in orbital energies (due to the Y-R effect) equal in mag-
is European Space Agency Fellow at the nitude to the shrinkage under the dissipative forces (RP + P-R),
Lund Observatory during 1987. as a function of thermal inertia (units J/m2/sec1/2/K) for var-
ious albedoes. The plot is independent of particle size. Also
shown are the thermal inertias of terrestrial (close-packed) ice,
silicates and iron; the thermal inertia for Geminid meteoroids
is probably about 100 - 500 J/m2/sec1/2/K.

References
•<abad:;,iunoi>, F.b.; Obrubov, Yu.V.: 1980, in Solid Kramer, E.N.; Shestaka, I.S.: 1985, in First Globmet
Particles in the Solar System (Eds. I.Halliday and Symposium (Academy of Sciences of the U.S.S.R.,
B.A.McIntosh; Reidel, Dordrecht, Holland), p.157. Moscow), p.77.
Bubad-.'.hunoo, P.B.; Obrubov, Yu.V.: 1984, Soviet Leinert, C.; Roser, 5.; Buitrago, J.: 1983, Astron.
Astron. J., 6J, 1005. Astrophys., 118, 345.
burns, J.A. Lenny, 1979, Icarus,to,1. Mclntosh, B.A.; Hajduk, A.: 1983, Mon. Not. Roy.
CaruJ:', A.; Kvsadkood, M. ; Vals^^cki, G.B.: 1983, Astron. Soc., 205, 931.
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McDonnell; Wiley, Chichester, England), p.527.
Olsson-Steel, D.: 1987b, Astron. Astrophys. (in press).
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Roy. Astron. S o c , 199, 313. Opik, E.J.: 1951, Proc. Roy. Irish Acad., A51, 165.
Fox, Williams, I.P.; Huy'uu, D.W.: 1983, Mon. Not. Paddack, S.J.; Rhee, J.W.: 1976, Lecture Notes in
Roy. Astron. S o c , 205, 1155. Physics, 48, 453.

Banner, M.J.; Giese, R.H.; Wicja, K.; Zerull, R. 1981, Parubaan, V.: 1978, Bull. Astron. Inst. Czechosl.,
Astron. Astrophys., 104, 42. 29, 218.

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S o c , 185, 727.
Radzievskii, V.V.: 1954, Dokl. Akad. Nauk. S.S.S.R.,
Hauc'.r, .'•!. iS.; Gautiev, T.U.; Good, J. ; Lou, F.: 1985, 97, 49.
in Properties and Interactions of Interplanetary
Dust (Eds. R.H.Giese and P.Lamy; Reidel, Dordrecht, Ratcliff, K.F.; Hisaoni, N.X.; Paddaok, S.J.: 1980, in
Holland), p.43. Solid Particles in the Solar System (Eds. I.Halliday
and B.A.McIntosh; Reidel, Dordrecht, Holland), p.391.
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J.Geophysical Research, 90, 12381.
Hunt, Williamo, I.P.; Fox, A'.: 1985, Mon. Not. Roy.
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Sykes, M.V.; Lebofsky, L.A.; Hunten, D.M.; Low, F.:
Jonw, -'.: 1982, Mon. Not. Roy. Astron. S o c , 193, 23. 1986, Science, 232, 1115.
Jon,:.;, J.: 1985, Mon. Not. Roy. Astron. S o c , 217, 523. Whipple, F.L.: Astrophys. J., 113, 464.
oiu:s, J.; Hxjkcc, H. 1986., Mon. Not. Roy. Astron. Whipple, F.L.: 1972, in From Plasma to Planet: Nobel
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Jon,:j, r!.; J U ; T O ; , 7. ; ;'eiiL,-.<. Stockholm, Sweden), p.209.
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Inst. Czechosl., 36, 116. Wood, J.A.: 1986, in Proc. Comet Nucleus Sample Return
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160
 D I S C U S S I O N

i: r i f o: With respect to your remark c o n c e r n i n g U l s s o n - S t e e l : ft is not just the Y-R elect w h i c h

r o t a t i o n s induced by gas d r a g , I just w i s h Ts ac t i ng.- T b e l i e v e that largely it is the
to m e n t i o n that s i m p l e e s t i m a t e s of B r o w n i a n P-R ( P u y n t i n g - H o b e r t s o n ) e i f e c t w h i c h c a u s e s
r o t a t i o n s of small grains in c o n d i t i o n s a p p r o - the mass s e g r e g a t i o n , with the Y-R e f f e c t
p r i a t e to r.nmetary e j e c t i o n s near 1 All from c a u s i n g a d i s p e r s a l of o r b i t a l e n e r g i e s
the Sun indicate angular r o t a t i o n s pretty about the mean orbital s h r i n k a g e (for a
h i g h . I t e n t a t i v e l y s u g g e s t 10 r a d i a n s /second p a r t i c u l a r size m e t e o r o i d ) <Hie to the P-R ef-
for mm s i z e . Does that lit with your c o n c e p t s ? f e c t . N o t e that this could have c o s m o g e n i c
0 1 s s o n - S t e e l : I hank you for m a k i n g this p o i n t . s i g n i f i c a n c e : in the early sular s y s t e m , when
Ihis is very useful to k n o w , b e c a u s e until the solar flux was m u c h h i g h e r (T-Tauri
now I had been w o r r i e d that if the m e t e o r o i d s s t a g e ) , particles would have suffered much
i n i t i a l l y had very low spin r a t e s , then the q u i c k e r orbital decay due to P-R e f f e c t .
initial d i s p e r s i o n would be h u g e and h e n c e H o w e v e r , the o r b i t a l decay of p r o g r a d e - s p i n -
p r e d i c t much larger v a r i a t i o n s in orbital riing p a r t i c l e s would be much lower (due to
e n e r g i e s than are actually o b s e r v e d . Y-R) than for s i m i l a r r e t r o g r a d e - s p i n n i n g
H a u a d z h a n o v : How d o e s the Y o r k o v s k i - R a d / i e v s k i p a r t i c l e s , for wiiich the Y-R and P-R e f f e c t s
e f f e c t p r o d u c e a mass s e g r e g a t i o n of metc-oruid would c o m b i n e to c a u s e much faster i n s p i r a i -
:, t r e a m s ? ling. T h u s , the r e m n a n t p a r t i c l e s would
mainly heve prograrie s p i n , and this may be
a p a r t i a l e x p l a n a t i o n of why the p l a n e t s
g e n e r a l l y spin in this d i r e c t i o n a l s o .
 OH APPLICABILITY OP METEOR STREAM MEMBERSHIP CRITERIA

J. Stohl and V. PorubSan

Astronomical Institute of SAV, 84228 Bratislava, Czechoslovakia

Meteor stream membership criteria used in evaluating potential associations be-

tween individual meteor orbits and the mean orbit of a stream are discussed on the
basis of precise photographic orbits of some meteor streams (the Taurids, Geminids
and Perseids). Serious shortcomings of the D-criterion are disclosed and suggest-
ions on a more relevant use of the criteria for estimating Btream memberships are
presented, with attention paid to the distributions of the orbital elements of the
streams.

Introduction D ia calculated from the expression:

Several criteria have been devised for D 2 = (Ae^ 2 +(Aq) 22 +[2sin(I/2)] 2 +r(e A +e B ).
distinguishing meteor streams and their asso- .sin(TT/2)J .
ciations with comets and asteroids. Most com-
monly used is the D-criterion introduced by The angle I and the difference TT i s given by
Southworth and Hawkins (1963); similarity of the equations:
two orbits is here evaluated by a quantita-
tive measure, the D-value, which represents r 2 s i n ( I / 2 ) ] 2 = [2sin(/M/2)I 2 +sin i A . s i n i B .
an overall difference between the orbital ele-
ments of the two orbits. The D-criterion ap-
plied to the observed orbits has enabled to and
recognize several unknown streams and asso-
ciations (Southworth and Hawkins, 1963; Lind- TT-Au)+2
blad, 1971a and 1971b; Sekanina, 1973 and
1976; Gartrell and Elford, 1975; etc.).
Some modifications of the D-criterion have where Ai = 1 A ~ 1 3 »
been also suggested in the search of meteor while
hil th the signs i ((+) and (-) hold for
streams (Porubcan, 1977{ Drummond, 1981). In
the study of asteroidal families, which is
°
180° and lAfl-l>180°, respectively.
At the streams search serious intrinsic
basically the same kind of problem, the problem of the discriminant D arises from the
at -criterion was used (Carusi and Valsecchi fact that the difference between any one of
1982), devised by Gavriehin (1974) and applied the elements of two orbits which are to be
first in geological studies (Coradini et al., compared enters only into the overall combi-
1976). It should be emphasised that all these nation of the differences between all other
criteria have statistical value only; it is elements, i.e. into the total value of D.
necessary to have this fact in mind when eva- Since the rejecting procedure is only based
luating the significance of any results based on the D-values themselves, totally neglec-
on their application. ting actual distributions of the orbital ele-
In this paper we will deal mostly with the ments in the searched meteor stream, some of
D-criterion ae applied to the search of mete- the actual members of the stream can be re-
or streams. Generally speaking, there are two jected if most elements have large, though
approaches how to use the D-criterion in the plausible deviations from the mean orbit. On
streams search. If there is no a priori know- the other hand, a meteor can be included into
ledge of a meteor stream, the search consists the stream while not being its actual member,
in computing the D-values between all members if most of the orbital e1 ements of the meteor
of a given set of orbital data and in finding do not differ too much from the mean orbit
serial associations between the orbits. An- though one or two elements differ substanti-
other approach consists in the comparison of ally from it.
the corresponding element* of an orbit and To demonstrate this problem in an acute
of the mean orbit of a known stream. At both way we can use the orbital data on the Taurid
these approaches ther* are shortcomings by stream, which is exceptionally diffuse. At
which the results can be strongly biased, the investigation of the stream it appeared
though they are usually neglected in the that some oT the meteors designated in the
studies. The aim of this paper is to demnti- catalogues of photographic meteor orbits as
strate some more serious of then. the Taurids cannot be recognized as such be-
cause of very large deviations from the mean
Application of the D-criterion orbit of the Taurids at the corresponding
solar longitude at least in one of the orbi-
The Sonthworth-Hawkins' discriminant D is tal elements (PorubSan and stohl, 1987a and
defined by a combination of suitably chosen 1987b). As a typical example of this kind
and weighted differences between the elements the meteor Ho. 9311 from the catalogue by
of two orbits, A and B, in a four-dimensional Posen and MsCrosky (1967) can be given, which
coordinate system, consisting of the diffe- has been designated as the Northern Taurid.
rences A e » ex - «g and A q • qx - <LB» of Its inclination is i-10?9, which ia much
the angle I between the orbital planes and higher than the mean inclination of the North-
of the difference 17 between the longitudes ern Taurids, wh: -jh is i»3?0±l°l as derived
of perihelion measured from the intersection from 42 most preoise orbits of the If Taurids.
of the orbits. The value of the discriminant At the same time the differences of other

163
 Table 1 be rejected by a usuel procedure of the D-
Orbital elements and their dispersions for criterion, let us return ap;ain to the Tau-
the Northern and Southern Taurida rids. The mean elements, derived from the
most precise orbits of the Northern and
Southern Taurids (42 and 96 orbits, respec-
B Taurids S Taurids tively), together with their standard devi-
ations are shown in Table 1. (We should note
e 0.828 ± 0.051 0.814 ± 0.048 that in our previous list of the mean ele-
q 0.367 0.096 0.366 ± 0.090 ments of a larger sample of the Taurid or-
a} 292?6 ± 12?2 114 ?3 t 11 °3 bits, given in Table 2 of the paper by Po-
225?7 ± 35°4 rubcan and Stohl, 1987a, an inevitable error
n 7
3?0 I?! 1
5?5 ±ih occured inJl; the proper values should read
219?2 for the Taurids and 36°7 for the South-
T ern Taurids). The orbits with the elements,
elements with the exception of Jl are very say, e = e ± Oe, q = q ± cr. etc., which
pmall: Ae = 0.029, M = 0.005, Aw = 1?8 (for should be considered as unsmbiguouly belong-
the mean values of the orbital elements of ing to the stream, have the D-va^ues of about
the Taurxds cf. Table 1 ) . The D-value of its Dq« = 0 . 5 . For the orbits wi th e = "e ± 2<re
q
orbit is relatively high, but as a closer to the ± 2 o~"n ..., still apparently belonging
inspection reveals, substantial part of the e stream, extremely high values D > 0 . 8
2
value D (86%) is caused by the difference
in the ascending node ASl = 28?8 (which equals
to 1.33 o^,), and not . n the inclination
(which amounts to 9.91<*i! ). a.H
It is evident that the E-value by itself
is not an unambiguous tool for deciding about
the membership of a particular meteor to a a.3
given meteor stream. At our investigation of
the Tauride 10 out of the 158 meteors clas- B.2
sified as the Northern or Southern Taurids
in the cetalogues of the precise photographic
orbits had to be rejected not due to their
large D-velues, but on the basis of an extre-
mely large deviation from the mean orbit in
at least one of the elements e, q or i (Po-
rubcan and Stohl, 1987b).
Let us note that the rejection level, i.e.
the maximum value of the discriminant Dmax IH)
is usually taken the sane for all searched
streams and associations, depending only on
a.3
the number of meteors in the investigated
sample. Southworth and Hawkins (1963) adopted
the value Dma;?. = 0.20 for their sample of 360 B 2
orbits, with The D^ax ~ value depending on
the fourth root of the sample size. Lindblad 0. i
(1971b) takes a more strict value D m a x =
= 0.80 N~1'4. It car. be demonstrated, nowever,
that the actual distribution of the D-ve'i^s J
of the members of a stream dependens strongly e a n
on the concentretion of the particular stream
(cf. e.g. Pig. 1 in Porubcan, 1968. At such
a diffuse stream ae the Taurids are even the
value D > 0 . 4 is not exceptional. In the ori-
ginal sample of the 158 meteors classified as
Taurids 24 orbits (i.e. 15.2?<-) have the value
D > 0 , 4 , while the mean values of D are:
% T = _0.227 ± 0.178 for the Northern Tauride
and '5s'p = 0.217 ± 0.133 for the Southern
Taurids. Even when we exclude the 10 meteors
with large deviations Ae, A q or A i , and
also another 10 meteors with their aphelie
Q > 5 . 1 (Porubcan and Stohl, 1987b), still the
mean values of D for the remaining 42 North-
ern and 96 Southern Tauride are Djjff = 0.195 ±
± 0.157 and D S T = 0.194 ± 0.117, respectively;
total number of orbits with D > 0 . 4 from this
sample is 13, i.e. 9.495.
The other intrinsic problem of the D-cri-
terion, which consiBts in its inability to
recognize a real member of a stream if the
calculated value of the discriminant D is too
large, seems to be less obvious. In a previ-
ous paper one of the authors has pointed out
to the fact revealed by the examination of
the frequency distributions of the orbits
that many a meteor classified as sporadic 0.Z B.2 B.H 0.6 E.B j)
ones appeared to be in fact members of the
examined stream of the Taurids (Porubcan, Pig.l. The values of D» vs. D for the North-
1968). ern Taurids (a), Southern Taurids (b), Gemi-
To show how a real member of a stream can nids (c) and Perseids ( d \

164
are obtained. It should be emphasized that value ot D beini?; D = u.404. While fit the
for these high values of the discriminant D discriminant D two thirds of the D2-velue go
the angular elements co and SL are responsible to the fourth component which represents a
in a dominant way. If we accept, e.g., the weighted function of the difference between
values of the deviations in the eccentricity, the longitudes of perihelion, at the discri-
perihelium and inclination to be equal to minant D' the element q alone is responsible
zero (Ae = A q = A i = 0 ) , even then the de»- for 885? of the D 2 -value, though the devia-
viations Aio=eCj and ASl = oi, alone are large tion Aq = 0.190 only slightly exceeds 2ffq
enough to lead to the value D ~ 0 . 5 , while the and the deviations of the angular elements
deviations A w = 2ff to andAJi= 26^ alone give are AUJ = 21?5 (which equals to 1 . 9 O and
D « 0 . 9 . Orbits with such high values of D AJl = 43?6 (which equals to 2SJI). Overemphasis
would be excluded from the stream membership on the deviation An at the discriminant D*
at the usual procedure. is evident in this case, B S it is also in
The dominant role of the angular elements many other caBes. The Southern Taurid No.
in the D-values at the orbits of the very dif- 12189, e.g., has an extremly large deviation
fuse and enduring Taurid stream is what could in the inclination of its orbit, Ai = 16?0
be expected from the discriminant D as it is (which equals to 14.5 <5"i! ), but still for
defined. In addition to usual procedure of 49% of the D'2-value the element q is res-
applying the D-criterion careful investiga- ponsible, the prohibitive deviation Ai being
tion of the distribution of the orbital ele- almost neglected in the D 2 -value.
ments, together with a more balanced weighting Among the neminids (Pig. lc) at both the
of their components in the D-value appears to orbits with the two largest values of D'(0.178
be necessary. and 0.171) the element q is almost entirely
responsible for these values, with the cor-
Problem of weighting the D-components responding components adding to the D' 2 -va-
lues 98% and 96%, respectively.
In his modification of the discriminant D On the other hand, in the case of the lar-
Drummond (1981) introduced a revised discri- gest D'-value emong the meteors of the high-
minant D1,which utilizes a particular set of inclined stream of the Perseids, the effect
weights to render each of the elements into of q on the D'j-value is completely negligible,
natural, dimensionless units, with each com- with 91% of Vi1 coming from the difference in
ponent making an approximately equal contri- the eccentricity, Ae = 0.365.
bution to D', which is not the case at D, as A need to distinguish between various
we have seen. Drummond's discriminant D* is showers at the weighting of both the D- and
given by the formula: D*-components seems to be obvious, and a more
thorough analysis of different showers is
D'2 = rAe/(e A +e B )] 2 +rAq/(q A +qg)] 2 +fl/180 o J 2 + inevitable for estimation ••* eny oroper
+ {[(e A +e B )/2](©/180°)} 2 \ weights.
A note should be added about the ineffi-
where ciency of the discriminants D and D» to solve
I = arccos(cosi A .cosi B + sini A -sini B -cosAJl), unambiguously the question of the membership
of a particular meteor orbit to a shower.
Q= arcos (sin/Jl- 9infl'R + cos& • cos/3g.cos A X ) , Orbits of the meteors classified as TauridB
in the photographic catalogues, but removed
with the ecliptic coordinates of the perihe- from our list of the Taurids because of large
lion point: deviations in their elements e, q or i, do
not have the largest values of D'. In the case
X =Jl+arctg (cosi . tgu>), for cosu)<0, of the meteor Wo^ 4670, classified in the ca-
talogues as the Southern Taurid, the D*-va-
A'=Jl+arctg (cosi.tgiu )+180°, for cosu/>0, and lue js as low as D* = 0.139, not leaving any
doubt on its membership to the stream.Still,
d= arcein (sini . sintu). its difference Ai = 1 0 ? 6 i n the inclination
(which equals to 9.6 a±) shows clearly that
In average, the relation between D and D' the meteor cannot be taken as a real member
is roughly linear, with the values D = 0.250 of the Taurid stream.
and D* = 0.105 corresponding to each other In general it is possible to state that
(cf. Pig.l in the Drammond's paper). Prom the the discriminant D',though perhaps with a
point of view of the problems with the dis- better weighting of the D'-value components,
criminant D it is of special interest to see still does not solve the problem of the short-
to what degree its shortcomings can be sup- comings of the stream membership criterion
pressed if the discriminant D' is used inste- because of its neglecting the actual disper-
ad of D. sion of the orbital elements. On a possible
Figure 1 shows the relations between D and way how to include the dispersions of the
D»for the Northern and SouthernTaurids, Gemi- orbital elements into the stream membership
nids and Perseids. It includes also the pho- criterion has been pointed out by one of the
tographic orbits from less precise catalogue authors with his S-criterion CPorubSan,1977).
by'McCrosky and Posen (1961), where the or-
bits had been derived by graphical method. It
is seen that the relation for streams with The D-criterion based on the varied mean
low inclination (the Taurids, Geminids) is orbit
very loose, which was to be expected. At these
showers several orbits with very large values At the streams of a short duration, not
of D do not correspond to the orbits with the exceeding a few days, it is usually suffi-
largest values of D* and vice versa. Inspec- cient to represent their orbit by the mean
tion of these cases can be revealing on the orbital elements, unvaried in the courae of
actual relation between the discriminants D the streams activity. The mean orbit, howe-
and D', and also on the weighting problem. ver, is not sufficient at the streams with
As an example of this kind we can take their activity extending over several weeks
the Southern Taurid No. 11912 with the lar- or months. The D-values of meteor orbits
gest value of D' = 0.373, the corresponding calculated with respect to the mean orbit of

165
 DiscuB8ion
0
' * TIUIK The aim of this paper was to nresent some
• S TIUIK
more serious problens and shortcomings of
l.l the usual application of the D-criterion. A
new method of weighting the D-va3ue compo-
nents with attention paid to the dispersions
of the orbital elements appears to be neces-
I t
sary, though its formulation is outside the
scope of the present paper.
It should be emphasized once more that a
.; •
I.H carefull use of the D-criterion is strongly
recommended when it is applied to the orbits
at the search of potential associations. Its
shortcomings shown above should be taken into
1.2 account to avoid both the underestimation
A and overestimation of the associations.
»
*
One important note should be added. While
•-••
the D-criterion can be a very usefull tool
IM Mi in statistical studies of the streams present
in a large sample ot the orbits, end to some
degree also in finding the associations bet-
> ween various streams and objects, its applic-
> • IRUIIM
- S TMHS5 ation to the genetic relations must be taken
1.4 with a reservation. As was pointed out by
Drummond (1981) and stressed by Babadzhanov
a • and Obrubov (1983), application of the relat-
ionship criteria to the present-state orbits
1.2 * • * "

' •
neglects important fact that because of the
. • a
perturbations and orbital evolution,the or-
i * .
" • . • •
:
. "'»••
bits which are very similar at present could
a •-
: • • • •
differ very much in the past. Even a low cal-
culated value of the discriminant D (or any
other discriminant) does not necessarily
eonfirm the filiation between a meteor stream
Pig. 2. D-valueo of the Taurids V B . solar and a comet or an asteroid.
longitude La, with respect to the mean orbit
(upper plot! and varied mean orbit (lower REFERENCES
plot).
Babadzhanov,P.B. and Obrubov,Yu.V.: 1983,
such a long-enduring stream cannot give rele- In Asteroids, Comets, Meteors, eds. C.I.
vant information about the membership, espe- Lagerkrist and H. Rickman, Uppsala Uni-
cially of those meteors which are at the out- versity, 411.
skirts of the stream. Carusi,A. and Valsecchi.G.B.: 1982, Astron.
On Pig. 2 the D-values versus the solar Astrophys. 115, 327.
longitude L© are plotted for the Taurid stream Coradini.A.; Fulchignoni.M. and Gavrishin,
extending its activity over more than four A.I.: 1976, The Moon 16, 175.
months. Systematic charge of the D-values cal- Drummond,J.D.: 1981, Icarus 45, 545.
culated with respect of the mean orbits of the Gartrell,G. and Elford.W.G.: 1975, Aust. J.
Northern or Southern Taurids presented in Phys. ?8, 591.
Table 1 is evident (Fig. 2, upper part). The Gavrishin,A.I.: 1974, Gidrogeokhimicheskie
lower part of Fig. 2 shows clearly to what issledovaniya s primeneniem matematiches-
degree the D-values are reduced, if calcula- koi atatistiki i EWM, Nedra, Moscow,
ted with respect to the varied mean orbit 145 pp.
which takes into account systematic change of Lindblad.B.A.: 1971a, Smithson. Contr. Astro-
the orbital elements in the course of the phys. 12,1.
streams activity (for the values of the varied Lindblad,B.A.: 1971b, Smithaon. Contr. Astro-
mean orbit cf. PorubSan and Stohl, 1987b). phys. 12, 14.
The mean value of D calculated with respect McCrosky.R.E. and Posen.A.: 1961, f^mithson.
to the varied mean orbite is Smm •= 0.124 ± Contr. Astrophys. 4, 15.
± 0.099 for the ±2 precise orbits of the North-PorubSen,V. : 1968, Bull. Astron. Inat. Cze-
ern Taurids and D S T = 0.101 ± 0.068 for the chosl. 19, 327.
96 precise orbits of the Southern Taurlda, as Porubcan.V.: 1977, Bull.Astron. Inst.Czeehosl.
compared with the corresponding values Dwm =• 2 8 t 257.
» 0.195 ± 0.157 and D S T = 0.194 ± 0.117 deri- Porubcan.V. and Stohl,J.: 1987a, in Diversity
ved with respect to the mean orbits, as given and Similarity of Comets (in press).
above. PorubSan,V. and Stohl,J.: 1987b, This volume.
At any searoh for associations between me- Posen.A. and McCrosky.R.E.: 1967, NASA CR-862.
teor streams and/or their potential parent Sekanina,Z.i 1973, Icarus 18, 253.
objects it is necessary to apply the D-erite- Sekanina, Z . : 1976, Icarus 27, 265.
rion with respect to the varied mean orbit, Southworth.R.B. and Hawkins,G.S.: 1963,
if the association should not be underestima- Smithson. Contr. Astrophys. 7, 261.
ted (cf. Porubcan and Stohl, 1987b, for the
associations of some minor streams with the ful to find first the Earth-crossing orbit of minimum
Taurid stream). D-value with respect to the comet and then to refer
the data to this orbit. For some showers this might
Comment^ provide a better resolution from the sporadic back-
ground.
Kreaaki When comparing the orbits of individual meteo-
roids with that of their parent comet, it might be use-

]66
 THE UETEOR COMPLEX OF P/ENCKE

V. Porubian and J. Stohl

Astronomical Inatltuta SAV, 84228 Bratislava, Czechoslovakia.

The Taurid meteor complex associated with P/Encka Is studlsd on the baaia ot relevant photo-
graphic and radar orbits. Orbital characteristics, radiants and durations of the postperlhell-
on showers are compared with corresponding theoretical values derived fron the observation!) of
the preperlhellon Taurlde. Heallty of the proposed associations of minor showers with the Tau-
rld complex and the total duration of Its activity are evaluated and discussed. Some of the
associated showers fthe Northern and Southern % Orlonlds, Northern Plsclda and Southern Arietlds)
are confirmed to be in fact parts of the Taurid shower itself.

Introduction es was much larger the difference between their

mean orbits and that with the exception of the in-
From the point of view of the evolution and equi- clination and orientation the orbits of the Nor-
librium of the whole meteoric complex in the Inner thern and Southern Taurids were practically iden-
part of the solar system the study of the showers tical (cf. Table 2 in Porubcan and Itohl, 1987).
and bodies associated with the short-period comet More rigorous Investigation of the shower, inclu-
P/Encke is of a special interest(whipple, 1967 and ding radiants of all its individual members re-
1976; Delseane, 1976} Kresak, 1980; Napier, 1983J veals, however, that both the branches are in fact
Clube and Napier, 1986 etc.) All these showers com- clearly distinct
prise a very dispersed and rich complex which, be- The varied mean orbits war* therefore again de-
cause of Its very low inclination, is met by the rived, separately for the Northern and Southern
Earth twice a year, both at the preperlhellon and branches of the stream. From the whole aet of 198
postperihelion encounters. orblta listed in the catalogues as the Northern or
With different degree of assurance it la possib-
le to include Into the complex about ten meteor
showers (Sekanlna, 1973 and 1976; Drummond, 1981)
touthern Taurids (Porubcan, 1978; Porubian and
tohl, 198?) 10 orbits had to be excluded due to
their wrong original classification as the Taurlds,
a very diffuae stream of sporadic meteors (Stohl, which was revealed by a thorough inspection of the
1986), some larger meteoric bodies, and also a few distribution of individual orbital elements (Nos.
Apollo asteroids (Clube and Napier, 1986; Olsson- 2263, 2473 and 2630 by Whipple, 1954; No. 3886 by
Steel, 1987). The most significant representative Jacchla and Whipple, 1961; Nos. 9311, 12114 and
of the complex is the Taurid shower, consisting of 12189 by Fosen and McCrosky, 1967; Nos. 4670 and
the Northern and Southern branches, observed in the 5298 by Hawkins and Southworth, 1961; No. 71942 by
nighttime hours at the preperihelion encounter, Babadzhanov et al., 1968). In the present Investi-
with its duration extending over three months. At gation we have excluded further 10 orbits with
the postperihelion encounter the complex is obser- aphelia beyond the orbit of Jupiter (in the range
ved as the daytime/& Taurlds, of considerably shor- from 5.5 to 7.3 A U ) , which might misrepresent the
ter duration (about two weeks according to Cook, stream's original orbit (Nos. 1526, 1893 and 2957
1973, and about one month according to Sekanlna, by Whipple, 1954; No. 5511 by Jacchia and Whipple,
1976). 1961; Nos. 9504, 11037, 11208 and 12064 by Posen
Because of the very large spread, long duration
and complex structure of the Taurid stream, associa-
tions of various showers and objects calculated re-
lative to the "mean orbit" of this stream (or of
its branches) might lead to ambiguous results and
need a reexamination. The aim of the present paper
V
is to investigate in more details observed charac-
teristics of the stream and to evaluate the asso-
ciations and the extension of the whole complex.

Orbits and radiants of the Taurid stream

Most precise orbit* of meteors are provided by

photographic observations which, however, sxa bound
to the nlghttlue period yielding thus only data
from the preperlhellon encounter of the Taurid
stream with the Earth. At the postperihelion en-
counter the geocentric radiants of the straaa are
concentrated In an area close to the Sun, producing
thus daytime meteors which can only be observed by
the radio technique.
As was demonstrated in a previous paper analy-
sing photographic orbits (Porubcan and Stohl, 1987),
the mean orbit of the Taurlds varies considerably
In the course of the atream's enduring activity. The
varied mean orbit of the Taurids given In the pre-
vious paper was derived for the stream as a nhole. Fig. 1. Orbits of the 138 photographic Taurlds pro-
It was justified by the fact that the intrinsic dis- jected into the plane of the ecliptic (J, B - or-
persion of the orbits within each of the two branch- bits of Jupiter and Earth).

167
 Table 1
Variations of the orbital elements of the North-
ern and Southern Taurids with solar longitude L o
(L* = L o - 220°)

Northern Taurids:
a * 2,15 + 0.00409 l/\_
e » 0.836 - 0.00066
q = 0.347 + 0.00241
i =»3908 - 02036 L*
294°9 - O°34 L*
% = 154° 9 + O?66 L*
Southern Taurids:
a = 2.05 + 0.00865 I K 210-230 23B-27B
e » 0.811 - 0.00063 L
q • 0.381 + 0.00310 L*
i = 5?32 - 0?0l4 L*
u) = 112?6 - 0°42 h
It = 152?6 + 0^58 L*

and McCrosky, 1967j No. 643282 by Babadzhanov et al,

1968; No. 436 from MORP data).
In Fig. 1 the precise orbits of the remaining
sample of 138 Taurids (42 Northern and 96 Southern
Taurids) are shown in projection on to the plane of
the ecliptic (it should be compared with Fig. 1 of
the quoted paper by Porubcan and §tohl, 1987 where
the 10 large orbits are included). Dominant charac-
teristic of the stream, is its large spread of the Fig. 2. Distribution of the nodes of the Taurids
orbits, with their longitudes of perihelia ranging in the plane of the ecliptic (heavy arcs - the p n
over more than 75°, from JC ~ 113° up to Tt ~ 190°. perihelion nodes} dots - the postperihelion nodes
Very long duration of the shover's activity exten-
ding over 100°, in between the solar longitudes which the meteoroids collide with the preperihelii
170° and 270°, corresponds to this spread. period lie exactly on the Earth's orbit. The posi-
Variations of the orbital elements with the so- tions of the other corresponding nodes are deflnei
lar longitude derived by the least squares fit are by Intersection of the lines of nodes with the ec-
liBted in Table 1 both for the Northern and Southern liptic and can be found from the orbital elements
Taurids. As the reference solar longitude the value a, e andui.
of 220° was chosen, which is close to the maximum The distribution of both the nodes of 138 pho-
of the shower's activity. Theso varied mean orbits tographic orbits of the Taurids is shown in Fig.2,
should be referred to when evaluating possible asso- The preperihelion nodes are denoted by the heavy
ciations of individual meteors and other showors arcs on the circular orbit of the Earth, which at
with the T a urids. the same time delineate the periods of the Taurid
Geocentric radiants of 106 Taurids (30 Northern activity for the corresponding solar longitudes,
and 76 Southern Taurids) listed in the photographic indicated by the numbers above each circle. The
catalogues have been used for the calculation of postperihelion nodes are marked by dots. In the
the daily motion of their radiants. It is evident upper left plot the 0, mplet set of the nodes from
that because of the long duration of this stream it the whole period of the Taurids activity Is pre-
is meaningless to express the daily motion of the sented, while the following three plots depict th<
radiants as a linear function of the equatorial coo- distribution of the nodes for three different pe-
rdinates. The mean daily motion of the radiants has riods of the stream's activity, around the core ol
been therefore derived rather in the ecliptical co- the stream (210 s ln< 230°) and at both its wings
ordinates; it is presented in Table 2 again with (170°«L o <210°, 230°<L o i270 o ).
the solar longitude 220° taken as the reference The plots indicate that the mean radius vector
point. of the postperihelion nodes of the Taurids increa-
ses systematically with the solar longitude; this
Postperihelion appearance of the Taurid 6tream Increase is identical both for the Northern and
Southern Taurids. It is evident that only a rela-
In the preperihelion period the Earth meets the tively small part of the night Taurid meteors ob-
Northern and Southern TauridB at the descending served at the preperihelion passage can intersect
and ascendiug nodes, respectively. The nodos at the orbit of the Earth at both nodes (cf. the last
plot of Fig. 2) and only these could be observed
Table 2 also at the postperihelion passage as the daytime
The mean daily motion of the geocentric ra- shower. There are altogether 10 orbits only (4 N
diants of the Northern and Southern Taurids Taurids and 6 S Taurids) out of the complete set
(IT - L o - 220 ; equinox 1950.0) of the 138 orbits, which have both their nodes clo
se enough to the Earth's orbit to be observed. All
these orbits correspond to the meteors observed at
Northern Taurids: the end of the Taurids activity, in between the so
52?6 + 0^89 LL" lar longitudes 245° - 270°. The equatorial coordi-
5 L
- 0501 nates of the expected daytime radiants correspon-
ding to the mean orbit* of this staple, computed
Southern Taurids: separately for the 4 Northern and the 6 Southern
0°82 Taurids are given in the first two rows of Table 3
° L*
p. -5°1 - 0°02 The daytine showers associated with the nightime
Taurid shower, i.e. thep Taurids and theJT Pereeids
revealed by radio observations after the theoreti-
cal prediction by Whipple (1940), have their geocen-
tric radiants very different from the expected ones
(cf. in Table 3 the corresponding values, as deri-
ved by various autors). Though the period of the
activity of the expected daytime Taurids coincides
with that of the?Perseids, the radiants are distin-
ctly different, especially in the right ascension.
It can be concluded that the derived daytime appea-
rance of the Taurids cannot be looked upon Just as
the extensions of the known/5 Taurids and f Perseids
and that these two showers should be considered as
distinct branches of the Taurid complex.

Evaluation of tentative associations

The Increase of the radius vector of the Taurids

poatperihelion nodes with the solar longitude re-
flects the fact that the size and orientation of
the mess Taurid orbit is dependent on the solar lon-
gitude (cf. Pig. 3 in Porubcan and Stohl, 1987),
which is also evident from the variations of the
orbital elements (Table 1 ) . Let us verify to what
degree the streams for which associations with the
Taurids has been proposed do agree with the derived
varied mean orbits of the Taurids, as are presented
in Table 1. At the preperihelion encounter the ten-
tatively associated streams include: the Southern
ArietidB, Northern Piscidea, Northern and Southern
7.0rionids,p Qemlnids and Canids, while the postpe- Fig. 3. The nodes of the showers associated with
rihelion complex includes thefiTaurids,£"Perseids the Taurids (open circles - the preperihelion nodes;
andEArietidB (Sekanlna, 1973 and 1976; Cook, 1973). crosses - the postperihelion nodes; full circles -
In Figure 3 the positions of the nodes of the the mean nodes of the Taurids for five 20° - inter-
mean orbits of the showers are shown. The preperi- vals of the solar longitude).
helion orbits have the nodes designated by open cir-
cles connected by full lines, and the nodeB of the expected coordinates of the theoretical radiant
postperihellon orbits are marked as crosses connec- «.£ = 109 ,<ts= +13 at Lo = 107°, while the descen-
ted by dashed lines. The full circles mark the nodes ding node of the Canids is toe far from the Earth
of the Taurid mean orbits for five intervals of the to be observed.
solar longitude, each of 20° wide (170° - 190°, As can be seen in Fig.3, the nodes of thoXOrio-
190° - 210°, etc.). The change of the radius vector nids are practically identical with the nodes of
of the postperihelion Taurid nodes with L o is evi- the last Taurid period (250° * L 0 < 270°). In his
dent. The/3 Taurids are observed at the solar longi- list of meteor showers Cook (1973) distinguishes
tude, where the mean postperihelion Taurid node two branches of the XOrionids, i.e. the Northern
should intersect the Earth's orbit, taking into and Southern JCOrionids. A comparison of their or-
account the systematic change of the nodes. It is bits and radiants with the mean orbits and radiants
likely that thepGerainids and Canids follow progres- of the Northern and Southern Taurids corresponding
sion of the Taurid postperihelion node, too. The to the same period has revealed that the Northern
postpsrihelion node of the p Geminids is close to branches on the one hand and the Southern branches
the orbit of the Garth and, consequently, they on the other hand of both these showers are identi-
should be observed also as a daytime shower, with cal. We thus can conclude that theXOrionids are in
fact regular parts of the Taurids. The same conclu-
Table 3 sion holds true also for the Southern ArietidB,
List of geocentric radiants of the daytime postpe- which are in fact regular parts of the Southern
rihelion showers associated with the Taurid meteor Taurids, and with a less certainty also for the
complex (equinox 1950.0) Northern Plscldes, which seem to be regular part of
the Northern Taurids.
L Duration Heference Table 4
€>
The geocentric radiants of the showers which should
N Taurids (C): be considered as regular parts of the Taurids, with
the corresponding radiants of the Northern (N) or
76U +21" 77° -20 present paper
Southern (S) Taurids
S Taurids (C):
76 +30 77 -20 present paper Shower Ref.
ATaurids (0):
' 86 96 S Arietids 24° +9° a 188
+19 13 Cook (1973)
S Taurids 25 c 188
80 +21 94 24 Sekanlna (1973) +5
84 +24 94 43 Sekanlna (1976)
N Piseids 26 14 b 199
86 +18 98 Orummond (1982)
N Taurids 31 c
+15 199
t Perseids (0):
62 N XOrionids 84 26 b 258
+23 76 17 Cook (1973)
N Taurids 86 +26
32 c 258
60 +25 77 Sekaniaa (1973)
64 +27 81 44 Sekanina (1976)
S XOrionids 85 16 b
21 +21 77 - Drummond (1982) 259
S Taurids 83 +17 c 259

(C - calculated, 0 - observed) Ref.: a - Sekanlna (1973); b - Cook (1973);

c - present paper.

169
 Tahla 5
Mean orbits of the showers listed in Table 4

Shower a e 1 uj Jl 1t Hef. L D
o
S Arl 1.723 0.841 1°4 126:9 ?:s 134:7 a
S Tau 1.77 0.831 5 .8 126 8 134 c 188° 0.082
N Pis 2.06 0.80 3 291 199 130 b
N Tau 2.06 0.850 3. 8 302 199 141 c 199 0.190
-N XOri 2.22 0.79 2 281 258 179 b
N Tau 2.31 0.811 1 .7 282 258 180 c 258 0.042
S XOri 2.18 0.78 7 101 79 180 b
S Tau 2.39 0.786 4 .8 96 79 175 c 259 0.087

Ilef.: a - Sekanina (1973); b - Cook (1973); c - present paper

The positions of the geocentric radiants and of of the stream. Very large age of the Taurid com-
the elements of the mean orbits of all these pre- plex (> 105 years) seems to be plausible from this
perihelion showers are presented in Tables 4 and 5, point of view, though the definite solution can be
together with the corresponding values for the Nor- expected only from very precise calculations of
thern and Southern Taurida, derived by the extrapo- long-term evolution of the orbits of the whole com-
lation of their radiants daily motion (Table 2) and plex.
of their varied mean orbits (Table 1 ) . The values
of the Southworth-Hawkins* D-criterion (Southworth
and Hawkins, i'j63), calculated for the minor showers REFERENCES
orbits with respect to the corresponding varied mean
orbits of the N'orthern or Southern Taurids, are gi- Babadzhanov, P.B.; Getman, T.I.; Zausaev, A.F.;
ven in the last column of Table 5. It is seen that Karaselnikova, S.A.: 1968, Bull. Inst. Astro-
the l;-values are in general very low, confirming phys. Tadzhik. Acad. Sci. 49, 3.
very close relation of these showers to the Taurids, Clube, S.V.M. and Napier, W.M.: 1986, in The Gala-
For comparison it can be noted that the mean values xy and the Solar System, 260.
of the D-crj terion of all precise individual orbits Cook, A.F.: 1973, in Evolutionary and Physical Pro-
of the Taurij.'j nalculnted with respect to their va- perties of Meteoroids, NASA SP-319, 183.
ried mean (•.'••its are 0.141 and O.llG for the North- Delsemrae, A.H.: 1976, in Interplanetary Dust and
hern and 3O..U;orn Taurids, respectively. The asso- Zodiacal Light, Lecture Notes Phys. 48, 314.
ciation of the pGeminids (D = 0.163) and Canids Drummond, J.D.: 1931, Icarus 45, 545.
(D - 0.205) is not so obvious, while the associa- Drummond, J.D.: 1982, Icarus 49, 135.
tion of the^i Oeeiinids (I) = 0.715) remains highly Hawkins, G.S. and Southworth, K.B.: 1961, Smithson.
spurious. Contr. Astrophys. 4, 85.
Jacchia, L.G. and Whipple, F.L.: 1961, Smithson.
Conclusions Contr. Astrophys. 4, 97.
Kresak, L.: 1980, in Solid Particles in the Solar
•--in-it-• - i the orbital elements of the North- System, 211.
ern cuid :•• ,-n rauri'is-, derived from the precise Lindblad, B.A.: 1971, Smithson. Contr. Astrophys.
photograpi. ..its c^::ii:-L-i that the preperihelion 12, 1.
activity cl ,. :) i'auric .r';:;ilex associated with Napier, WVM.: 1983, in Asteroids, Comets, MeteorB,
°/Encise ext.njius over a ,;.?riod of the solar longi- Eds. C.-I, Lagerkvist and H. Rickman, Uppsala
tudes of 130° at least, from the first half of Sep- Univ. 391.
tember till the second half of January, i.e. in be- Olsson-Steel, D.: 1987, The Cbservatory (preprint).
tween the soiar longitudes of about 170°- 300°. The Porubcan, V.: 1978, Bull. Astron. Inst. Czechosl.
minor showc-i - of the Southern Arietids (Northern 29, 218.
Piscids), Northern and Southern X Orionido and pos- Porubcan, V. and Stohl, J.: 1987, in Diversity and
sibly c Com;;, ids should be considered as regular Similarity of Cometh, ESA Spec. Publ. SP-278
parts of tin' i.-iurid shower. (in press).
Investit^'ion of the postperihelion activity of Posen, A. and McCrosky, R.E.: 1967, NASA CH-862.
the Taurid t .implex confirms systematic increase of Sekanina, Z.: 1973, Icarus 18. 2 5 3 .
the mean ru>li;.s vector of its postperihelion nodes; Sekanina, Z.: 1976, Icarus 2 7 , 2 6 5 .
the fi TauriUs and £ Perseids do not correspond to Southworth, R.B. and Hawkins, U.s>.: i?u3, Smithson.
the expected positions of the nodes, radiants and Contr. Astrophys. 7, 261.
orbits of the Taurids and should be therefore con- Stohl, J.: 1986, in Asteroids, Comets, Meteors II,
sidered as another branches of the complex. Uppsala Univ. 565.
Large spread of the orbits and very long durat- Whipple, F.L.: 1940, Proc. Amer. Phil. Soc. 83, 711.
ion of the activity of the Taurid complex make it Whipple, F.L.: 1954, Astron. J. 59, 201.
difficult to explain in a simple way the process Whipple, F.L.: 1967, in The Zodiacal Light and the
of its origin and evolution. The present value of Interplanetary Uedlum, NASA SP-150, 409.
the longitude of perihelion of its parent comet Whipple, F.L.: 1976, in Interplanetary Dust and Zo-
P/Encke is JT«16O°, while the spread of the longi- diacal Light, Lecture Notes Phys. 48, 403.
tudes of perihelia of the whole complex extends
from the value 1t ~ 115° up to JT = 190°. Since the
longitude of perihelion of P/Encke increases with
time (with a complete period of more than 50 000
years), large part of the Taurid complex Is with
their 71*-values much ahead of the comet, which is
hardly possible to explain by a diffusing process

170
 D I S C U S S I O N

Olsson-Stael: This is a very important complex Babadzhanov: Your results correspond to the
of material since it seems to be the major calculations of secular perturbations. But
source of the zodiacal dust cloud.Apart from because of the secular variations of the
P/Enike, the Taurid complex includes several orbital elements of the stream meteoroids,
Apollo asteroids anri also perhaps a long the value of the D-criterion also changes
period comet (19t7 II Rudnicki). and sometimes becomes too large. This must
Stohjl: I absolutely agree that the complex be taken into account.
is vsjry important, as it is stressed in the Stohl : I completely agree that the evolution-
introduction of the paper (not read at the ary change of the D-value must be taken f.nto
session). One should be, however, careful account, but the results of the evolution of
in accepting the associations derived by the orbital elements as derived by various
using the D-criterion, as it is shown in authors are entirely discordant. At present
another paper by myself and Dr. Porubcan it is therefore impossible to explain the
(this volume TS-2). origin of the whole Taurid complex in a unique
way.
 PARTICLE DENSITY VARIATIONS ALGNG THE ORBIT OF ThE HALLEY METEOR STREAM

M. Hajdukova
Department of Astronomy, Comenius University,
84215 Bratislava, Czechoslovakia

Mechanisms leading to higher particle concentrations in several places along the

.meteor stream associated with comet Halley are discussed. The positions of the mass
concentrations represented by the mean anomaly of the stream orbit, as determined
fn.il long series of observations of the Orionids and Eta Aquarids, are correlated
with the deviations in the semi-major axis and nodes of the evolving orbit of the
comet. It is shown that random deviations in the orbital elements of the comet may
be responsible for the nonstable mass concentrations in the stream.

1. Introduction AQ influence the distribution of particle

orbits, and hence, to what extent they can
The activity of meteor showers associated cause mass concentrations along the stream
with comet Halley does'nt show any standard (and also across it), related to the obser-
features. The flux of particles varies with ved variations in the activity of meteor
the solar longitude, as well as in consecu- showers. As it is seen in Fig. 1 and Fig.
tive returns of showers. The structural fea- 2, the effect of both deviations is random
tures of the stream have been studied in de- and there is no correlation between them.
tail by Mclntosh and Hajduk (1983), giving But the number distribution of both sets
satisfactory explanation for most of them of data, as it is shown in Fig. 3, is con-
within their shell model of the stream (es- centrated about the mean values of devia-
pecially for the particle distribution and tions. In the same time the value of A Q =
variations in the stream's cross section). = 1° represents also the mean step in the
However, some aspects of the stream structu- gradual change of 0, at least for the time
re may be explained by mechanisms working span of the considered revolutions. Howe-
with the different speed, as suggested by ver., the number distribution of A Q values
Jones and Mclntosh (1986). In the present alone, does not represent either the con-
paper an explanation of the particle mass centration of particle orbits at A Q -» 0 ,
concentrations along the stream, occuring nor the largest spread at A Q - » 2 , as the-
semiperiodically in the returns of the Orio- se values should be projected in the direc-
nid meteor shower is suggested as a possible tion of the orbital velocity of the comet
consequence of the deviations in semi-major at the point of particular nodal distance
axis Aa and nodes A Q of the orbit of the pa- r A , corresponding to a given Q. The gradual
rent comet and particles ejected from it du- change of Q and r^_ with the revolutions of
ring its perihelion passages. the comet is caused by the gradual tilt of
the orbital plane of the comet along the
major axis and therefore is independent on
2. The deviation in semi-major axis the consecutive changes of Aa. Hence, at
and nodes of the comet orbit the Earth distance the values of Aa/a and
A Q in combination with % represent two
In consequence of planetary perturbations different mechanisms, influencing the pos-
and nongravitational forces, the orbital sible spead cr concentration of particles
elements of the parent comet vary in conse- along the whole meteor stream.
cutive returns. The particles, produced by
the comet during its perihelion passages ha-
ve initial orbits close to the orbit of pa- 3. The evolution of particle orbits
rent comet. Deviations in elements of the and the mass concentrations
comet orbit may then cause either a larger within the stream
spread, or a concentration of particle or-
bits. The largest influence on the particle The evolution of orbits of the meteoro-
orbits will have elements, undergoing to the id size particles, ejected from the nucle-
largest changes in consecutive revolutions, us of the comet at the different perihe-
and these are the semi-major axis a and the lion passages, has been studied by Jones
ascending node 0, as seen from the tables of and Mclntosh (1986) and Babadzhanov et al.
osculating elements, calculated for comet (1987). Different masses of particles or
Halley by Yeomans and Kiang (1981) or by different ejection velocities have been
Landgraf (1986). As the elements of both considered. The orbital evolution of par-
sets tend to disagree for the revolutions ticles, especially the time required for
before 240 BC, as shown by Sitarski and the Earth-crossing orbits depends strongly
Ziolkowski (1986), we will take for our ana- on the position of nodes and of nodal dis-
lysis data since 240 BC, the errors of which tances of the initial orbit, because of the
diminishes towards the present. In Pig. 1 progressive change of these parameters with
there are give.'< the values of a and Aa in the evolving orbit of the comet. From the
astronomical units for 31 revolutions, from location of nodes for the returns of the
240 BC to 2061, with the elements for 1986 comet and from the minimum distances bet-
and 206) according to Yeomans (1977). Simi- ween the orbits of the Earth and comet
Halley (sea Fig. 2 - 4 of the paper by Haj-
larly in Fig. 2 there are given the values duk, 1983) it is clear, that particles re-
of AQ. leased from the comet during the passages
The question of our present interest is, shortly before 836 BC, when the nodal dis-
to what extent may the deviations of Aa and

173
 A3 Aa (AU)

1 A/
0.20
O.OW

I ru-JL
O.OO5

0
0.10

0
' f\ J\h, \i\ 2 AQ

Fig. J. The number distribution of Aa/a and

-OJ105
AQ values for P/Halley o r b i t s .
-0.10

- 0.010
-0.20
-
-aois

-0.020
-0.30
- '1r
30 25
i i
20 15
i i i
0
/
M (•) 180
(240 BC) N(rev) 12061)

Fig. 1. The deviations of semi-major axis

of comet Halley for its successive
revolutions.
180 270 M(°) 360

Fig. 4. The activity of the Orionid meteor

shower from 1910 to 1986, corres-
ponding to the particle flux along
the whole length of the stream;
A/A - the level of activity, H -
mean anomaly.

Halley showers since the beginning of this

century up to the present have been shown in
a serie of papers (Hajduk 1970, 1973, 1985,
Hajdukova et al. 1986). The particle flux
variations along the whole stream, deduced
from the Orionid shower observations are
30 25 20 15 10 5 0 shown in Fig. 4 in four levels of activity.
N(rev) (2061)
The origin of the activity maxima or minima
(240 BC)
respectively cannot be seen in simple gravi-
tational perturbations caused by Jupiter, as
assumed earlier, as the change of activity
Fig. 2. The deviations of Q between the in most cases is slow and the segment of the
successive orbits of comet Halley. orbit to be perturbed, as seen from the mean
anomaly values, is too large. The spectrum
of perturbations of particles distributed
homogeneously along the whole orbit, sugges-
tance of the ascending node was r^ < 1 AU, ted by Yabushita (1972), leading to the dis-
could reach the Earth's orbit very quickly tribution of A Q values depending from the
in the next returns; but particles ejected longitude of Jupiter, would require six pe-
after that time, with r^ > 1 AU need hund- riods of activity changes, following from
reds of revolutions to reach the Earth's the ratio of orbital periods of the comet
orbit (Jones and Mclntosh 1986, Babadzhanov and Jupiter, /t least eight periods can be
et al. 1987). Comparing the present orbit identified from the observations of Orionids
of the comet with the orbits of Eta Aquarid in Fig. 4 and the variations corresponding
and Orionid shower particles obtained from to the Eta Aquarid observations are even mo-
meteor observations Kramer and Shestaka re complicated (Hajduk 1973, 1985). Whilst
(1984) came to the conclusion that these the particle flux distribution across the
particles might be released from the comet stream can be attributed to the different
earlier than 4000 years ago. In each case, belts of particle orbits within the stream,
observing the shower particles, we have lit- caused probably by the libration cycles of
le to do with the cometary ejecta from the the comet orbit (Mclntosh and Hajduk 1983),
last 30 revolutions. Therefore we canno'. there is no other reasonable explanation for
find any direct relation between the posi- the mass concentrations along the stream as
tions of 0 or r n and aa values from these that, originating from the Aw, r ^ and Aa/a
returns with the observed concentrations of distributions of the comet orbit. As both
the particle flux within the stream. However, these distributions are not corielated each
the form of the variation of the orbital pa- to other the local crossings of particle or-
rameters can be related to the form of the bits, leading to the mass concentrations
variation of meteor flux. should occure differently at the different
The particle density variations, based on distances from the stream center, which ex-
the visual and radar observations of the plaines the difference in the variation of

174
activity maxima along the stream at the po- -: 1985, Proc. First GLOBMET Symp. (Dushan-
sition of Orionids and Eta Aquarids. be) in press.
This conclusion could be verified by ob- Hftjdukova, M.; Hajduk, A.; Cevolani, G.;
servations of the radiant fields of both Formiggini, C . 1986, Proc. 20th ESLAB
showers: At the actiTltyminima a relative- Sjrnp- on the Exploration of Halley's Co-
ly homogeneous dispersion of the shower me- met (Heidelberg;, BSA SP-250 II, 371 -
teor radiants should be observed, but at Jones, J.; Uclntosh, B. A.: 1986, Proc.
the activity maxima, when crossings of or- 20th ESLAB Syap. on the Exploration of
bits with particular a and 0 are assumed, Halley's Comet (Heidelberg), E3A SP-250
it should be structured from two well dis- II, 233.
tinguished smaller fields of radiants wit- Kramer, E. N.; Shsstaka, I. S.: 1984, Mete-
hin the total radiant area. We may hope that ornye Issledovania, No 11, Akad. Nauk
the recent International Halley watch obser- SSSR, Moskva, p. 52.
vations will be able to answer this question Landgraf, W.: 1986, Astron. Astrophys. 163,
definitely. 246.
liclntosh, B. A.; Hajduk, A.: 1983, Monthly
Notices Roy. Astron. Soc. 205, 931 -
REFERENCES Sitarski, G.; Ziolkowski, K.: 1986, Proc.
20th ESLAB Symp. on the Exploration of
Babadzhanov, P. B.; Obrubov, J. V.; Pushka- Halley's Comet (Heidelberg), ESA SP-250
rev, A. N.; Hajduk, A.: 1987, Bull. Ill, 299.
Astron. Inst. Czechosl. 37, in press. Yabushita, S.: 1972, Astron. Astrophys. 20,
Hajduk, A.: 1970, Bull. Astron. Inst. Cze- 20?.
chosl. 21, 37. Yeomans, D. K.: 1977, Astron. J. 82, 435.
-: 1973, Bull. Astron. Inst. Czechosl. 24, 9. Yeomans, D. K.; Kiang, T.: 1981, Monthly
-: 1983, in C. - I . Lagerkvist and H. Rick- Notices Roy. Astron. Soc. 197,633.
man (Eds): Asteroids, Comets, Meteors
(Uppsala) p. 425-

•v, IfC
 DUST PRODUCTION OF COMET HALLEY WITH ACCOUNT OF LARGE PARTICLES CONTRIBUTION
A. Hajduk

Astronomical Institute, Slovak Academy of Sciences, 84228 Bratislava, Czechoslovakia

Critical analysis of the results of space experiments, taking into account the contribution
of large particles to the total mass production of comet Halley leads to much higher values of
the dust production rate than those derived from the firBt analysis of space measurements. As
a consequence it seems necessary to correct the gas to dust ratio of the mass production by a
factor of 10, from 0,1-1.0 to 1.0-10. The corrected values of dust production rate are In much
better agreement both with the current concepts of the comet's history and with the evolution
of its meteor stream.

1. Introduction 10 kg, where they reach a maximum value with 5-1

(Mazets et al., 1986; McDonnell et al., 1986).
In spite of enormously great amount of data, ga- Then, as shown from tbe large dust experiments and
thered by the International "alley Watch net and by radio-metric data (McDonnell et al., 1986; Edenho-
the space probes to comet Halley, many physical cha- fer et al., 1986; Hajduk and KapiSlnsky, 1987) the
racteristics of the comet are known only within ve- mass index decreases again, up to the mea. ved mass
ry large limits and many problems, concerning the limit at 10~ 3 kg particles with SAO.5. But this
physical processes going on on the nucleus surface means, that shifting the mass range of the ejected
remained open. There are broad discussions about the particles from its upper limit of 1 g, as usually
principal characteristics of the comet: its mass and assumed, to 1 kg, we obtain the dust:gas ratio
density, with the estimates, differing by an order Md:Ug=3:1 instead of 0.3:1, as given in most con-
of magnitude. siderations. This is approximately the same value
Some paradoxical relations see I to occur from as suggested by Crlfo (1987), giving Ml]:M£-3.4 as
the different models of cometary nuclei: when tak- a most probable value, assuming contribution mostly
ing a high density nucleus, corresponding to the from particles with mass m < 10~ 1 kg. For the mass
chondritic material (Jessberger et al.,1986), then limit of m < 30 kg Crifo gives M d :Mg- 19. In extra-
the measured dust:gas ratios are too low; when, on ordinary cases, concerning the split comets, we do
the other hand, the mass production with a low dust not have any mass limit for the fragments or parts
to gas ratios are aasiwed to be real, corresponding of the nucleus. In any case, this means that the
to a very low density material, then the total mass maximum contribution of the cometary ejecta is in
of the nucleus seems to lie too small, to supply the the range of largest particles. This conclusion is
mass of the meteoroid stream over the long orbital also supported by the radar detection of large fra-
history of the comet, corresponding to the stabili- gments of the comet IRAS-Araki-Alcock (Goldstein et
ty of the comet orbit. al., 1984).
We would like to show here, that at least one of Naturally, with the increasing mass of particles
the weak points in calculations of the characteris- (or bodies, respectively) decreases the particle
tics of the comet is in the low dust:gas ratios flux by many orders of magnitude and we cannot ver-
used, and consequently in the low value of the co- ify these conclusions by the short-term experiments.
met's mass production. We need here observations of particles, spread in
the meteor stream over many revolutions of he co-
2. The dust .-gas ratio, the mass index met. But tho meteor observations, corresponding to
and the limiting particle mass particles with the masses m > 10"^ kg still have
mass indices Si1 (Hajdukova et al., 1986) and tbe
Tho dust:gas ratio estimates for the comet's mass contribution of shower meteors has a •aximum
mass production prefer, in general, gas ov.->r dust, for particle masses at abo'i*. ni»3x10~^ kg (ilajduk,
with values of MjpMg between 0.1-1.0 (wheie Md is 1986). Hence, these observations do not confirm th«
mass loss for a given time unit and Mg gas loss, presence of larger bodies in the amount, correspond-
respectively). Rarely were higher values reported, ing to the extrapolated values Train space experi-
with the upper limit of 2.0 (Helmich and Keller, ments. (E.g. if we would change S froa 1 to 0.9, we
1981). The estimates for P/Halley tend to prefer would obtain twice es high particle flux for the
the value of 0.3 (Whipple, 1986} Kresak, 1986). How- particle masses differing by 3 orders, or for mete-
ever, in a very few cases give the authors mass li- or magnitudes differing by 7.? mig.) This discrepan-
mits, for which these values are valid. Usually it cy can be explained by accepting thu evolution of
is tacitly assumed that the estimated dust:gas ra- tb.3 mass index with the time as suggested recently
tio is valid generally, over the whole scale of (Hajduk and KapiSinsky, 1987) for the mass distri-
particlu masses. But this iB exactly the weak po- bution of particles ejected from P/Halley. p o r the
int of such estimates. With the assumption of a fresh ejecta with S»0.5, corresponding to the halo
general validity of the dust:gas ratio it is, in particle population around the nucleue we thus have
fact, assumed that *Jio integrated mass index S (de- the maxiBun mass contriln.iw< \ from particles of the
fining the slope of this particle flux - mass dis- mass m»10^ kg. As tho value of S increases up to
tribution) is ovnr the whole mags scale S > "i. Only 0.8 and 1.1 for the young <-•• aid stream particles,
this condition decreases the mass contribution of respectively, the maximum rase contribution is
larger particles. Moreover, it is assumed that the shifted to 10" 3 kg-10~' kg particles. Hence the
contribution of larger particles has a cut-off at most probable dust:gas ratios of tha fresh cometary
a certain inasB value. But these assumptions, espe- material should be between 1.0-10 and not between
cially the former one, are hardly fulfilled. 0.1-1.0.
The results of the space experiments show mass The change of S is In agreement with the results
indices increasing towards the larger masses up to of Simek (1987) deduced froa the observations of

177
 five n t e o r showers, and It Beans that the coaetu-y REFERENCES
ejecta undergo to a permanent change In their *ise,
excluding gradually larger bodies from th» stream Crlfo, J.F.: 1987, X.th European Regional Astrono-
in course of their returns to the perihelia>. The my Ueetlng, Prague, this Volume.
effect! influencing this process say be different Bdenhofer, P.; Buschert, H.; Bird, U.K.) Vollard,
(collisions, evaporation or combined effects), de- H.j Porsche, H.; Brenkle, J.P.j Kursins' , E.R.;
pending on the composition and structure ef partic- Mettinger, N.A.; Stelzried, C.T.: 1986, 20th
les. The result of this process Is the M a x i m a con- ESLAB Symp., Hefdalberg, ESA SP-250, Vol. II,
tribution of particles of the Intermediate masses 215.
of about I O ' ^ - I O " ? kg as obtained froa meteor show- Goldstein, H.U. et al.: 1984, Astron,, J. 89, 1745.
er data, and Independently from the studies of the Griin, E.: 1987, X.th European Regional Astronomy
microcrater distributions (Grim, 1987). Keating, Prague, this Volume.
Hajduk, A.: 1985, Dynamics of Comets: Their Origin
3. The influence of the corrected dust:gas and Evolution, Dordrecht, 0. Heidel Publ. Co.,
ratios on the physical parameters of the 399.
nucleus and on the orbital history of Hajduk, A.: 1986, 20th ESLAB Sysp., Heidelberg,
the comet ESA SP-250, Vol. II, 239.
Hajduk, A.; Kapisinsky, I.: 198?, Diversity and
The result that the l a T l w n contribution of the Similarity of Comets, Brussels, ESA SP-278, in
fresh conetary ejecta is in the range of largest press.
•asses, has a great influence on the calculation of Hajdukova, U.j Hajduk, A.; Cevolani, G.; Formiggi-
the comet's age and lifetime. The larger dust:gas ni, C : 1986, 20th ESLAB Symp., Heidelberg, ESA
raties are in better agreement with the observations SP-250, Vol. Ill, 371.
of Halley showers. The mean dust production obtained Hughes, D.W.: 1985, Mon. Not. Roy. Astron. Soc.
from these observations is 3.3x10'1 kg/rev. (Mcln- 213, 103.
tosh and Hajduk, 1983), referred to a lone-term phy- Hughes, D.W.! 1986, ESA SP-249, 173.
sical history of the comet. This value is 2 times Jessberger, E.K.j Kissel, o.j Fechtig, H.; Krueger,
larger than that one adopted by Whipple (1986) and P.R.I 1986, ESA SP-249, 27.
Kres&lc (1986) from the results of space experiments Krasnopolsky, V.A. et al.i 1986, Nature 321, 269.
and ground-based observations, assuming jildjMg«0,3, Kresak, L.s 1986, 20th ESLAB Symp., Heidelberg,
and corresponding to the observational value of M,j ESA SP-250, Vol. II, 433.
-6x10 3 kg. s" 1 at 1 AU. Mazets et al. (1986) obtain- Mazets, E.P. et al.i 1986, Nature 321, 276.
ed from Vega 1 SP2 sensors a value of U°do4x103 kg. a 1 McDonnell, J.A.U.} Grard, It.J.L. t Griin, E.; Kissel,
at 0.79 AU and Krasnopolsky ot al. (1986) from Vega J.; Langevin, Y.j Oleaxcxyk, H.E.; Perry, C.H. j
2 obtained 1^-1x103 kg.a" 1 at 0.83 AU. Adopting a Zarnecki, J.C.1 1986, 20th ESLAB Symp., Heidel-
moderate lncreaae of the dustigas ratio we would berg, ESA SP-250, Vol. II, 25.
agree completely with the results of meteor obser- Uolntosh, B.A.} Hajduk, A.: 1 983, Mon. Not. Roy.
vations and with the required 2 300 revolutions of Astron. Soc. 205, 931.
the comet (Hajduk, 1984; Hughes, 198?, 1986). With Rickman, H.: 1986, ESA SP-249, 195.
much higher dust:gas ratios it would be possible to Sagdeev, R.Z.j Elyasberg, P.E.} Moroz, V.I.: 1987,
shorten the orbital history of the comet. Diversity and Similarity of Comets, Brussels,
The value of Ug«2.8x10 1 ' kg/rev, was used by preprint.
Bickaan (1986) in his calculations of the nuclear Slnek, U.1 1987, Bull. Astron. Inst. Czechosl. 38,
mass of P/Halley froa the effects of the nongravlta- 80.
tional forces on the orbit of the comet. He obtain- Whlpple, F.L.: 1986, 20th ESLAB Syap., Heidelberg,
ed for the comet's mass 1^.(0.5-1.3)x10'"It leg, what ESA SP-250, Vol. II, 281.
gives, with the ebserved size of the nucleus and its
volume of 5x10 1 1 m? a very low density In the range
D I S C U S S I O N
of 0.1 < p < 0.2 g.cB~3. In a similar way Sagdeev,
Blyasberg and Uoroz (1986) determined the nucleus Griin: What are the biggest particles in me-
mass of P/Halley ts U c -2x10 1 4 kg and density P-0.4 teor streams? Cannot these partic}es he taken
g.cm"3 with errors SM-±3 U,, and tJp » I 3 9 , using as the biggest particles released from comets?
dust:gas ratios of 0.1 < Hd/Mg < 1.0. Because of the Ha.jduk: The fireballs correspond to about I kg
low velocity of the dust, in comparison with the particles, but larger bodies released from the
gas outflow from the nucleus, the dnst production nucleus undergo a relatively quick process of
is less essential for the calculation of nongravi- evolution (Hajduk, ESA SP-27B, 1987, Tab. 1 ) .
tstlonal forces. The uncertainties arise here most- This explains the observed maximum of mass
ly from the A^ and A2 parameters, ao shown by Whip- contribution in meteor showers at the particle
ple (1986). However, the dust production is very mass of 10 g.
essential for the calculation of the comet's life- Crifo: I think your investigations receive
time and for its orbital history. This is connect- increased importance in view of the limited
ed with the spatial density of particles observed capabilities Df the enmetary optical sounding
within the stream and with the total aass of the method with respect to the determination of
stream. The maas • c «5x10 1 * kg deduced by Hughes mass-loss rates in large grains. This limited
(1985) for the nucleus of P/Halley Is im the best capability has been overlooked previous to
agreement with the comet's orbital history of about P/Halley flyby, with most authors fitting
2 300 revolutions and with the about equal future the optical data with 'a dust size distribution,
lifetime. Rlckman's value for the nuclear mass which arbitrarily excludes large ( > 10' (])
would shorten extremely the lifetime of the comet. grains. If you perform fits of the same data
The values of Sagdeev et al. may agree with those with distributions, which allow for large
given by Hughes near their upper limits. grains, you find that an order of magnitude
increase in the mass-] us:; rate is allowed,
and therefore yo,u coir" up with a large
(jncertainty in M ,/M .
Fechtig: The latest value for
VMg as d i s c u s -
sed by G e i s s is 0.b . However I t h i n k 0.3 is a
g o o d v a l u e , too .
Ha.jduk: S u r e , b u t f o r p a r t i c l e s w i t h m < l g.

178
 ACTIVITY OF THE METEORIC COUPLE! OF COMET HALLEY

G. Cevolani 1 ' and A. Hajduk2''

1/ FISBAT Institute, Nationel tteaearoh Council, Bologna, Italy

2/ Astronomical Instituta, Slovak Academy of Sciencas, BratialaTa, Czechoslovakia

Results of radar observations of the Orlonid and Eta Aquarld netaor ahowera carried out In
Budrio (Italy) within the IHW program are compared with the simultaneous data froa Ondrejov
(Czechoslovakia). The activity ot these showers Is studied in the relation to the motion of lar-
ge particles ejected fron the comet. The activity m a found to be independent on the approach
of the parent comet.

1. Introduetery Notaa 2. Observations

Two meteor showers, the Eta Aquarids in early The program of simultaneous observations of the
May and the Orlonlda in lata October, have a long- Orionld meteor shower at Ondfejev Astronomical Ob-
-recognized association with comet Halley. Recant servatory (50 N) 13 B) In Czechoslovakia and at
simultaneous observations of the showera in Czecho- the Budrio radar station (44.5 N; 12 K) in Italy,
slovakia, USSR and Italy (Hajduk et al., 1984; Ce- ware carried eut In the second half of October,
volanl and Hajduk, 1984; Hajdukova et al., 1986) starting froa 1978. For the overlapping perloda of
revaaled structural feature* not well explained by both seriea of data froa 1981-86, the shewer-te-
the previous toroidal model of the stream. Mclntoah -sporadie background ratiaa R deduced from the
and Hajduk (1983) show that particles ajacted from range distribution are represented In Table 1. The
the comet will be diaperaad over a segment of a range distribution of the recorded meteor echoes
shell which thickens to fora a bait. The present has bean used ta determine the shower radiant
orbit of the coswt ia not too far from the ads* of transit, and stance to discriminate the shower froa
the bait, whereas at the tim« of the showers the aporadic meteors (Hajduk and CovolKul, 1981). In
Karth passes through the bait closer to its mid-li- order ta compare the data, the ratios R are norma-
ne: the Sta Aquarid passage ia above the aid-line, lised to the same mean value each ymmr tor both
and the Orionld passage below. This "shell aadel" sats (Fig. 3 ) . The discrepancies in the two trends
ia consistent with the small difference of the ob- especially in 1984 at L s - 210 indicate possible
served activity of both showers as wall as with contamination of the echo counts by the Bpsllen
their almost Identical width. Changes in nodes and Gemlnids, a minor shower whoae aeteera occur in
periods give a good explanation of the filamentary larger distances of recorda. Budrio and Ondrejov
structure of the stream. sets of data can be Influenced in the opposite way
A schematic representation of both observed me- and differences in the observed echo rates enlarg-
teor showers within the spread of the orbits Is ed. The range diatributlon method shows that maxi-
given In Fig. 1, with the full line belonging to mum contributions ot Epellen Gemlolds were record-
the orbit of the comet. The points represent the ed on October 24 (Ls - 210.5) in 1984, but alee an
past nodea of the comet orbit for each fifth of its October 27 (L s - 213.7) in 1983. A characteristic
returns back up to 1404 B.C. double peak in the 207-211 solar longitude Inter-
The zonea of increased particle flux density are val la scan very often but it ls completely absent
assuaed to repreaant the belts corresponding to the in 1983 from both stations. This is rather unuaual
individual llbration cyclea of tba comet. The cross- for Orionids and it can be explained only by a
sectlon of the stream la shown in Fig. 2. higher diffusion of particles in the central belt
of the stream, probably caused by planetary per-
turbations.

Fig. 1. A schematic representation of the shell of

orbits of comet Halley froa 1404 B.C. up ta its
present return. The points correspond to the nodes
of each fifth return; at the longitudes of both Fig. 2. A auggeated acheaatls view on the creaa-
meteor showers (Orionlds and Eta Aquarids) the ac- -aeetlon of comet's stream, oenaistlng of about
tivity of the showers is sketched. (Symbols: q is five belta of higher particle density ( 1 ls the
the perihelion distance,A the longitude of the orbital inclination, P. cl the pals of the eoliptic,
ascending node, V the position of the vernal equiv POrbit t n 9 Pol* of the comet orbit, L s the solar
nox, <x> the argument of perihelion.) longitude).

179
 1 I I I I I 1 I I I T I I I I 1

18 22 26 30 14 18 22 26 30

R 2.0
• BUDRIO 1983
o ONDREJOV
1.5

1.0

0.5

0.0 i i i r i i i i

14 18 22 26 30 14 18 22 26 30

R 2.0 2.0
1986 • BUDRIO
o ONDREJOV
1.5

1.0

0.5

0.0 0.0 I • I , • I I i I 1 l_J 1 ! 1 1, _|

18 22 26 14 18 22 26 30
October October

Pig. 3. The Orlonid meteor shower activity in 1981-1986. The mean shower-to-sporadic ratios 11 during
the shower period. The data from 1986 are preliminary.

180
 Table 1. Shower-to-sporadic ratios H of radar meteor echo rates (B(B)Budrio data, R(0)OndreJov data), de-
duced by the method described in Hajduk and Cevolani (1981).

fear 1981 1982 1983 1984 1985 1986

R(B) R(0) R(B) H(0) R(B) R(O) R(B> R(0) R(B) R(O) R(B) R(O)

Oct. 14 _ _ 0.93 0.75 _ —

15 - - - - 0.94 0.73 - - - 1.07
16 _ 1.33 0.95 _ _ 0.95 0.47 0.81 0.60 _ 1.03
17 1.53 1.34 1.31 - - - 0.99 0.77 1.25 1.21 1.46 1.12
18 2.14 1.72 1.11 2.49 •i.62 1.00 1.00 0.76 0.41 0.40 1.26 _
19 2.23 1.47 0.79 2.89 0.62 0.71 0.69 1.42 0.59 0.66 0.90 1.67
20 1.31 1.57 0.96 1.07 0.64 0.95 1.15 1.54 1.00 0.96 1.39 1.41
21 1.81 1.53 1.20 1.69 0.86 0.75 1.14 1.26 0.97 1.16 1.24 0.9*
22 1.41 2.02 0.92 1.78 0.76 0.85 1.15 0.61 1.14 1.45 0.99 0.90
23 2.28 2.11 1.09 0.74 0.92 0.73 0.88 1.65 0.79 0.85 0.96 1.12
24 1.83 1.59 1.16 0.71 0.80 0.62 0.82 1.82 0.88 0.94 0.67 1.06
25 1.38 1.09 1.13 1.69 0.76 0.41 1.22 1.14 1.20 1.76 1.00 0.77
26 2.73 2.04 1.03 0.97 0.71 0.39 0.80 0.81 1.48 1.41 1.57 0.87
27 1.95 2.18 1.22 0.56 0.71 0.95 0.96 0.68 0.79 0.60 1.22 0.90
28 3.24 _ - 1.17 0.69 1.01 1.05 0.35 1.15 0.52 0.99 _
29 1.56 - - 0.66 0.69 0.31 0.57 0.94 0.73 0.67 1.11
30 2.24 - - - 0.42 0.55 - - - - -
31 2.59 _ _ _ _ _ _

Nsh Nou
ETA AQUARIDS 1986 ONDREJOV
BUDRIO
1.5
400
1.0
0.5
300

L s (1950.0)
200
Fig. 4. The activity variation (in sh»wer-t*-spo-
radic background ratios) of meteor echoes during
the shower period (in solar longitudes, L s ) from
simultaneous observations. A m i n denotes the posi- 100
tion of the minimum distance between the orbit of
the comet and Earth.
1980.0 1982 1984 1966

3. Observations in 1985-86 at the approaches

of the comet N1S
In connection with the close approaches of the
conet to the Earth's orbit in October 1985 during
the Orionid shower period (0.154 AU) and in May 40
1986 during the period of the Eta Aquarids (O.O65
AU), some authors (Yeomans, 1977; Buhagiar, 1986)
have suggested an increase of the meteor rates, as 30
a consequence of a possible cloud of particles
ejected from the comet in the previous returns and
hence moving in the vicinity of the comet itself.
This would require either the existence of a broad 20
cloud of particles around the comet, or the vali-
dity »t the toroidal model of the stream with an
increasing density towards the present orbit of
the comet. Neither of these models, however, seem 10
to correspond to the recent observations of the
comet Halley meteor showers.
Observations of the Orionid and Eta Aquarid me- 1980.0 1982 1984 1986
teor showers carried out simultaneously at Ondfe-
jov (CSSR) and Budrio (Italy) have been extended
in the 1985-86 years to cover the periods proposed Fig. 5. Mean meteor echo hourly rates for the cen-
by the International Halley Watch (IHW) program tral part of showers (heavy lines) and peak rates
(Babadzhanov et al., 1985). The total number of (light lines) for all echoes N a m (upper part) and
about 10000 radar meteor echoes, recorded in the for long duration echoes N 1 S (lower part).
interval of October 16-29, 1985 and May 1-14, 1986.
during 2 hours around toe time 0> the meridian LS, 1» shown in Fig. 3 (Orlonids 1985) and In Fig.
transit of the shower radiant, has been analysed. 4 (Eta Aquarids 1986). The level of activity for
The activity, expressed in shower-to-sporadlc back- both showers is lower than the mean values in other
ground ratios of echoes along the solar longitude years and the activity variations are typical.

181
 Although no fixed poaltlona of tbe activity ma- REFERENCES
xima in both showers have been detected in reported
results of simultaneous observations, the present Babadshanov, P.B.j ifejAuk, A*| U n d s l M * 8 . A. ami:
results show clearly that, at least for tbs partic- Ifclntosh, B.A.: 1985, U i t m StoMww, IH* Jfcws*.
le aassts • > 10"° kg, the particle space density l e t t e r , 7, tt-17.
in the distances between O.OC5 and 0.194 AC froai Buhagiar, M.i 1984, EBV Aasteur Oka*. *i»ll. tto. 3 ,
the coaet orbits (i.e. in the uiniaua distances be- 3.
tween the orbit at the const and ths position of Cevolanl, Q. and Hajduk, A.t 1984, II Nuovo Claen-
the Earth In the period of the Eta Aquarid and Ori- t o , 7C, 447-457.
onld showers respectively), was not increased as a Hajduk, A. and Cevolanl, G.t 1981, B a l l . Astron.
consequence of the approach of the parent comet. I n s t . Csectwsl. 32, 304-910.
Fig. 5 shows that the mean activity of the central Hajduk, A. f Cevolanl, 0 . ; F o m l g g l n l , C. and Baba-
part* of the showers, between 44 < L s < 4 8 and dshanov, P.B.: 1984, Bull. Astros. l o s t . C»»-
206 < l g < 210, as well as the peak values froa the chosl. 35, 1-5.
whole shower period as observed at Ondrejov In dif- H*JduVova, M.} Hajduk, A.j Cevolanl, 0 . and Forai-
ferent years, are considerably lower in the years g g l n l , C.: 1986, Proc. 20th ESLAB Syqi. On the
1985 and 1986 than In the previous years and, over Exploration of Halley's Comet, Heidelberg, 27-
a longer time scale, lower than the average values 31 October 1986, ESA SP-250, 371-373.
(Fig. 5, upper part). Wood (1985) confirm the Mo- Uclntoah, B.A. and Hajduk, A.t 1983, Mon. Not. R.
derate activity of Eta Aquarids 198? return and UA- Astron. Soc. 205, 931-943.
lutchenko (1987) the low activity of the central Uilutchenko, I . A . : 1987*, Ueteornyje issledovania,
part of Orlonlds in 1985. Sinanns (1986) gives a Akad. Nauk SSSil, Uoskva, No. 13, 105.
•oderate activity of (he Orlonids in 1985. The trend Sinmons, K.i 1986, Meteor News No. 72, 7.
appears somewhat different In the range of large Wood, J . i 1987, Meteor News Noc 70, 7.
particles with durations t S* 1 sec. (Fig. 5, lewer Yeoaacs, D.K.: 1977, Astron. J . 82, 435.
part). The observed decrease In the rate of long-
duration echoes N 1 S (t > 1 sec) is saallar for the
Orlonlda 1985 and Eta Aquarids 1986 In comparison
with the decrease in the rate of all echoes N a n .
The proportion of long-duration was therefore lar-
ger than In the last years. Hence the recent decrea-
se of the aeteoroid flux is caused aostly by the
absence of small particles.

182
 METEOR PHYSICS
P. Peclna

Astronomical Institute, Czechoslovak Academy of Sciences,

251 65 Ondrejov, Czechoslovakia

Some comments on problems connected with our knowledge ,inel understanding of events observable
during the meteoroid flight through the atmosphere are presented. The review is divided into
three parts. The first part deals with the section of flight characterized bv the increase
of body temperature from the value reached at the heliocentric distance 1 AU, i. e. at the
frontier of the Earth 's atmosphere, which was estimated to be approximate! ly ?H0° K, to the
temperature at which the evaporation of the meteoroid can start. This process is designated
as pre-ablation heating. The second part deals with efects connected with the visible trajectory
as well as with ionization trails and problems related to them. There exists generic connection
between luminous flight of meteoroids and dark flight with possibility of finding the meteorites
fallen to the ground namely with the predictability of the impact area jnd the impact itself.
This is the subject of the third part.

Pre-ablation heating was extensively studied can significantly contribute to our understanding
since the beginning of the physical studies of the whole pre-ablation process. Maybe they
of meteor events. Pioneering works were published can most simply be accomplished as a by product
by one of the most famous scientist who began of the remote sensing of the Earth surface.
to develop the theory of the heating, by Levin After reaching sufficiently high temperature,
(1956). Other contribution was made by Cepiecha the meteoroid can start to ablate, which itself
and Padevet (1961) and by others, recently by makes it possible, the meteor to be directly
Kruchinenko (1986). From the mathematical point observable either by optical or radar methods.
of view, the problem consists in the solution Let us mention first the general features or
of the heat transfer equation subjected to the problems. The motion of each meteoroid during
appropriate initial and boundary conditions. its flight in the atmosphere is governed mainly
In general, the solution is not easy to obtain by the drag force, the slowest of them can signifi-
if realistic situation is to be described. There- cantly be subjected also to the Earth's gravitation
fore > some authors have simplified the problem force. Let us neglect this force in our further
by assuming the meteor body can be approximated considerations. Then the drag equation takes
by infinitely long cylinder. Then the solution the form
could be found in the relatively simple analyti-
cal form. But this assumption seems to be highly m v = - TSpv 2
unrealistic. Therefore, the theories dealing
with, say, realistic shape of meteoroids should (e.g., Hronshten - 1981). As already stated,
be preferred. All analytical solutions were obtained sufficiently high temperature leads to the evap-
under the assumption that the body is not sub- oration of the meteoroid's material from its
jected to any deceleration during its flight. surface. This process is believed to be governed
This can be true for sufficiently large bodies.
by the evaporation equation
But in case of small bodies, they can significant-
ly decelerate and, moreover, thermal radiation
from their surfaces can dominate the efect of S Pv'
thermal conduction into the centre, which highly
complicates the whole situation. Then, the theo-
retical beginning heights of meteors can be (ttronshten, 1981). The quantities entering those
in doubt. M'crometeorites can not even constitute two equation1-, have the following meaning:
the visible trajectory. Also the frequently m - is I he instantaneous meteoroid mass,
used assumption of the exponential atmospheric v - its velocity at the same time instant,
profile can substantially change the conclusions S effective cross-sectional area of the bodv.
obtained. The portion of flight in the pre-abla-
c the air density at the point at whicf
tion heating conditions is undoubtedly the largest
the m e t e o r o i d velocitv e q u a l s to v,
one from all of them. Therefore, the knowledge
of precise atm. profile is of great importance.
r the rir.iq coefficient,

Also possible rotation of the heated body was

g the heat of ablation of the meteornid
material,
not considered so far. All these mentioned problems
the heat transfer coefficient.
are worth solvinq to ensure further development A-
of meteor physics. As for me I believe that
As is well known. Ihese two equations possess
this is possible using the modern computing
the first integral of the form (e.g., Bronshten
technique available at' present. The theory of
- 1981):
meteoroids heating depends on such physical
parameters as thermal conductivity of the material,
rxp
its capacity and bulk density. These parameters
can be, on the other hand estimated to some
extent by the knowledge of the thermalization where m ro and v „, are the pre-atmospheric values
curve. The great part of this curve comprises of the corresponding quantities and 0= X /(2Q F)
the temperature region giving the radiation is the ablation parameter. It is necessary to
inside the infrared range. Therefore, the infrared stress that the integration was performed under
observations made either on the ground (if possi-
ble at all) or aboard the Earth orbiting satellites

183
 the assumption of a being constant. The integration from some point of the light (or ionization)
ma'1"' with \ and P depending on v was published curve to infinity; Other investigation made
by Bronshten (1980). But this case seems to by Ceplecha (1983) has revealed the fact that
be rather exceptional because the coefficients even one atmosphere used for all fireballs
in question and maybe the other implied parameters in the whole year can significantly change
can, in principle, depend on other quantities the results on v^ and o . He concluded that
as for example on m, p , chemical composition, the instantaneous (i.e. for example for every
the bulk density of the meteoroid itself and month different atmosphere) must be used In
on parameters, which are not still known or order to obtain reliable results on v^ and
sufficiently well understood (e.g. on porosity, o . Computations and their comparison with
ReVelle, 1983). But the criterion for the validity observations lead to the conclusion, that the
of the theory is to be only the observation. assumption of constant 0 and K is mostly quite
It is north trying to prove whether the assump- acceptable. The theoretical trajectory fitted
tion of constant parameters can work in reality. the observed very well and errors of 1 following
To be able to compare the predictions of the from the new method are well comparable with
theory with observations, we must further integra- those from the geometry of problem. Another
te the basic set of eq. Inserting the first very significant conclusion can be drawn with
integral found into the drag equation and adopt- respect to the determination of ablation para-
ing the exponential atmospheric profile we arrive meter o . The new method can get it with the
at another integral: accuracy never previously reached (several
percent for good observations). Statistics
of ablation coefficients determined from this
( avJ/6 ) fi < 0 6) l (, ) method is significantly better and enables
better classification of meteoroids.
b cos l
The results and conclusions discussed
R so far are not dependent on the light curve
where Fi(x) is the exponential integral, b stands itself. If we want to determine other parameters
for the air density gradient, Z R i s the zenith of meteoroids we must add to the basic set
distance of the meteor radiant and K is the of equations, in optical case, the luminous
shape-density coefficient. By the year 1983, equation
these relations served as a basis for the compar-
ison of theory with observations. They give I - - T-£- m
the dependence of v and m on the measurable ?
height (through P ) or time. But v as well as wheretis called luminous efficiency. As shown
m are not directly observable quantities. v by Pecina and Ceplecha (1983) the present expres-
must be obtained by numerical derivative of sion for I can be considered the most general
measurable lenght passed by meteoroid in its possible with T depending on velocity v. Inter-
flight. Because it is known from numerical mathe- esting efect arises when integrating the drag
matics that numerical derivative could be highly equation and determining from it the meteoroid
unprecise depending on the quality of input mass m (dynamical) and integrating the luminous
data, it is clear that conclusions based on eq. for obtaining the other massm (photometrical).
them can be scarse. It was believed that the In most cases they differ and 'usually m^< m
integrations I presented so far are all which If requiring ">.=m we obtain bulk densities
can be done in solving the basic equations. of meteoroids lower than the corresponding density
But surprisingly, Pecina and Ceplecha (1983) of water. But this contradicts the fact, that
have proved the existence of the third integral many meteorites deposited in various museums
giving the dependence of distance 1 along the have bulk densities well comparable with Larth's
trajectory on the velocity v. So they obtained materials. Padevet (1977) made an attempt of
the complete integral of basic equations of avoiding the problem ^f low densities by introduc-
motion and evaporation 1 = l(t) in the para- ing the notion of Jvnamieally significant coma
metrical form, the instantaneous velocity v which led him to the conclusion that S in the
being the main connecting parameter. It is neces- drag equation cannot coinside with the same
sary to remind that 1 is a directly observable quantity in the evaporation equation. The criti-
quantity in photographic observations. The error cism of Bronhsten and Stanjukovich (see Bronhsten's
with which it can be determined is only several book - 1981) meant that this idea had to be
tens of meters depending on equipments used. abandoned. The principal equations of meteor
Using the new integrals the authors have arrived physics were also modified for faint meteors
at the conclusion that it is necessary to use to explain their shorter light and ionization
the instantaneous atmosphere for bright meteors curves (in comparison with those following from
(i.e. for fireballs) (e.g. in the interpolation the single-body theory). The interested reader
table form) . Other cone" ision lies in the can see Kashcheev s et al.(1967) work or Bronshten
finding that using the <Aponential atmosphere book. Recently, when dealing with decelerations
can lead to errors in prediction of Va> » which and bulk densities of faint photographical meteors,
can then be far outside the three standard Lebedinets (19S7) (together with Novikov et
deviation box and, therefore, can significantly al. (1984 a,b)) have developed a theory of quasi-
influence the prediction of the heliocentric continuous fragmentation of meteor bodies. Lebedinets
orbit of meteoroid under consideration. The conclusion can be summarized by the statement
second integral must then be replaced by that .inly 3 meteors from 92 sporadics were produced
by low density (fluffy) particles. The author
of present work is convinced that the same fact
- ti(av2/6) = could be revealed by the classical single-body
dh
C0S Z
theory. The measure for the ablation type is
oo R
the ablation parameter o . Higher values of
this parameter can be the evidence for the frag-
For details see Pecina and Ceplecha (198ft).
mentation where the fragments are negligible
The function /*°° pdh can be easily tabulated.
in comparison with the parent body. If the parent
The general statement can be established: the body would disintegrate into a fen comparable
new form of the second integral must be used debris, the single-body theory must surely fail.
in each case in which the Integration is made

184
 The other problem consists in the fact that the theory of these events we must add ionization
for application of new equations to observed equation
meteors, the number of measured distances along
the trajectory should be sufficiently high for envy = - 6m .
getting reliable results. But this is not the
case for faint meteors. On the other hand, long a is the electron line density in the train,
and bright fireballs offer, when using this V is the mass of the atoms ablated from the
method, the possibility of studying, for example, surface of the meteoroid and B is the ionization
the variability of a . If the values were known probability which is considered a function of
from other investigation, we could ascribe the v
. Because 6 plays the same role as T in the
observed differences between observed and theore- luminous equation it is clear that its knowledge
tical distances to difference of the actual is of great importance. It seems that the most
atmosphere in comparison with the used one. used form is 6= 0ov" (see Kashcheev et al.,1967),
Thus, some meteors can serve as natural and where n = 3.5. B^jt Tokhtasyev (1976) has put
not expensive indicators of the instantaneous forwardg=Bo(v-8.8) with the same n. He believed
state of the middle atmosphere. As for the bulk his probability better colnsides with the reality.
densities of meteoroids, the work of Pecina But there are also scientists saying we don't
and Ceplecha (198*) leads to another conclusion: have the satisfactory formula for g (e.g. Oones,
use of the exponential profile of the atmosphere (1984). It seems, therefore, that the improvement
can cause considerable decrease of the bulk of our understanding of g is necessary. The
densities (in the cases presented 4356 and 92%)'. theory of scattering of radar-emitted radio
From this fact the importance of the knowledge waves from meteor ionization has a principal
and namely the usage of the realistic atmospheric significance for meteor radar physics, the first
model is again clearly visible. Another improve- extensive work was published by Kaiser and Closs
ment of the observational possibility is represent- (1952) and followed then by Lebedinets and Sosnova
ed by the new television technique which is (1968a,b) and (1969), Jones and Collins (1974),
capable of registering the meteors down to 9th Poulter and Baggaley (1977), Chumak and Mojsja
magnitude. As TV observations will develop, (1977), Solyanik and Tkalchuk (1983) and many
the theory of extremely faint meteors brigther others. It seems from the study of these papers
than mlcrometeors should probably be improved. that the theory is still unsatisfactory. For
As shown by Millman and Clifton (1979), this example, the resonance of polarization ratio
technique is capable of providing us also with cjj. /gj (g being scattering coefficient) of the
high quality spectral information. Unfortunately, order of 100 found by Lebedinets and Sosnova
Millman's pioneering work was not followed by as well as by 3ones and Collins was according
anybody. Spectral data can get information on to Chumak and Mojsja (1977) never observed.
the conditions in meteoric plasma and the chemical Moreover, in the discussion in literature it
composition as documented by Ceplecha (1973). was stated, that the inconsistency of theory
His work was done under the assumption of LocaL with observations can be due to wrong sign of
thermodynamic equilibrium which is probably imaginary unit used in computations. I am convinced
not true. But since that time the knowledge this cannot be true in the physical reality.
of spectral line formation has further developed I think it is inconsistency of the approach
and, therefore, it is worth trying to apply to the problem itself. Any way, common conclusion
these new ideas to the physics of meteor spectra. can be drawn. The echoes from meteor ionization
It is believed that the end height theory can be divided into two main categories. The
can provide us with other information on meteoroids. first one is usually designated as underdense
Padevet (1987) has therefore attempted to develop and the second one as overdense. Two main types
this theory to solve the problem of the origin of echoes are completed by transient ones. A
of meteoroids. His theory seems to be still much better understood type of reflection is
at start because of some semi-empirical criteria the underdense than the overdense one. The under-
which, I think, should result from the theory dense scattering from forming trail enables
itself. Wetherill and ReVelle (1981) have analysed the meteor velocities and ambipolar diffusion
documented falls of meteorites and established coefficient to be relatively precisely determined,
some conditions on end heights which would ensure if Fresnel characteristics are employed. The
that meteoroid can be expected to get meteorite shape of amplitudes and their decay can largely
fall. The cause of fragmentation observed seems be influenced by deionization processes causing
not to be well understood. McCrosky and Ceplecha faster decrease of electron volume density n
(1970) have considered the disruption due to inside the train. The main factor affecting
thermal stresses. Padevet (1987) and others the duration of echoes is believed to be the
(see Bronshten's book - 1981) have assumed that ambipolar diffusion. The other possible processes
the fragmentation was due to loading pressure such as recombination, attachment and others
of the atmospheric drag. In Bronshten *s book were reduced to the attachment itself. The exten-
the possibility of emitting electrons from surfaces sive studies of these processes were published
of solid bodies is mentioned. If the outflux by Baggaley (e.g. 1972, 1978),and (1980). Present
of electrons from body prevails over the influx, concept prefers the view that electrons do attach
the body will get the positive charge which to atoms ablated from the meteoroids (Bibarsov,
would contribute to its easier disintegration.The 1972). The behaviour of n under this process
best observational evidence of meteoroid frag-
mentation was obtained by Babadzhanov and Getman is described by Bibarsov et al. (1980). A minor
(1980) and Babadzhanov (1983) by method of very objection can be raised against the value of
short (instantaneous) exposure. To terminate their attachment coefficient, which was determined
the section on light efects we will mention from photographical observations of only three
trains left by meteors which persist up to several meteors with large scatter of resulting values.
dozens of minutes. Their nature seems to be It is also possible that the attachment coefficient
unclear at present. depends on the chemical composition of the meteor-
The other set of effects connected with oid. As shown by Novikov et al. (1979), the
meteors is the consequence of the fact that formation of negative ions and their presence
meteoroids flying through the atmosphere can inside the train can significantly change the
leave behind themselves trails consisting of shape of echo amplitude. It is possible to obtain
weakly ionized plasma. Id order to construct an underdense echo followed after a short time

185
 interval by another one. Both shouid appear their constants (e.g.,f - luminous efficiency).
in the same range. This was also observed in It is possible that the sound usually heard
Ondrejov radar measurements. It looks like meteors during the fall (as to Its frequency and intensity)
appearing in pairs. The negative ions can change near the impact point can contain information
the form of Fresnel characteristics as reported about this mass. I think this Is another challenge
by Novikov et al. (1986). The important quantity to the theory of meteors.
limiting radar observations is the initial radius
of meteor trails. It was considered a function
of p and v (e.g. Baggaley, 1970). But different
authors have published results differing one
from another. Most extensive work dealing with
measurements of initial radii have been performed
by Baggaley (1970) and (1981) as well as by
Baggaley and Fischer (1980). Interested reader REFERENCES
can find the old theory of the radius for example
in Kashcheev et al. (1967) work. The new insight Babadzhanov, P.B.; Getman, V.S.: 1980, I.A.U.
in this problem has recently been published Symp. 90, 111.
by Kolmakov (1982). His theory fulfills the Babadzhanov, P.B.: 1983, in Asteroids, Comet,
natural condition that there cannot be any initial Meteors (ed. C.-I. Lagerkvist, H. Rickman),
radius if the electron line density of corre- p. 439, Uppsala.
sponding trails is zero! This theory can be Baggaley, W.3.: 1970, Monthly Notices Roy. Astron.
classified as a substantial development of the Soc. 147, 231.
physical theory of ionized columns of meteoroid's Baggaiey, W.3.: 1972, Monthly Notices Roy. Astron.
origin and it is worth trying to develop it Soc. 159, 203.
further. Hawkes and Oones (1978) have pointed Baggaley, W.3.: 1978, Planet. Space Sci. 26,
out the possible connection of the rotation 979.
of the meteoroid body with the initial radius. Baggaley, W.J.: 1980, I.A.U. Symp. 90, 85.
All I said so far could be connected mainly Baggaley, W.3.; Fischer, G.W.: 1980, Planet.
with underdense echoes. The theory of overdense Space Sci. 28, 575.
echoes seems to me to be much worse then that Baggaley, W.3.: 1981, Bull. Astron. Inst. Czechosl.
of the underdense. Therefore, its other development 32, 345.
is extremely needed. By analogy with optical Bibarsov, R.Sh.: 1972, Komety i meteory 21,
spectral research, there is the possibility 32.
to learn more of the conditions governing the Bibarsov, R. Sh.jBlokhin, A.V.; Novikov, G.G.:
evolution of ionized meteor trails from the 1980, Geomag. Aeronom. 20, 1116.
study of the profiles of observed radar pulses Boykov, V.I.: 1986, Geomag. Aeronom. 26, 752.
(analogy to the study of the profiles of spectral Bronshten, V.A.: 1980, Astron. Vestnik 1*, 25.
lines in optical branch). Theoretical background Bronshten, V.A.: 1981, Fizika meteornykh yavlenij
has been published by Boykov (1986). (Nauka Moscow).
A small portion of echoes was observed, Bronshten, V.A.: 1983, Astron. Vestnik 17, 94.
named head echoes: only limited information Cepiecha, I.; Padevet, V.: 1961. Bull. Astron.
is known about them and their nature is still Inst. Czechosl. 12, 191.
unclear (see, e.g. Bronshten - 1981). At the Cepiecha, Z.: 1973, in Evolutionary and Physical
end of this part I would like to point out a Properties of Meteoroids, I.A.U. Coll. 13,
few unresolved problems of meteor physics. The (ed. C.L. Hemenway, P.M. Millman, A.F. Cook),
first one Is connected with the possibility p. 69, Washington.
that meteor trains are sources of their own Cepiecha, Z.: 1983, in Asteroids, Comets, Meteors
radiowaves. The general treatment of electro- (ed. C.-I. Lagerkvist, H. Rickman), p. 435,
magnetic radiation from an inhomogeneous plasma Uppsala.
was made by Means et al. (1981). Bronshten (1983) Chumak, Vu.V.; Mojsja, R.I.: 1977, Probleny
tried to estimate the emitted power and has kosmicheskoj fizlki No 12, 70.
arrived at the conclusion of mutual connection Epifanova, O.V.: 1981, Astron. Cirk. No 1182,
of the generation of radiowaves with electrosound 5.
fireballs. But nothing has been stated by him Hawkes, R.L.; Oones, 3.: 1978, Monthly Notices
about the possible wavelength of the radiation. Roy. Astron. Soc. 185, 727.
Hawkins (1958) stated that meteors show a surpris- Hawkins, G.S.: 1958, Nature (London) 181, 1610.
ingly low efficiency in converting kinetic to radio Jones, 3.; Collins, 3.G.: 1974, Monthly Notices
energy. Keay (1980) has reported on the anomalous Roy. Astron. Soc. 168, 433.
sound from entry of fireballs, heard before Clones, 3.: 1984, private communication.
they are seen. Nevertheless, Epifanova (1981) Kaiser, T.R.; Closs, R.L.: 1952, Philos. Mag.
has announced that there were registered radio 43,1.
Impulses during regular solar radio observations Kashcheev, B.L.; Lebedinets, V.N.; Lagutin,
carried out at the Saratov State University, M.F.: 1967, Rezul't Issled. IGY-Issled. Meteorov
which she could not ascribe to the Sun. Impulses No 2.
had durations of 10-15 seconds and were registered Keay, C.S.L.: 1980, Science 210, 11.
at the wavelength of 3 cm. She made an analysis Kolmakov, V.M.: 1982, Komety 1 meteory 32, 41.
and concluded that the radio emission of meteoric Kruchinenko, V.G..- 1986, Vestnik Kiev. univ.
origin was observed. It seems, therefore, the 28, 76.
theory has another field on which it is to act. Lebedinets, V.N.; Sosnova, A.K.: 1968a, I.A.U.
At the end of my contribution I would like Symp. 33, 27.
to remind that the meteorites fallen to the Lebedinets, V.N.; Sosnova, A.K.: 1968b, Geomagn.
ground were also meteors. It is, therefore, Aeronom. 8, 697.
necessary to stress that prediction of impact Lebedinets, V.N.; Sosnova, A.K.: 1969, Geomagn.
area depends on the meteor "history", namely
Aeronom. 9, 680.
on the atmospheric profile used, as It was clearly Lebedinets, V.N.: 1987, Astron. Vestnik 21,
demonstrated by Pecina and Cepiecha (1984).
The last problem of finding the meteorites consists 65.
In the fact, that the predicted Impact mass
can strongly depend on the theory used or on

136
Levin, B.Yu.: 1956, Physical Theory of Meteors
and Meteor Matter in the Solar System (in
russian), Moscow.
McCrosky, R.E.; Ceplecha, Z.: 1970, Bull. Astron.
D I S C U S S I O N
Inst. Czechosl. 21, 271.
Means, R.W.; Muschietti, L.; Tran M.Q.; Vaclavik,
3.: 1981, Phys. Fluids 24, 2197.
Millnan, P.M.; Clifton, K.S.: 1979, Sky and Sabadzhanov.- Photographic o b s e r v a t i o n s of
Telescope 57, 21. meteors by The method of instantaneous expo-
Novikov, G.G.; Tsigankov, S.F.; Blokhin, A.V.: sure and t h e o r e t i c a l i n v e s t i g a t i o n s are i n d i -
1979, Dokl. Akad. Nauk Tadzh. SSR 22, 657. c a t i v e of q u a s i - c o n t i n u o u s f r a g m e n t a t i o n of
Novikov, G.G.; Lebedinets, V.N.; Blokhin, A.V.: m e t e o r o i d s . This phenomenon s t r o n g l y a f f e c t
the observed l i g h t - c u r v e s of meteors. But i n
1984a, Pisma v Astron. Zhurnal 10, 71. your p r e s e n t a t i o n you d i d not mention t h i s .
Novikov, G.G.; Lebedinets, V.N.; Blokhin, A.V.:
1984b, Pisma v Astron. Zhurnal 10, 785. Pecina: The l i m i t e d time span prevented to
Novikov, G.G.; Pecina, P.; Blokhin, A.V.: 1986, do s o , but i t i s mentioned i n the paper.
Padevet: The s i n g l e body theory of meteors
Bull. Astron. Inst. Czechosl. 37, 189. d e s c r i b e d by d r . Pecina does not c o n t a i n the
Padevet, V.: 1977, B u l l . Astron. Inst. Czechosl. t h e o r y of end h e i g h t s of meteors; t h e r e f o r e ,
28, 90. the end h e i g h t s of f i r e b a l l s cannot be d e t e r -
Padevet, V.: 1987, Bull. Astron. Inst. Czechosl. mined froir. t h i s theory w i t h o u t e m p i r i c a l l y
38, 156. f i x e d end i n v a r i a n t s . We have to c o n s t r u c t
Pecina, P.; Ceplecha, Z.: 1983, Bull. Astron.
a more general p h y s i c a l theory of meteors
Inst. Czechosl. 34, 102. f o r t h i s purpose.
Pecina, P.; Ceplecha, I.: 1984, Bull. Astron.
Inst. Czechosl. 35, 120.
Poulter, E.M.; Baggaley, W.3.: 1977, 3. Atmosph.
Terr. Phys. 39, 757.
ReVelle, D.O.: 1983, Meteoritics 18, 386.
Solyanik, O.A.; Tkachuk, A.A.: 1983, Meteornye
Issled. 8, 67.
Tokhtasyev, V.S.: 1976, Izv. Astron. Engel'gardtovsk.
Observ. Kazan, No 41-42, 228.
Wetherill, C.W.; ReVelle, D.O.: 1981, Icarus 48,
308.
 ON THE LIGHT PULSATIOII OF BRIGHT GEMIBIDS
ACCORDIHG 10 PKOTOWUPHIC DATA.
P.B.Babadzhanov and N.A.Konovalova.
Institute of Astrophysics, Dushanbe, 734670,USSR

/
The photometric light ourvee of bright Geminids are inveetigated. The analysis
of the light curves reveals a peculiar nature of meteor luminosity with ra^id fli-
ckering and email brightness fluctuations. This peculiarity of the luminosity of
the bright Geminida points to a certain ablation process of these meteoroids in
the Earth's atmosphere. According to estimates of the energy of ablation a conclu-
sion was made that the investigated Geminid meteoroids were disrupted in the atmo*
sphere by the melting and cyclic ablation of the surface-}ayer of meteoric matter.

The photographic data of bright Geminids

allowed to reveal a peculiar nature of the
meteor luminosity with rapid flickering and
small brightness fluctuations. A period of
the flickering of the Geminids is nearly an
order I O B S then that of early known flicke-
ring meteors (Kramer, 1966).
Beginning from the middle of the trajec-
tory the flickeringa become stable with
small brightness fluctuations.
In the papers on the meteor flickering
phenomenon (Kramer, 1966) it has been estab-
lished that light pulsations are expected to
occur only with the meteors produced by mas- 60 H km
sive meteoroids deeply penetrating into the
atmosphere; And the amplitude and the period Pig. 1. The light curves for the Geminids.
of brightness fluctuations vary with a mete-
oroid penetrating deeper and deeper into the Shutter breaks enable to measure with high
atmosphere. accuracy the time intervals between the
It should be noted, however, that regular two subsequent flickerings. The variation
flickering is observed not for all meteors of the frequency of flickerings N versus
produced by large meteoroids and deeply pe- the height H is plotted in Pig. 2. Aa is se-
netrating into the atmosphere. en from Pig. 2. the frequency of flickering
The present paper investigates the mecha- increases continuously with an accompaning
nism of desintegration of the Geminid meteo- decrease of the height from 111 s"1 to1 490 a"1
roide in the atmosphere. We have studied the for the meteor No 643S81, from 35 a" to 380
light curves of the three flickering Gemini- s"1 for the meteor No 761b83 and from 83 s"1
de No 643881, No 761683 and No 821691 photo- to 625 s"1 for the meteor No 821691.
graphed in Dushanbe. For these Oeminids the It is interesting that our estimates of
stable regime of rapid flickering of small periods of the Geminid flickerings," decrea-
amplitude (~0T5) is set up from the middle se in the periods of these flickeringa ver«-
of meteor trajectory approximately at the eus time and the height range where pulsati-
height of 75 km and lasts till the end of ons occur coinside completely with Hallidays
^he flight. photographic data of the Geminid No 60c ob-
Calculated data for these meteors are gi- served in Canada (Halliday, 1963). This po-
ven in Table 1 in which the data on the fli- ints to the fact that rapid flickering for
ckering meteor No 60c studied by Halliday the meteors of such type is distinctive fea-
(1963) are shown for comparison as well. ture of the luminosity of the bright Gemi-
Fig. 1 presents the light curves of Geminids. nids in the atmosphere.
The autofluctuatlng nature of evaporati-
Table I on has been supposed to explain the observed
flickering phenomenon. A fluctuation may be
Basic data on the Geminide. set up when the pressure of saturated vapors
and th? outer pressure regular each other
automatically (Oleak, 1964; Kramer, 196*;).
No 643881 761683 821691 60c The calculation of the heat-conductivity
equation:
Year,month 64.XII 76.XII 82.XII 60.XII
Day(UT) 14.022 15.699 13.992 13.167
V«.(km/s) 34.5 34.4 38.4 36.1 at boundary conditions
H. (km) 95.2 87.2 92.7 72 .9
f-» -T ( x - 0, t 0 )
H?(km)
n^(km)
60.8
53.0
61.4
<61
64.8
51.8
61
46 .1 W J
T ( x - 0, t )
4R
t (s)
36S8
1.55
54*9
>1.33
21*6
1.19 0 .84
has the form:
-3:5 -5T7 -4T6 -8'
11.62 >19 10.04 ro (3)
"©5)
18?
where ft*=X/gc and X , S , C - are the heat- Table II.
conductivity, the specific heat and the deny The period of flickerings a t , the heat-tra-
sity of a meteoroid respectively;k=V>C0SZR/H
and V , E R , p 0 are the velocity, zenith dis- nsfer coefficient A and the energy of abla-
tance of the apparent radiant and the atmos- tion Q for stone (1) and iron (II; meteoro-
pheric density for a given height (CIRA, ids.
1972)i H*is the scale height; it is the pe-
riod of flickering; T m and T v are the mel- No A '.Q erg/g
ting and boiling temperature; <P(y) is the in
tegral of the probability; o(x) is the Dirac (.Aiani Z
n nno n m , 0.084*0.022 1.5*3.1
delta-function. 643881 n 0.009*0.002 0.376*0.097 3.7*7.1
As kit is sufficiently small (0.006 ^ k <
0.01) we may assume ek4'ta!i and <£(Vk&t) — 761683 Jr 0.025*0.003 !
2-Vk"it/5f.Then using the equation (3) we ob-
tain the expression for the heat-transfer
coefficient: . 0.012*0.0016 °:§85S:!f7
/4«-A5c A
(4)
W I T ? y?" B - igftv- Using the luminosity equation:
where A and B are constants characterising I =
the chemical composition of meteoric matter
(Allen, 1973). and the equation of mass loss:
Using the equation (4) and the obtained
values of the period of the flickering & t
for several points of meteor trajectory dt
f
2Q
with known ft,and V we have found numerical
values of the heat-transfer coefficient A . we can obtain the following expression to
Calculations were done for the three types calculate the parameter A / Q s
of meteoroidd, namely for crumbly stone, sto- A 2 X
ne and iron meteoroids. For the case of cru- (5) ^
5)
mbly stone meteoroids there were no accorda-
nce between the calculated and observed va-
lues of the period of flickering at any va-
T IPS" * V < W / 3
= T
The parametr A / Q was calculated for the
lues of the heat-transfer coefficient A . several points of meteor trajectory. Here s,
This fact allowed to exclude the crumbly sto- A,Co - are the midel, the form and the lumi-
ne composition for the Geminids. nosity factor respectively. According to the
The values of A were obtained for the sto- obtained from (4) values of A and from (5)
ne and iron meteoroids and it turned out values o f A / Q we haye found the energy of
that they vary along the meteor trajectory. ablation Q which also vary with height. The
The variation of A vereuB heignt is shown in increase of Q appears to occur at these seg-
Pig. 3. As is seen the heat-transfer coeffi- ments of the meteor trajectory where the de-
cient decreases continuously when a meteoro- crease of the luminosity is observed. The
id penetrates into the deepths of the atmos- value of Q decreases at the increase in the
phere. luminous!ty and reaches its minimum at the
maximum meteor brigtness.
Analysis of instantaneous images the
bright Geminid No 821691 indicate that this
meteor have wakes* As was shown by McCrosky
(1958), Babadzhanov and Konovalova (1983)
the formation of meteor wakes is connected
with the separation of meteoroid matter from
the parent body. Meteor wakes available for
the Geminids as well as the obtained values
of the energy of ablation suggests that the
large Geminids deeply penetrating into the
Earth's atmosphere were disrupted by the me-
lting and cyclic ablation of the surface-la-
300 yer of meteoric matter with the period cor-
responding to the observed period of the
flickering.
100 •
R E F E R E N C E S
70 60 Hkm
Allen, C.W.; 1973, Aetroptiyeical quantities.
Pig. 2. The variation Pig. 3. The variation London univer. press.
of the frequency of of the heat-transfer Babadzhanov, P.B., Konovalova N.A.; 1983,
flickerings versus the coefficient A versus Doklady Acad. Nauk Tadzh. SSR. 26, 8.
height, the height. 1 - Ho Cospar International Reference Atmosphere
821691, 2 - No 643881. 1972. Berlin Acad. Verl., 1972.
Halliday, I.; 1963, Smithson. Contrib. Ast-
Results of calculation are given in Table 2. rophya. 7«
The analysis of the obtained values of A Kramer, B.1I.; 1966, Problemy cosmich. fisi-
should provide a reasonably good estimate of ki. 1, Meteory, p. 75.
shielding effect and determine the nature of McCrosky, R.E.; 1958, Astron. J. 63, 3.
the meteoroid ablation. To resolve this qu- Oleak, N.; 1964, Astron. Nachr. 1.
estion it is nessesary to estimate the para-
meter A /Q, where Q ie the energy of ablati-
on.

190
 D I S C U S S I O N

Grun: You suggested that flickering may also

be caused by spin (rotation) of the particle.
If this thesis can be proved, then one has
finally a method to determine the spin of
meteoroids, the knowledge of which has great
implications in the dynamics of meteoroids
(Yarkovsl-cy-Radzievski j effect) .
Babadzhanov: Until now, vie did not consider
the influence of meteoroi.J rotation of flic-
kering of Geminid meteors. But this we could
do in a close future.

191 /
//
 THE TRUE HEIGHT DISTRIBUTION AND FLUX OF RADAR METEORS
Duncan Olsson-Steel 1 ' 2 and W.G.Elford2

1) Lund Observatory, Box 43, S-22100 Lund, Sweden.

2) The University of Adelaide, South Australia.
When compared to satellite detector measurements of dust particles of mass < 10"6g and optical meteor
observations for mass > 10~2g, the flux of the interstitial radar meteors is discrepant: the radars
render fluxes which seem too small by a factor of about 20-30. This has usually been explained as
being due to the majority of the flux being held in low-velocity meteors which produce little
ionization and hence have limited radar detectabilities.
We propose an alternative hypothesis: that the discrepancy is due to wavelength-dependent effects,
implying that conventional meteor radars {f > 20 MHz) only detect the lower-altitude underdense
meteors. To test this we have determined the height distribution of radar meteors at 2 and 6 MHz, at
which frequencies the echo ceilings are much higher than the 100-105 km limits of VHF radars. We
find that the distributions peak at "105 km, fully 10 km above the peaks of VHF radars, with many
meteors occurring to at least 140 km altitude. Additional observations using the powerful Jindaiee
radar in central Australia confirm these results, and show that the cumulative flux of particles of
mass > 10~ 6 g is about 9 x 10" 8 m" 2 sec" 1 ; this is consistent with satellite data and is over an order
of magnitude larger than derived in previous radar meteor experiments.

1. Introduction 2. Factors affecting the radar meteor height

The fact that VHF meteor radars are unable to detect distributions
many meteors at height above "100-105 km, the so- The data presented in this paper were largely gained
called 'under-dense echo ceiling', is well-known at much lower frequencies than most meteor research-
(HcKinley, 1961). In an important paper Greenhow ers will be familiar with, and therefore as a start-
(1963) studied the implications of the echo ceiling ing point we will describe the factors affecting
and showed that the true height distribution, and underdense radar meteor height distributions using as
hence true flux, could only be determined by using a an example the distribution as observed at 54 MHz;
radar of much lower frequency than usually utilized: this frequency is much nearer to those utilized in
meteor radars have most often operated at around 20- the vast majority of meteor radars.
60 MHz, and Greenhow pointed out that a radar at a In Figure 1 we show the height distribution of
frequency of just a few MHz was necessary' in order to 2302 sporadic radar meteors determined using our
detect the high-altitude underdense meteors. One of 54.1 MHz radar at Buckland Park (40 km north of Adel-
us (Elford, 1980) has previously presented some res- aide; latitude 35°S). The transmitter power is quite
ults gained at 2 MHz, and suggested that the majority low (a few kWatts) bat the same high-gain antenna
of the flux of small meteoroids has remained undetec- array (a filled square 80 x 80 m) is used for both
ted since it ablates above the echo ceiling of VHF transmission and reception, and in addition a micro-
radars. This fits in well with the known discrepancy processor system is used to accomplish coherent sig-
in the radar meteor flux when compared to the flux of nal acquisition and averaging: the limiting meteor
dust particles measured by satellite instruments and line density corresponds to a magnitude M R = +9. The
the flux of larger, optical, meteors (Hughes, 1978). beam zenith angle (z) is steerable along a line
This leads us to the hypothesis that rather than the running approximately East-West, and in the present
low ionization-efficiency of slow meteors (e.g. Cook instance was set at z = 34°. Since the beam width
et al., 1972), in fact it is the wavelength-dependent (half-power, half-width) is only -1!5, the heights
selection effects (described in section 2) that are (h) of individual meteors can be found directly from
the origin of the discrepancy. h = R cos z , where R is the range. Instrumental
In order to test our hypothesis we have determined limitations upon R lead to the cut-offs at h s 72 and
the height distributions of underdense meteors using 106 km in Fig. 1. The data have been plotted . • !
radars of frequency 2 and 6 MHz (i.e. HF radars); for weighted number nf meteors: that is, the effect of
comparison purposes the height distribution from a the Increasing range and the changing atmospheric
VHF radar (f = 51 MHz) is also given. The HF distri- collecting area have been allowed for, and then the
bution: indicate that the bulk of meteors actually points were normalized to the peak at h s 92-93 km.
occur at too high an altitude to be detected by VHF This height distribution is typical for VHF radars: a
radars. Although these HF height distributions are radar at f = 30 MHz might show a slightly higher peak
remarkably different from those gained at VHF, in fact (at 95 - 98 km), but there is always a rapid fall-off
they are as expected from simple modelling based upon above this, with few meteors above 105 km and almost
stiindjrd er.ho attenuation factors, and are also in none at h > 110 km.
agreement with other forms of observation not limited
by echo ceiling effects (e.g. Evans, 1966; Hawkes and We have given elsewhere a modern review and dis-
Jones, 1930; Cook et al., 1980). cussion of the factors affecting the amplitude of a
radar echo from an underdense meteor train during its
Additional observations have been made at a variety formation and initial evolution (Olsson-Steel and
of HF frequencies using the Jindalee over-the-horizon Elford, 1986; 1987a,b ; Elford and Olsson-Steel, 1987;
radar in central Australia. This radar is, we bel- Thomas et al., 1986, 1987), and these factors are only
ieve, the most powerful ever used for meteor detection, briefly mentioned below. Other recent work on this
having a limiting magnitude of between +16 and +17. problem includes that of Poulter and Baggaley (1978)
The results back-up our hypothesis and lead6 to a value and Novikov et al. (1986). All attenuation factors
for the total influx in the mass range 10" < m <10" 2 g (a) given here are for attenuation of the returned
which is about 30 timesl3 the previous estimates; the amplitude rather than the power.
total mass influx (10" < m <10 +6 g) as a result is
about four times the previous estimate, and is of the The initial radius (r Q ) causes attenuation:
urder of 16,000 tonnos per year (Thomas et al., 1986).
* / A2 ) (1)

193
 Fig. 1. The height
140- distribution of
meteors to limiting
magnitude +9 observed
130- using a 54 MHz radar.
The uncertainty bars
indicate ± the square
120- root of the number of
meteors contributing
to each point. The
solid curve shows the
model calculation,
as described in the
text.

5 4 . 1 MHz METEORS
1986 JUNE/JULY

0-2 0;4 0-6 0-8 1 1-2 1-4

WEIGHTED NUMBER OF METEORS
where X is the wavelength; r (in metres) is given by: Hz. As a source function for our model we use, as
justified later, a 'time' number of meteors at height
log]() rQ = 0.019 h - 1.92 + log 1Q (V/40) (2) h of:
(Baggaiey, 1980a, 1981) where the height (h) is in km NT ( 72< h < 105 km) = { (h - 72) / 33 ) 2
and the meteor velocity (V) in km/sec.
NT (105< h < 140 km) = 1
(8)
The finite-velocity effect is described by:
and the number we expect to detect at any height is:
a v = (1 - exp (-A)} / A (3) NE (h) = o N T (h) (9)
where Meteors are only observed at one particular height
using our equipments: we interpret this height as
A = ( 8 >r2 D / V ) ( 2 R / X3 V (4)
most probably being the height of maximum ionization.
and the ambipolar diffusion coefficient 0 is found
from: In Fig. 1 the results of our calculation of IV (h)
is shown as a solid curve. Clearly there is an
D = 290 T2 / p (5) excellent fit, giving us faith in this simple model,
except possibly at h > 100 km where there are only
where the temperature (T) and the pressure (p) have
about half as many meteors as the model predicts: we
values taken from the U.S.Standard Atmosphere (1976).
believe that this is an artifact of the data analysis
Radial diffusion of the train, usually recognized (real-time minicomputer processing of signals output
as causing decay-type echoes, also cause attenuation by the microprocessor) and the problem will be rectif-
since the first radar pulse to meet the train may do ied in future experiments.
so some time after its formation: this would be an
3. Height distribution at 2 MHz
acute effect for low-prf radars, and some earlier work
(Elford and Lindblad, 1978) was carried out with the At Auckland Park we have another radar which can be
Onsala meteor radar (prf = 50 Hz) especially in mind. operated at either 2 or 6 MHz. The receiving array
If it is assumed that the train is formed just after consists of a filled circle of dipoles, "1 km in diam-
the passage of a transmitted pulse through that volume eter. By transmitting a wide beam, using a smaller
of space then the attenuation factor is: array, and making phase comparisons between rows of
antennas of known separation amongst the receiving
= exp ( - 16 TI2 D / \2 (prf) ) (6) array, the heights of radar meteors can be determined
from the range and zenith angle determinations. Some
and this expression is used throughout the present earlier results were reported by Elford (1980), and
paper. However, in rea'Hy the train may be formed at the present experiment (which benefits from improved
any time between pulses, and since the formation takes transmitter power, and real-time analysis of echoes
a finite amount of time one cannot assume that on using a minicomputer) has been described in detail by
average the train forms midway between pulses; the Olsson-Steel and Elford (1987a). The effective limit-
exact expression applicable will depend upon the crit- ing magnitude is M n 3 +7.
eria applied for the recognition of meteors (Elford K
and Lindblad, 1978). Later work will encompass a more In Figure 2 we show the 2 MHz height distribution
rigorous expression for a (Olsson-Steel and Elford, of 1461 meteors observed in 1985. Some of these met-
d
1987b). eors are Eta Aquarids, but predominantly they are from
the various showers of July/August, and in particular
The total attenuation will be:
the Delta Aquarids: for details see Olsson-Steel and
Elford (1987a). Selection effects (range, antenna
a = >r iv ad (7) patterns etc.) have been removed, and the distribution
and for particular /alues of A, V, h and the prf the normalized to the peak at ~105 km. Also shown, as a
three attenuation factors make different contributions solid line, is the model calculated as described in
to a. It turns out that for the Buckland Park 54 MHz section 2; input parameters were prf = 20 Hz and
radar the .i tern1 dominates except for low-velocity V = 35 km/sec. Except at low velocity (where av is
(V < 25 km/sec) meteors in which case a., is the most important) the total attenuation a is dominated by the
important; here we use in uur model V = 3 5 km/sec diffusion term a ., due to the low prf; since a . does
(since the meteors are sporadics), and the prf = 1024 not depend upon the velocity (equation 6 ) , the actual

194
 Fig. 2. As for Fig.
1 except for meteors
observed with a 2MHz
radar; the majority
of these were shower
meteors detected in
early May, late July
and early August in
1985. Because the
antenna spacing was
more than U / 2 ) ,
phase comparisons
did not render the
2enith angle (and
hence height) unam-
biguously for some
meteors, but this FILL 2 MHz DflTfl, 1985
could be deduced
with high confidence
since the positions x = UNRMBIGUOUS METEORS
of the shower rad-
iants are known. + = flMBIGUOUS METEORS
For details of the
models (sol id and 0-2 0-4 0-6 0-8 1 1-2 1-4
dashed curves), see
text. WEIGHTED NUMBER OF METEORS
value of V input to the mod<:', makes little difference. height distribution being determined only for
We note that: 84 < h < 117 km. The limiting magnitude of our pres-
ent 6 MHz system is M B - +6, but this will be improv-
(i) The vast majority of meteors occur above 100 km, ed by the provision of a steerable transmitting array
with many seen right to 140 km (the equipment which is now under construction.
cut-off);
(ii) The model underlies the data by about a factor In Fig. 3 the 2015 meteors observed at the time of
of two at h > 120 km, and this may be due to the the Daytime Arietid and Zeta Perseid showers in 1986
unrealistic expression for a. used (equation 6 ) , June are shown: for more details see Elford and
as discussed in section 2: rough updated calcul- Olsson-Steel (1987). These two showers have velocit-
ations bring the model into line with the data, ies of "37 and "27 km/sec respectively, and V = 35
and will be discussed by Olsson-Steel and Elford km/sec was used in the model, along with prf = 20 Hz.
(1987b); Due to this low prf the diffusion term a . dominates
(iii) At 105-140 km, the model indicate that even this the total attenuation for all velocities, and the
2 MHz radar only detects about half of the true precise value of V used in the model is not important.
influx, as was suggested independently by Thomas The model gives a reasonably good description of the
et al. (1987) on the basis of their observations trend of the data, predicting the peak at h s 105 km
with the Jindalee radar; with the majority of the detected meteors being below
(iv) At low altitude the crude empirical model used 110 km (cf. the model of Milsom, 1985) even though
(equation 8) is not a good fit. A realistic most of the influx, according to equation (8), is
model for low-altitude meteors would need to above 110 km. The following points are worthy of
include other effects, such as recombination comment:
(e.g. Baggaley, 1980b). A revised linear model: (i) Points A and B are in error and have the same
N T ( 72 < h < 105 km) = ( h - 72 ) / 33 (10) origin. Patches of evolving sporadic-E ioniz-
ation at h = 110-112 km detected in the 33°
is shown as a dashed line. beams and incorrectly picked out by the mini-
Fig. 2 illustrates well the major point of this computer as being meteors cause point A to be
paper: that the true height distribution of radar met- amplified; the sporodic-E reflections in the
eors peaks well above 100 km, probably close to 110 km, vertical lobe cause the error in point B (B is
and is strongly asymmetric with many more meteors at 93 km s 110-112 km x cos 33?2).
ablating at high altitude. Thus, VHF radars detect (ii) Point C appears anomalously low, but there is
only the lower-altitude fraction of this overall no apparent reason for this.
di stri but ion. (iii) The data at D show an upturn in the number of
4. Height distribution at 6 MHz meteors: this is probably due to meteors which
are really at h < 88 km causing echoes in the
Our large receiving array has a row spacing of 100 z = 50!7 beams and then having their heights
yards, which is equivalent to about 0.6U at 2 MHz or incorrectly assigned.
1.S3X at 6 MHz. Connecting all dipoles to form a co- (iv) Near E the low-altitude data underlie the model
phasal array, the antenna pattern at 6 MHz consists of by about a factor of two.
nine grating lobes: one is vertical, four occur close
to the cardinal points of the compass at z = 33?2, and 5. Total meteoroidal influx to the Earth
four occur at the interstitial azimuths at z = 50.7.
By transmitting a wide beam and then analysing only Using our observed 2 MHz height distribution (as
signals from ranges 101 < R < 139km, any meteor echoes shown in Fig. 2) as a model for the true height dist-
in the z = 5057 lobes are ignored except for a few ribution, Thomas et al. (1986, 1987) have analysed
echoes from h < 88 km. There should be no meteor data from the Jindalee radar in order to estimate the
echoes from the vertical lobe, so that almost all met- total meteoroid influx to the Earth's atmosphere.
eors are observed in the z = 3352 lobes which have More details of the radar are given by Thomas et al.,
half-power, half-width ~1!5; as for the 54 MHz meteors, but here we can mention that the system has a "mega-
the height can then be deduced directly from the range. watt transmitter separated by 150 km from an electron-
The range limitation of 101 < R < 139 km results in the ically steerable, 2.8 km long receiver array, and is
fully tunable from 3-30 MHz. Meteors are detected at

195
 140-f

130- Fig. 3. The height

distribution of Day-
time Arietid and Zeta
120- Perseid meteors to
limiting magnitude +6
observed with a 6 MHz
110- radar. The error
bars show ± the square
LU root of the number of
meteors at each height.
100- The solid curve is the
cc
o model distribution.
The points labelled
LU 90- DRTTIME RRIETIDS RND A to E are discussed
LJ in the text.
ZETfl PERSEIDS, 1986 TUNE
80- 6 MHz METEORS

0-2 0-4 0-6 0-8 1 1-2 1-4

WEIGHTED NUMBER OF METEORS
ranges out to several thousand kilometres via a number Cook, A.F.; Flannery, M.H.; Levy, H. II.; McCrosky,
of different modes: direct backscatter, scatter via R.E.; Sekanina, Z.; Shao, C.-Y.; Southjorth, R.B.;
the F-region of the ionosphere and return along the Williams, J.T.: 1972, in Meteor Research Program
same path, and a number of paths involving F-region (NASA CR-2109; Washington, D.C., U.S.A.).
and ground/sea reflections. Meteor echo rates of the
order of five to ten per second are not unusual; an Cook, A.F.; Weekes, T.C.; Williams, J.T.; O'Mongain,
atmospheric collecting area of the order of 106 km2 E.: 1980, Mon. Not. Roy. Astron. S o c , 193, 645.
can be simultaneously monitored. Elford, w.G.: 1980, in Solid Particles in the Solar
The meteor observations of Thomas et al. (1986, System (Eds. I.Halliday and B.A.McIntosh; Reidel,
1987) correspond to meteoroid masses in the range Dordrecht, Holland), p.101.
{ 2 x 10"' < m < 8 x 10"1* g), so that for the first Elford, W.C.; Lindblad, B.A.: 1978, The effect of
time there is substantial overlap between the masses pulse sampling on radar meteor rates (unpublished
obsei-ved by a meteor radar and by satellite detectors. manuscript).
The subsequent analysis by Thomas et al. renders a
flux of particles of m > 10"6 g of 9 x )0"8 m"z sec"1 Elford, w.G.; Olsson-Steel, D..- 1987, J. Atmospheric
and a mass exponent index c = -1.0, which is consist- Terrestrial Phys., (submitted).
ent with satellite data (Hughes, 1978; McDonnell, 1978; Evans, J.v.: 1966, J. Geophysical Research, 71, 171.
Laurance and Brownlee, 1986): this flux is about 30
times the previously-believed radar meteor flux, and Greenhou, J.S.: 1963, Smithson.Contrib.Astrophys.,7,5.
implies an upward revision of the total solid- Hawkes, R.L.; Jones, J.: 1980, in Solid Particles in
particle influx to the Earth (all masses from 10"l3g the Solar System (Eds. I.Halliday and B.A.McIntosh;
to 1 tonne) by about a factor of four to 16,000 tonnes Reidel, Dordrecht, Holland), p.117.
per year (Thomas et al., 1986). The interpretation of
the Jindalee data depends critically upon the input Hughes, D.W.: 1978, in Cosmic Dust (Ed. J.A.M.McDonn-
model height distribution, and requires a meteor comp- ell, Wiley, Chichester, England), p.123.
onent at high altitude (h > 110 km); these data there- Laurance, M.R.; Brownlee, D.E.: 1986, Nature, 323, 136.
fore support our radical model for the true meteor
height distribution. Although this model is extremely McDonnell, J.A.M.: 1978, in Cosmic Dust {Ed 0.A.M
simplistic, we believe that it is at least a realistic McDonnell; Wiley, Chichester, England), p.337.
basis for future work aimed at deducing the true char- McKinley, D.W.p.: 1961, in Meteor Science and Engineer-
acteristics of the meteoroid influx to the Earth's ing (McGraw-Hill, New York, U.S.A.).
atmosphere. Clearly the results presented in this
paper have important implications for the chemistry Milsom, J.D.: 1985, in International Conference on Ant-
and dynamics of our atmosphere, the supply of meteor- ennas and Propagation (IEE Proc. No. 248), p.515.
oids by comets and asteroids to the interplanetary Novikov, O.G.; Pecina, P.; Blokhin, A.V.: 1986, Bull.
complex, and the maintainance of the zodiacal dust Astron. Inst. Czechosl., 37, 189.
cloud.
Olsson-Steel, D.; Elford, W.G. 1986, Proc. Astron. Soc.
Australia> 6 , 4 3 6 .
Acknowledgements
This work was largely supported by ARGS grant number Olsson-Steel, D.; Elford, U.G., 1987a, J. Atmospheric
Terrestrial Phys., 19, 243.
B 8415432, and the University of Adelaide. Discussions
with Dr.R.M.Thomas are gratefully acknowledged. During Olsson-Steel, D.; Elford, W.G.: 1987b, J Atmospheric
1987 D.O-S. is European Space Agency Fellow at the Lund Terrestrial Phys., (to be submitted).
Observatory, Sweden.
Poulter, E.M.; Baggaley, W., 1978, Planet. Space
References Sci., 26, 969.
Baggaley, W.J.: 1980a, Bull. Astron. Inst. Czechosl., Thomas, R.M.; Hhitham, P.S., Elford, W.G.: 1986,
31, 308. Proc. Astron. Soc. Australia, 6, 303.
Baggaley, W.J.: 1980b, in Solid Particles in the Solar Thomas, R.M.; Whitham, P.S.; Elford, W.G.: 1987,
System (Eds. I.Hall'day and B.A.McIntosh; Reidel, J. Atmospheric Terrestrial Phys. (submitted).
Dordrecht, Holland), p.85.
Baggaley, W.J.: 1981, Bull. Astron. Inst. Czechosl.,
32, 345.

196
 D I S C U S S I O N

Fechtig: Concerning the total influx of mate- Olsson-Steel: Our implementation of the 2 MHz
rial to the Earth: Hughes giv^s for masses system uses two identical beams pointed East
between 10 and 10 g a number of 44 tons and West. If the flux were predominantly due
per day. If one uses this number, your total to the sporadic meteors at the times of
mass would go up to approximately 60 tons observation, then the count rates in the two
per day! directions should in fact be the same, and
this is not the case: by far the highest
Olsson-Steel : W> must look at actual figures rates are found in the beam, in which the
in morp detail . Certginly the, total influx is shower meteors are expected, confirming that
dominat3d by Ine 10 to 10 g mLteoroids, most of the meteors detected are from the
from these observations. shower. Thus, we must conclude that the mass
Hajduk: How can you distinguish that you do distribution index is in errcr, due to the
not record ionospheric inhomogeneities selection effects described in this paper.
instead of meteor echoes at 2 MHz and 140 km
heights? Have you observed diurnal variation
of echoes?
Olsson-Steel: It is a major problem that with
a strong ionosphere the vast majority of
echoes are from E-region jonization during
the daytime. To avoid the problem we start
observing at about 3 a.m. local solar time
(when the E-region has died down) and must
stop at sunrise (about 7 a.m. for these obser-
vations). Thus we cannot observe diurnal
variations.
Hajduk: Because of a lower mass index s
of Eta Aquarids, the contribution of faint
shower meteors should be nebligible in compar-
ison with the background rates.

197 /
 MASS DISTRIBUTIOK OP UKDERDENSE METEOR ECHOES: SELECTION OF BASIC DATA

Milos Simek

Astronomical Institute, Czechoslovak Academy of Sciences,

251 65 Ondfejov, Czechoslovakia

Volume of recorded underdense meteor echoes ie determined by the transmitted

power, treahold sensitivity of the receiver, antenna gain including its directi-
vity and by the range of reflecting point on the meteor trail. These parameters
must be considered when the mass-distribution index s is evaluated.

In basic model of underdense meteor trail where P^, is transmitted pulse power, G is
the incident radio wave is scattered by free antenna power gain relative to an isotropic
electrons of ionized meteor path. These ele- radiator, S the antenna directivity in the
ctrons oscillate freely and behave as if no direction to the reflecting point at the
other ones were present (McKinley, 1961). range hQ, A - wavelenght, r g - classical
Upper limit for underdense electron line electron radius.
density <* is sufficiently bellow the transi- The model for the number of particles n
tional value oit r ~ 2.4x10-,14 electrons/m having masses between m and m + dm has usu-
(Kaiser and Closs, 1952). Using combine ally the form
transmitting and receiving antenna and neg- {2) 8
dm
n~ m
lecting the formative stage of an underden-
se t r a i l , the equation for received echo- Providing oC ~ m and putting P ~A , the
power i is integral or cumulative distribution of
P
t r a i l s , K, having the electron line density
TGo
(1) or greater is then given by
32

or, substituting for <* from

Eq. (1),
. . . . _. . -(B-1)
applied lity region of A (4)

applicability region of a Equation (4) i n l o g a r i t h m i c

form represents a straight line
of negative slope (s-1). In
practice, the term Jr' S x is
often considered a constant
which leads to an inappropriate
value of the mass-distribution
index s when all recorded un-
derdense echoes are applied for
the analysis.
Accord'. .Tg to tq. (1) Fig. 1
shows the relation between line
density, <K , and received echo
a
min. amplitude A with SfT-^2, as a
parameter. A similar diagram
was already presented by Aicln-
tosh and Simek (1969). With the
Amin.
minimum value of A, echoes are
log A recorded for line densities

199
between °(min .,_ and °<1n, where <V_.
min corree- (SR J / 2 ) 1 ? (SH • 3 / 2 ) m a x . We are
ponds to treshold sensitivity of the system then losing the region of highest counts
(P rjnin ) and °<m a x is maximum line density with << over the range of <* min to °<^.
of an underdense trail having the echo amp- Such a procedure does not require the
litude A m i n sufficiently lower than the un- application of "meteor s e n s i t i v i t y conto-
derdense-overdense cutoff. We do not reach urs" as described by Kaiser et a l . (1966)
UBually o< value having the amplitude and by Poole et a l . (1972).
A . because of the greater path loss and Minimum range of recorded shower meteors
hence reduced equipment sensitivity at gre- depends on the radiant zenith angle. This
ater distances. Sensitivity factor must be taken in account when mass-distri-
5 -3/2%
(SR" )„,„„ limits lower line density in bution parameter for a meteor shower i s to
max
the whole range of A. The volume of all re- be determined. The observing period i s then
corded underdense echoes is defined by A . , divided into s e r i e s , say, 1-hour intervals
A
max- (SIT 3 / 2 ),, ^ a n d ( S K " ^ " and averaged normalized echo-counts (in %)
re are used for parameter B calculation accor-
A___ represents maximum amplitude of an
max
underdense echo occuring in the region of ding to Eq. (4).
— 3/2
(Sh ) which, providing one discrete
level, ia reduced to one point (direction). hef erencee
Only in the same direction echo having <<
min
is observable. Kaiser, T.R.; Closs, R.L.: 1952, Phil. Mag.
We see that the number of echoes with 43, 1.
A ^ A , is reduced by limiting value of • * _ „ . Kaiser, T.R.; Poole, L.M.G.; Webster, A.R.:
-3/2 1966, Wion. Not. Roy. astr. Soc. 132,225.
lhe range of equipment s e n s i t i v i t y & Sh Mclntosh, B.A.; S"imek, II.: 1969, Canad. J.
is a constant for A . £?A — A-, and, therefo- Phys. 47, 7.
re, we may use only echoes within bounda- McKinley, D.W.fc.: 1961, Meteor Science and
ries A-,, A_.._., '(SR~
" " J' ).,,
' 1 ' (SR~ 'max"
) . All Engineering, McGraw Hill, New York.
echoes having amplitudes A>-A^ and line
Poole, L.M.G.j Hughes, D.W.j Kaiser, T.H.:
densities °< > °< , must be discarded. By
1972, Mon. Hot. Roy. astr. Soc.156, 223.
using line densities for the analysis, the
range of applicable °< i s allocated within

200
 THE IAU METEOR DATA CENTER IN LUND
B.A. Lindblad
Lund Observatory, Box 43, S-221 00 Lund, Sweden

The purpose of the IAU Meteor Data Center in Lund is to archive information on meteoroid orbits.
At present some 5 000 photographic double-station orbits and more than 60 000 radio determined
orbits are archived. The paper describes the available data and discusses some problems encountered
in the archiving process.

1. Introduction The radio orbit data have mainly been available on

tapes.
The extensive development of professional meteor
programs after the second World War involving photo-
graphic, radar and image orthicon techniques added 2. Photographic orbits
vastly to our knowledge of meteors. The Harvard
Super-Schmidt program, which operated from February Table 1 summarizes the photographic orbit
1952 to January 1959, recorded some 6 000 doubly catalogues which presently are included (or in the
photographed meteors. About 2 800 orbits have been near future will be included) in the IAU file. For a
reduced to date. About 2 100 meteoroid orbits have more detailed discussion of this data as well as
been obtained in various small camera photographic detailed references see Lindblad (1971, 1987). We
programs carried out in the USA, Canada, note that the number of available photographic
Czechoslovakia, the USSR and elsewhere. A quantum meteor orbits is of the order of 5 000.
jump in the number of available meteor orbits was
obtained in the 1960's when several multi-station As detailed in Table 1, there is some overlap
high-power meteor radar systems became operative. between the various catalogues. USSR meteor orbits
These stations recorded meteoroids down to are often reported in several places. The references
approximately 8-10 magnitude. The total number of given in Table 1 are judged to be the most complete.
meteor orbits recorded by these stations is of the Orbital and geophysical/photometric data are often
order of 70 000 or more. reported in separate publications, no doubt
reflecting various stages in the data reduction
Information on meteor orbits is widely scattered process. Recently a very complete catalogue of the
in the scientific literature and is often available Odessa data has appeared (Kramer, Shestaka and
only in publications with limited circulation. Markina, 1986).
Information about individual radio meteor orbits has
mainly been available as internal observatory Results obtained by the Czechoslovakian and
listings or tapes. In the absence of key scientific European camera networks have not yet been published
personal much of this information was in the 1970's in full. To date some 300 orbits have been reported
difficult to locate or even lost. by Ceplecha and co-workers in various numbers of
Bull. Astron. Inst. Czechosl. and in SEAN Bull.
At the 1976 IAU General Assembly Commission 22 (Smithson. Short-lived Event Alert Network Bull.,
proposed that a meteor data center be established £t Washington D.C.). Unfortunately the latter publica-
the Lund Observatory for the collection of meteor tion is seldom available in astronomical libraries.
observations by radio and photographic techniques. The Czechoslovakian data are of high precision and
The decision was confirmed by the 1982 IAU General they represent a random sample obtained over a
Assembly and a small sum was allocated for the period of more than 35 years. (In contrast the
support of the data center. The archived data are Harvard Super-Schmidt data were mainly obtained in
mainly two-station photographic orbits or multi- the three year period 1952-54). The publication in
-station radio orbits. Visual observations are not full of the Czechoslovakian meteor orbits is there-
archived, since such programs do not provide precise fore eagerly awaited by the astronomical community.
orbital information.
A number of two-station photographic orbits have
The photographic data were originally punched on been obtained in various amateur programs. See
80 column cards with two 80 column card images for reports by Nippon Meteor Soc. (1984), Ochiai (1985)
each meteor. The first card image contains the and Betlem (1985). It is planned to include most of
identification no., time of appearance and orbital these orbits in the IAU file. The orbits have been
elements plus mass; the second card image contains obtained using short focus cameras, hence the
identification no. and time plus geophysical/ precision of the data may be slightly lower than
photometric data such as heights, velocities and that obtained in the professional programs. A number
magnitudes. Data formatting, references and other of two-station TV-camera orbits have recently been
relevant information are documented in an informa- published (Jones and Sarma 1985 and references
tion pamphlet which is available on request. The therein). Also these orbits will later be included.
photographic data are now in the process of being
converted to tape.
3. Radio orbits
The major radio meteor programs (Harvard,
Adelaide, Mogadisho, Obninsk and Kharkov) h ave each Table 2 summarizes the major radio meteor orbit
produced some 5 000-40 000 orbits. The Harvard Radio collections presently included in the IAU file. The
Meteor Project alone obtained in the period 1961-69 column denoted "source" acknowledges the scientist
some 40 000 orbits. Owing to the vast amount of data or institute from which the present author has
individual orbits have as a rule not been published. received the appropriate tape.

201
 Table 1. List of photographic meteor orbit catalogues

Station rears No. of Authors

orbits

Harvard (Mass.) 1936-52 139 (144) Whipple

1951-52 27 Unpubl.
(New Mex.) 1952-54 413 Jacchia and Whipple
" II II
1952-54 313 (359) Hawkins and Southworth
II II
1956-59 353 Posen and McCrosky
n II
1952-54 1790 (2529) HcCrosky and Posen
" (Graphical reduction)

Prairie Network 1963-75 336 McCrosky, Shao and Posen

MORP " 1971-84 218 Halliday, Griffin and Blackwell
(and unpubl.)
Dushanbe 1. 1940-55 73 Katasev
2. 1957-59 181 Babadjanov and Kramer
it
3. 1960-63 72 it M ii

" 4. 1964 77 Babadjanov et al.

it
5. 1965-66 15 (18) Babadjanov and Getman
it
6. 1968-77 44 Babadjanov et al.
»
7. 1966-67 20* Babadjanov and Getman
Odessa 1. 1957-59 133 Babadjanov and Kramer
" 2. 1960-61 92 n M II

3. 1961-65 122 (124) Kramer and Harkina

» 4. 1962-72 50
5. 1973-83 62* Kramer et al.
Kiev 1. 1957-66 100 Benyukh et al.
•I
2. 1967-76 70* Sherbaum et al.
Ondrejov 1951-85 321* Ceplecha et al.

* An asterisk indicates that the data are not yet included in the IAU file.
A number in parentheses gives the total number of orbits listed in a catalogue
(including overlapping catalogue data and/or later rejected orbits).

Table 2. List of radio meteor orbits

Name of survey Year Station No. of Source Referencs

orbits

Harvard 1961-1965 Nov 61- Havanna, III. 19327 C. Murray Z. Sekanina, 1973, Icarus, 38,
Nov 65 253-284.

Havanna, 111. 19818 C. Murray Z. Sekanina, 1976, Icarus, 27,

Harvard Syn. Year 1968-69 265-321.

Adelaide, 2092 D. Olsson- C.S. Nilsson, 1964, Austr. J.

C.S. Nilsson 1960-61
Australia Steel Phys, 17, 205-256.

Adelaide, 1667 D. Olsson- G. Gartrell & W.G. Elford, 1975,

G. Gartrell 1968-69 Australia Steel Austr. J. Phys., 28, 591-620

9354 USSR Geophys V.N. Lebedinets et al., Two

Obninsk 1967-68 Obninsk
Committee catalogues, Mos.ow 1981, 1982.

Equatorial Jan 69- 5328 Two catalogues, 1975, 1977, World

lurvey June 70 Mogadisho
Data Center B, Moscow

Kharkov 1975 Kharkov 5317 B.L. Kaschev and A.A. Tkachuk, 1980,
World Data Center B, Moscow.

202
 The Harvard Radio meteor project was initiated by computer programming they can only be expedited with
F.L. Whipple with G.S. Hawkins and R.B. Southworth some delay and at cost.
as principal investigators. The Data Center is
indebted to the Director of the Harvard-Smithsonian
Observatory for kind permission to distribute the Acknowledgements
radio meteor data. The Adelaide survey was initiated
by G. Elford with C. Nilsson and G. Gartreil as The author is indebted to the scientists and
principal investigators. The Adelaide orbital data institutes mentioned in the text for valuable help
was retrieved through the efforts of D.Olsson-Steel and to the IAU for financial support.
and we are indebted to G. Elford for permission to
distribute these data. A tape with the USSR radio
orbits has been made available by the World Data REFERENCES
Center B, Moscow.
Babadjanov, P.B. and Kramer, E.N.; Ionosphere and
Meteors, Section V of IGY program. No. 12 (pp.
4. Accuracy of catalogue data 102-124), Moscow 1963.
Babadjanov, P.B. and Kramer, E.N.; 1967, Smithson.
In general it is difficult to assess the quality Contr. to Astrophys., 11, 67.
of data obtained at a particular station or by a Babadjanov, P.B., Getman, T.I., Zausayev, A.F. and
particular investigator. An investigator may select Karaselnikova, S.A.; 1969, Bull. Astrophys. Inst.
only the best photographic images for analysis, or Akad. Nauk Tadjikistan, SSR, 49, 3.
study a random sample of the data, or analyze the Babadjanov, P.B. and Getman, T.I.; 1970, Bull.
available data in full. In fireball-meteorite- Astrophys. Inst. Akad. Nauk Tadjikistan, SSR, 53,
-recovery programs the emphasis is on reducing 3.
photographic trails of meteors with low terminal Babadjanov, P.B. and Getman, T.I.; 1985, Bull.
heights. In some studies the time of appearance of Astrophys. Inst. Akad. Nauk Tadjikistan, SSR, 76,
the meteor was not precisely recorded, and the mid- 28.
-exposure time was used in the orbital computation •• Babadjanov, P.B., Getman, T.I., Konovalova, N.A. and
with resulting loss of accuracy. Some investigators Obrubov, Y.V.; 1982, Bull. Astrophys. Inst. Akad.
have included in their catalogues a measure of the Nauk Tadjikistan, SSR, 73, 22.
relative accuracy of each orbit. This index is Babadjanov, P.B. and Kramer, E.N.; Ionosphere and
included in our records. When no index of relative Meteors, Section V of IGY program, No. 12 (pp.
accuracy was given, various other measures of 125-141), Moscow, 1963.
orbital accuracy have been introduced. For a Babadjanov, P.B. and Kramer, E.N.; 1967, Smithson.
discussion see Lindblad (1973). Contr. to Astrophys., 11, 67.
Benyukh, V.V., Kruchinenko, V.G. and Sherbaum, L.M.;
The early orbital calculations were in many cases 1980, Astron. and Astrophys. (Kiev), 41, 68.
done by hand or with desk calculators, in which case Betlem, H.; 1985, Radiant, 7, 73.
computational errors are not uncommon. Some errors Halliday, I., Griffin, A. and Blackwell, A.; in R.
or misprints in the published data have been West, Highlights of Astronomy, 6, 399, Dordrecht,
corrected after correspondence with the original 1983.
investigators. At the Data Center the published Hawkins, G.S. and Southworth, R.B.; 1961, Smithson.
small camera meteor orbits have been checked for Contr. Astrophys. 4, 85.
internal consistencies, i.e. do values of V,, and a Jacchia, L.G. and Whipple, F.L.; 1961, Smithson.
agree?; are values of q, a and e consistent, etc. Contr. Astrophys. 4, 97
These checks revealed numerous inconsistencies in Jones, J. and Sarma, T., 1985, Bull. Astron. Inst.
the published orbital elements. Czech., 36, 103.
Katasev, L.A.; 1964, Photographic Methods in Meteor
An independent study of the errors in the photo- Astronomy, Monsun Press, Jerusalem.
graphic orbital data has been made by Koseki (1986). Koseki, M.; 1986, J. Brit. Astron. Assoc, 96, 232.
A list of errors and corrections from this study is Kramer, E.N. and Markina, A.K.; 1976, Probl. of
available at the Data Center and can be supplied on Cosm. Phys. 11, 51.
request. A similar study of the errors in radio Kramer, E.N. and Markina, A.K.; 1980, Probl. of
meteor orbits has been made by D. Olsson-Steel. Many Cosm. Phys. 15, 53.
of the detected errors appear to originate in the Kramer, E.N., Shestaka, I.S. and Markina, A.K.;
misuse of the inverse trigonometric functions 1986, Meteor Orbits from Photographic Observa-
(ascending and descending nodes have been inter- tions 1957-1983, Materials of the WDC B, Moscow.
-changed). In order to reduci. the computational Lindblad, B.A.; 1971, Space Res., 11, 286.
efforts involved in the data reduction of large Lindblad, B.A.; 1973, The Distribution of I/a in
radio orbit samples various simplifying assumptions Photographic Meteor Orbits, In Hemenway, C.L.,
have sometimes been made. The ellipticity of the Millman, P.M. and Cook, A.F., Evolutionary and
Earth's orbit appears to have been neglected in some Physical Properties of Meteoroids, NASA SP-319,
radio surveys. In view of the observational errors Washington, D.C.
inherent in radio meteor orbit determinations (as Lindblad, B.A.; 1987, Physics and Orbits of
compared with the photographic data) this procedure Meteoroids, in Fulchignoni, M. and Kresak, L.,
is probably acceptable. The Evolution of the Small Bodies of the Solar
System (Proc. Int. School of Physics "Enrico
Fermi").
5. Data requests McCrosky, R.E. and Posen, A.; 1961, Sraithson. Contr.
Astrophys. 4, 15.
Investigators have in the past asked for tapes, McCrosky, R.E., Shao, C.-Y. and Posen, A.; 1978,
cards or listings of data. Since card readers are Meteoritika, 37, 44.
becoming obselete in many countries, data will in Nippon Meteor S o c ; 1984, The Friend of Stars, No.
the future be distributed on magnetic tape. The 30, 59 (in Japanese).
possibility of making the data available on Ochiai. T.; 1985, Werkgroepnieuws, 13, 88.
diskettes is being studied. In the past many Posen, A. and McCrosky, R.E.; 1967, NASA Contr. Rep.
investigators have been rather specific in their CR-862.
requests - they are only interested in orbits from a Sherbaum, L.M. et al.; 1985, Bull. Kiev Univ. Ser.
particular stream; sporadic meteor orbits, etc. Such Astron., 27, 73.
requests are welcomed, but since they may involve Whipple, F.L.; 1954, Astron. J. 59, 201.

203
 D I S C U S S I O N

Ibadov: What do you think about using space- structed in the future, should probably be
craft Cmaybe in the future)? based on a modified Sisyphus type of instru-
L indblad: To date there has not been devised ment, i.e. a four-telescope instrument observ-
a good instrument for obtaining meteoroid ing the reflected light from a small inter-
orbits in space. Such an instrument, if con- planetary body.

204
 METEOROID DECELERATION AND THE, FRESNEL CHARACTERISTICS

P. Pecina
Astronomical Institute, Czechoslovak Academy of Sciences,
251 65 Ondfejov, Czechoslovakia

The work describes briefly the application of the complete solution of the basic
equations of meteoric physics, found in connection with solving the problems of
photographic meteor theory, to the construction of theoretical Fresnel character-
istics. It is shown how the meteoroid deceleration can be incorporated into concepts
of radar physics. The corresponding equations are derived and the possibility of
using these Fresnel characteristics for the evaluation of the ablation paramater^and
the'pre-a tmosptieric" velocity v from the registered amplitudes is briefly discussed.

I
The Fresnel characteristics are the tool R is the distance from this point to the
for determining the velocities of radar me-
teors. The starting point for their con- observer. In the past the quantities I were
struction must be the formula which would used mainly for evaluating v. But this is a
provide us with the power received after the quantity which must be converted to v^Cthe
reflection of radar-wave on the ionized trail. pre-atmospheric velocity) to be able to de-
We will be dealing exclusively with the under- termine correctly the heliocentric orbit of
dense type trails. Then,we can use the formu- the parent meteoroid. The first attempt to
la use the fresnel characteristics for finding
the Vgo | the ablation parameter i and the
other parameters has probably been made by
Kostylev and Kostylev (1980), Kostylev (1982)
G and Kostylev and Alferova (1985). But they
TGRre did not use the exact physical theory. There-
(i) P R =e T
fore, after the new exact solution of the
basic equations of meteor physics giving the
distance 1 as a function of time t'waB pub-
lished (see Pecina and Ceplecha, 1983, 1984),
it seemed worth trying to incorporate this
(e.g. Novikov et al., 1986). In the same pa- new concept also into the theory of Fresnel
per the interested reader can find the conclu- characteristics. In case of successful de-
ding radar equation valid for the nondecele- velopment of the theory we would be provided
rating bodies with the possibility to obtain the v^and ^
directly from the characteristics.
We will now briefly describe the deriva-
GTGRI tion of the desired formulae. The detailed
(2) derivation will probably be published in the
exp(- Bulletin of the Astronomical Institutes of
Czechoslovakia in 1988 under the title The
derivation of Fresnel characteristics when
the deceleration of the meteoroid is taken
into account. We will only deal with the
where quantity analogic to I from equation (2). Let
us consider the expression inside the absolute
value sign in the equation (1) and denote it
by
1=
TFF N e (r,t)
exp dVe
is the mathematical expression for Fresnel
characteristics themselves. Because the be-
haviour of the characteristics is given only One integration.can be performed profiting
by I, we will consider further only this from the fact that our problem is axisym-
quantity,where metrical and N depends only on the radial
distance r froS the axis, on the coordinate
z (which increases in the direction of mo-
tion of the body and gives the position of
the reflecting electron with respect to the
specular point for which it equals to zero),
The quantity t gives the time instant at and on the time t, as well. Then we can re-
Which the body passes the specular point. The write (3) in the following way:
meteoroid velocity v and the -ambipolar dif-
fusion coefficient D obtained from I are re-
lated to the values of these quantities at (4) X=,f$dzdrrN (r,z,t) K(r,z),
the specular point of the trajectory, as well, V
S e

205
 where It is evident that l>0 for h*hQ and l<0 for
h>h . The distance 1 is measured along the
meteor trajectory. So, we have obtained the
expression of cl which takes into account the
deceleration of the meteoroid. We have to
solve the equation of diffusion. Its solution
is given by the formula

The coordinate system used was described by t

Novikov et al. (1986). The sufficiently ac-
curate result of the last integration reads (12) Ne(r,z,t)=

(5) .QeC?;t')dVe,
^o»o(KD,

where the Green function of our problem has

where J (x) is the Bessel function of zero the form
order. Now, we must find the relation giving
N if the deceleration of the body is consid-
ered. Solving the set of equations of meteor
physics (12) CCf,T,t,f)-

(6a)
4D(z)(t-t')
(6b) 4D(z)(t-t')
2

(6c) and the source term Q e is given by

we can arrive at the expression

(13) exp(-

c*Km2/3
(7) ot(h) =
(e.g. Novikov et al., 1986). We^ have consid-
ered the initial condition N „("?, -*& - 0.Inser-
where i =X/(2QP) is the ablation parameter and ting expressions (12) and (13) into (11) we
h stands for the height above the ground. To get
complete equation (7) we must add the rela-
tion getting the dependence of v on h. But
it has already been done by Pecina and Ceple- Ne(r,z,t)=-
cha (1984): exp(-
r%4D(z)(t-tk)

(8) where

dt

where Ei(x) is the integral exponential func-

tion and
tiov, we can integrate equation (4) with re-
spect to r and z:

•"£
F(h)= \»(h)dh.
dZ
h

The quantity h can be related to the time t

by the integral
(14)
*= S ^
n+2 r 2T 2 i 2

t =t n +
0
S i»(h -xcoszR)v(x)exp|i-i x + -v (x)-
2** 2 . . ^ df
- 4(-TT ) 0(2) V
and the geometrical relation
w+iere we have u s e d ^ = A v n (see Kaschchesv et
a4. ; (1967). Using the dependence of the dif-
(10) •h=h Q fusion coefficient on z in the form

206
 - zcoszR)(»(ho-zcoszR) = 0 5 where

and realizing that the main contribution in

the integral comes from the part of trajecto-
ry adjacent to z«0, we obtain our final for- (IB)
mulae (for the imaginary and real part) of s2+ c2
the power received:

Ttie method due to Hauck (1971) (designated

(15a)
>4 usually as the
to satisfy the
following from
The method was
of parameters:
method of gradients) was used
condition (17). The formulae
it are given in the Appendix,
tested on the fallowing set ,
t_ = 0.02422s, voo=6D.0Q kms ,
= 59.50 kms -1 , 6= 0.030 s km , ha=97.62 km.
2 2
vQ

The following table lisU the results obtained

as a function of the relative accuracy with
which the integrals entering the computation
were performed as well as the CPU time need-
n +2 ed on EC 1040 computer:
i 2Tx
J * o
v v h
~ o <* o
,-3 0.02429
61.57 59.81 0.045 97.63
0.00015 1.56 0.57 0.008 0.14
CPU time needed = 39 ir.in.

o
£ l n t =10" 4 0.02426 61 .41 59.73 0.037 97.61
0.00012 1 .30 0.47 0.006 0.11
Then, the corresponding theoretical amplitude CPU time needed = 50 min.
is computable frorr the formula

,-5
0.02425 61.38 59.71 0.036 97.60
(16) 0.D0012 1.26 0.46 0.006 0.11
CPU time needed = 69 min.
where c is a normalizing constant into which
;ill constants from equations (7), (12) and
(13) HKere included. The index i labels the
measured impulse in the characteristics. To
find the required parameters we must apply
a procedure ensuring the following constraint: In the light of the presented results
I am convinced the method described can work
and is worth further developing. We will then
have at aur disposal the method providing us
= min, directly with v a o and4in case of faint radar
meteors with the sufficient accuracy for other
reliable statistics.

M
where A. stands for the measured amplitude The Appendix.
and N * gives their number. Then,we must
fired the values of the following quantities: The problem posed by the condition (17) is
c
> * > veo > v >^> ^ • ^ u ^ w e c a n av °i c ' the nonlinear in searched parameters. The Hauck's
nece§sity to find c if normalizing all am- metho.d enables its linearization. The math-
plitudes to the chosen one, say A,. Further, ematicall procedure consists in solving the
it was revealed during the numerical exper- set of following linear algebraic equations:
iments that it is better to compare squares
of the normalized amplitudes. It means the
s:atisfaction of the following condition:

= min,

207
where l<k<5,ahd

—n—
. V i c

i =2

and

N M

2
A
i
95.

The order of parameters used is listed in the

table:
HP
A
•where the following abbreviations were em-
ployed:
The iteration procedure starts with properly
chosen parameters p.. Parameters t , v^> , h ? 2V1 •
were assumed to correspond to those following
from the application of the old method rely-
ing on the quantity I on the observational
material where the relation On-,Jq-j = DP(h 0 )
served as a tool for finding h if D is known,
? 1
D 93 =4.25 m s was employed, v =v-0.5 and
A ? -2
6=0.01 5 km were used as other starting
values. CIRA atmosphere (1972) was utilized.
o l d with which the set of linear
So, we had p
equations was solved. Then p^ ^ew = p1? + dp. .p
i
new ld i
and p were substituted for p ° in the l5v
set of equations in question. This iteration +C
loop was terminated unless |dp.| was less l +L l
than any prescribed value for •* all j. The
sum of squared differences in sense of the
condition (17) was assumed to decrease during
the iteration procedure. In the opposite case
the iteration was terminated, as well. The
derivatives needed were computed according to
the following formulae:

All derivatives in these formulae are to be

computed in the explicit sense. The distances
1. were obtained by solving the transcendental
eguation (9) for corresponding time instants
t. related to A.. v.=v(l4) was evaluated mak-
X 1 1 1 -I
ing use of the inverse to Ei(x), £. (x), as
described by Pecina (1986). The derivation of
the formulae for3Q./^p. is tedious and was,
therefore, left to the paper dealing with the
detailed derivation of all formulae constitu-
ting the foundation of the described method.
REFERENCES

CIRA: 1972, Akademie Verlag, Berlin.

208
Hauck, W.W.: 1971, Foundation for Estimation
by the Method of Least Squares, Smithson. D I S C U S S I O N
Astrophys. Obs. Spec. Rep. No. 340.
Kashcheev, B.L.; Lebedinets, V.N.; Lagutin,
M.F.: 1967, Rezul't Issled. IGY-Issled. Meteo- Olsson-Stael: This effect would be important
rov No. 2. as regards the derivation of heliocentric
Kostylev, K.V.; Kostylev, K.K.: 1980, Astron. orbits even though the change in \IM is quite
Vestnik 14, 89. small. How big is the change compared to the
Kostylev, K.K.: 1982, Astron. Vestnik 16, 124. experimental uncertainties? Would this not
Kostylev, K.K.; Alferova, T.G.: 1985, Astron. be an even more significant effect for the
Vestnik 19, 159. few meteors detected by radar much lower?
Novikov, G.G.; Pecina, P.; Blokhin, A.V.: That is, closer to the point of maximdm
1986, Bull. Astron. Inst. Czechosl. 37, deceleration.
189. Pecina: I cannot say now, because I have
Pecina, P.; Ceplecha, Z . : 1983, Bull. Astron. presented a model computation. The full an-
Inst. Czechosl. 34, 102. swer could be given when applying the theory
Pecina, P.; Ceplecha, Z.: 1984. Bull. Astrcn. to observations. But this will be made after
Inst. Czechosl. 35, 120. the theory will be somewhat improved.
Pecina, P.: 1986, Bull. Astron. Inst. Czechosl.
37, 8.
Pecina, P: 1988, submitted to Bull. Astron.
Inst. Czechosl.

209
\Q
 NUMBtRS AND MASSES OK DIFFERENT POPULATIONS OF SPORADIC METEOROIDS
FROM PHOTOGRAPHIC AND TELEVISION RECORDS

Zdenek Ceplecha
Astronomical Institute of the Czechoslovak Academy of Sciences,
251 65 Ondrejov Observatory, Czechoslovakia

Double and multistation data on meteors from photographic and television records, are used,
to derive relative and absolute numbers of sporadic meteoroids coming to the Earth s vinicity
and their mass accession. Seven different jneteoroid populations are dealt with separately inside
a mass interval of 2 x 10' g to 2 x 10 g and their cumulative numbers with decreasing mass
determined. This paper is an abstract of more extensive paper, which will be published in Bull.
Astron. Inst. Czechosl. in 1588. level belongs to meteoroids originally denoted
by Verniani and Oacchia as "asteroidal". The C
Thirty years ago, meteoroids coming level meteors differ in their orbits partly in
to the Earth's vinicity were assumed to be approxi- analogy to comets. There are three different
matelly of the same structure and composition. groups among the C-level meteoroids: C1 with
In the years 1965 and 1967, Verniani and 3acchia short-period ecliptically-concentraced orbits,
argued in favor of ail meteoroids being low density C2 with long-period randomly-inclined orbits,
(0.2 g/cm ) friable bodies. This was based on and C3 with short-period randomly-inclined orbits.
their analyses of atmospheric trajectories of C3 meteors are only small population among bigger
roeteoroids photographed by Super-Schmidt cameras. bodies, but they become quijte dominant for bodies
This highly simplified view originated from biased with masses less than 10 to 10 grams. This
statistical handling of the data (Ceplecha, 1968). knowledge comes from recent analyses of double-
Different meteoroid populations were first recog- station meteor data obtained by TV cameras (Hawkes
nized even sooner, in 1958, and independently et al. 1984; Oones and Sarma, 1985; Sarma and
by Jacchia and Ceplecha, from systematic differences 3ones, 1985). The classification for TV-meteors
in meteor beginning heights. When the correct proved to be the same problem as for the brighter
dependence of beginning height on velocity was Super-Schmidt and small-camera meteors Oones,
applied to observations, several discrete levels 1985). On the other hand, the classification
of beginning heights were found (Ceplecha, 1968). of very bright meteors, the fireballs, is a little
The survey of all known meteoroid populations bit more complicated, due to the fact that the
is jiven in Table I. The two main levels separated bigger mass and bigger distances from the fireball
by 10 km difference were denoted A the lower, network stations add one parameter to the classi-
and C the higher. Another 10 km higher than C fication more (Ceplecha and McCrosky, 1976; Seka-
is the level D belonging to very fragile meteoroids nina, 1983; Wetherill and ReVelle, 1981a,b).
of the Giacobini-Zinner comet shower. 8etween Also the notation of the levels is different except
A and C is level B, with not too many sporadic for the C3 bodies revealed recently; Type I
meteoroids, but very distinct as belonging to bodies correspond to "asteroidal" meteors, type
Geminid meteor shower. Small perihelion distance II to the A-level, type IIIA to the C level and
is quite typical for the orbits of the B-group type IIIB to the D level. Our observational material
meteoroids. Another 10 km lower level than the A of photographic-and TV-meteors consists of b

Table 1
Survey of ffleteoroid populations aaong photographic and television mete

ObEeruational Television Super-Scheldt Snail cameras Fireball networks

otteriel cameras c&oeras Properties of the meteoroid,
material
JC&6G
rwfie b) 2S1O"5 t o 5x1O~3g izicT* to 1g 10"' to 5x102g !O2 to 2xlO7g
5 * Characteristic S Characteristic
Croup orbit orbit orbit Group orbit 6 Assumed composition
Parent todies
ob 8 . ObB. a e i g/cm3

"BEteroidal Ordinary ehondriteB

o.ce
reteors"
<1
°.i °af 18°
a)
1 2.« 0.64 15° 5 0.64 10° I 29 2.4 6" 3.7 0.017 /steroids
Carbonaceous chondrltes
k 2? 1.6 0.55 14° 50 2.3 0.(1 1° 39 2.5 0.64 4° 11 33 2.3 0,61 5° 2.0 0.041 Comets, Asteroids
Dense cometary naterial
B 2 2.1 0.95 29° 3 2.4 0.92 5° 5 2.5 0.90 6° - - - - - 1.0 0.06 Inner part of cometajPheeton
•fcegular coroetary aoterial
01
c) 21 1.7 0.63 16° 7 2.2 O.BO 6° 11 2.5 o.eo 5° IIIJ. O) 14 2.4 0.82 4 ° 0.75 O.10 Short period ccrete
ran- ran- ran- III/U 0.99 ran- Regular cemetery material
C2 IB »•» 0.99 dom 32 3<O 0.99 dom 21 S4« 0.99 dom 11 SfOO don 0.75 0.10 Long period cor.ete

ran- ran- ran- ran- Regular cojr.etary ceterJal

M c> 26 1.3 0.60 don 6 1.9 0.72 dom 9 2.1 0.77 dom "c> 4 2.7 0.67 dom 0.75 0.1O Long period coaelB
Soft corcetary material
i> 3 s.t 0.66 16° 1 3.3 0.70 25° 10 .3.1 0.77 10° IIIB 9 3.0 0.70 13° 0.27 0.21 Short period comets of
Ciacobinl-Zlnner type

aendmajor axiLB. e ... eccentricity, i ... Inclination, <J« ... bulk density of the meteoroid, tf... ablation coefficient,

e) only one meteor Ho 811104060 recognized as "aateroidol"; l t e elements are given.

b) total DBBC ranee: indS>idual croupe differ due to different distribution of velocities.
c) C3 corrected for rondo* 1 (instead of i >35°) Dy adding the coi -eupondinG port of Cl (lllA) to C3.

211
different systems of cameras in regard to sensiti- Table 3 contains incremental numbers
vity. The most important tool in making a coherent as they resulted from Table 2. For each mass
picture of all data lies In superposition of interval, Table 3 contains logarithms of numbers
the mass intervals of these * different sets and also logarithms of masses inside each of
of data, as you can easily check in Table 1. the 0.2 wide logarithmic mass interval, for each
sporadic meteor group separately. The last column
The observational material used in this gives the same for all sporadic meteors as it
paper consists of 362* sporadic meteors (561 resulted from summing up incremental numbers
sporadic fireballs: PN and EN fireballs), 812 and masses of all the meteor groups.
sporadic small-camera meteors, 18*8 Super-Schmidt
sporadic meteors (McCrosky and Posen (1961), The results of Table 3 for all sporadic
*03 TV sporadic meteors), which is practically meteors are compared in Fig. 1 with "visual"
all, and mostly published, of precise optical data published by Hughes (1978). The absolute
data on meteors available nowadays. The masses values in typically visual interval from 0.1
of individual meteoroids originate from integration to 10 gram agree almost perfectly, but outside
of the whole light curve and except for the ques- this interval the discrepancy is by orders of
tion of changes in luminous efficiency, these magnitude, and is systematic and of opposite
masses are highly preferable over any estimates slope. I think that this only points out, how
based only on one value of maximum brightness dangerous is any extrapolation of cumulative
with some kind of average velocity, as is the numbers byond the region of actual full-sensi-
case of interpretation of visual observations. tivity of a receptor. In case of interpretations
Also radar data are severly limited in this respect. of visual observations, more populated smaller
bodies of high velocities are added to few bigger
Table 1 contains only survey of all bodies of low velocities at the same maximum
meteoroid populations revealed so far. There brightness, unresolved. This makes the cumulative
is enough statistical material to study the mass slope seemingly steeper. We also compared our
distribution of individual groups in smaller results with a model of meteoroid fluxes given
mass steps. We used cumulative numbers of meteo- by Gru'n et al. (1985) and based on lunar micro-
roids and divided the whole interval of 12 orders cratering and Whipple s (1967) interpretation
in mass into small steps of 0.2 in log m. In of ^meteor ., statistics inside mass interval of
one type of observational material the relative 10 to 10 grams. The same order of discrepancy
numbers of meteors belonging to individual groups as with the Hughes values was found. Fig. 2 repre-
are given directly by observations. We started sents the comparison of our flux curve of all
with fireballs and used the cumulative numbers meteoroids with the flux curve of Grim et ai.
in log N-log m plot for each group of meteoroids The average slope is identical between log m
separately. The next observational material to = 0.7 and log m = -1.3, which is a typical interval
fireballs belongs to the small-camera meteors. for the visual meteor observations (and close
Their relative numbers, comparing the individual to SuperSchmidt sensitivity interval), on which
groups, are also given directly by observations. the slope given by Whipple (1967) mostly depends.
If we want now to join the cumulative-number The dimension of a crater, when related to the
plots of fireball groups and small-camera groups mass of its projectile, has similar big spread
of meteors into one plot for each group, we are due to velocity of the projectile as in the case
actually searching for one constant in logarithmic of "maximum brightness of a visual meteor". Again
representation, which should hold for all small-ca- more populated smaller projectiles of high veloci-
mera groups to continue smoothly the fireball ties are added to few bigger projectiles of low
groups. The low sensitivity bias is well defined velocity at the same dimension of their craters,
this way by the overlapping statistical distribu-
tions. This procedure can be used to join any
of the other neighboring systems of data, small-ca-
to
mera with Super Schmidt meteors, and Super Schmidt
•n
with TV meteors. In all cases, one single value
of the relative shift was found between the neigh- togM
boring observational materials. The absolute
calibration of the cumulative number curves was
' 1 , r^_
done by comparing the results on the type-I fire-
balls with the recent work of Halli*'.. •/ et al.
(198*) on meteorite falls and deep • .'tietratlng c)
fireballs. The slope of both independent analyses
of cumulative numbers are identical in two digits
(-0.69) and the difference in absolute terms
yielded a small correction of the mass scale
and of the absolute number of meteoroids.

log m (this paper)=

1 ^Y 1
'_
= log m(Halliday et al., 198*) + 0.2
= log m(Ceplecha and McCrosky, 1976) -0.3 *

The above described procedure gave also a perfect

check on validity and consistency of our results
based on much bigger observational material with
the results of Halliday et al. (198*). !°S m IE)
The results of all this computations Fig. 1.
are given in Table 2. The mass intervals are
0.2 in log m from 6.8 to-*.6 in logarithm of Incremental masses M in intervals of 4 log m-1.
gram. For each meteor group separately, Table M is in grams per year for the entire Earth s
2 contains logarithms of cumulative numbers already surface.
calibrated to the whole Earth "s surface per one a) the results of this paper
year. In the last column, the logarithms of cumula- b) the results of this paper with changing the
tive numbers are given for all sporadic meteoroids, lluminous efficiency according to equation (2)
as they resulted from summing the numbers of c)and d) the results From visual observations
meteoroids of all groups inside each mass interval. (Hughes, 1978)

212
 The results of this paper represented
by curve a) in Fig. 1., are distinctly preferable
to all so called "visual" or "visual-extrapolated"
data and aiso over lunar cratering data with
the following precautions:
The extreme wings below log m = -3 and
above log m = 5 are close to the boundaries of
the sensitivity of all the incorporated observa-
tional systems and may contain less bodies than
is the reality. Inside the interval from log
m = 5 to log m =-3 the incremental^ masses can
differ from reality maximally by -0.3 in log
m, but the relative change from interval to the
next interval is better than -0.1 in log m. Finally
the method of dividing the meteors into groups
and handling them separately, gives better results
than any procedure taking the meteors as only
one statistical body.
Fig. 3 represents the relative percentage
change of three types of the meteor bodies expres-
sed in incremental numbers:
a) the stony material
b) the A-group material (carbonaceous bodies)
•;) the cometary material.
I think that most of internal discrepancies in
results of studying meteors by objective optical
means in the past, originated just from the fact
that we first learned about meteoroids from the
mass interval of the complicated interlaced systems
of meteor bodies.
And I finish the presentation of the
paper by just one number more: the total influx
fig. 2. of sporadic meteoroids- in the mass inter-val of
M orders from 2 x g 1Q grams to 2 x 10 grams
Cumulative numbers N of meteoroids of greater mass resulted in 5 x 10 g per _ \r for the entire
than m (in grams).N is given for the entire Earth's Earth "s surface. And most of this mass is in
surface per year, a) the results of this paper, the form of bigger meteoroids.
b) the flux model of Griin et al. (1985). The a)
curve is extremely well defined for roeteoroids
with log m greater than -3. The discrepancy or
a) and b) at log m -3 is almost 2 orders of
magnitude. REFERENCES

unresolved. This makes the cumulative slope see- Ceplecha, I.: 1958, Bull. Astron. Inst. Czech-
mingly steeper. The detailed knowledge of the osl. 9, 154.
meteoroid velocity and its changes during the Ceplecha, I.; McCrosky, R.E.: 1976, 3. Geophys.
meteoroid atmospheric trajectory in case of photo- Res. 81, 6257.
graphic and TV meteors makes the results of this Ceplecha, 1.: 1968, Smithson. Astrophys. Obs.
paper on meteoroid fluxes and masses preferable Spec. Rep. 279.
over results of any indirect methods of mass Griin, E., Zook, H.A., Fechtig H., Giese, R.H.:
determination based mostly on one experimental 1985, Icarus 62, 244.
value (crater diameter or maximum brightness Halliday, I., Blackwell, A.T., Grifin, A.A.:
with the lack of velocity data). 1984, Science 223, 1405.
Hawkes, R.L., Oones, 3., Ceplecha, Z.: 1984,
From the results of this paper, the Bull. Astron. Inst. Czechosl. 35, 4S.
Incremental mass has the absolute maximum at Hughes, D.W.: 1978, in Cosmic Dust (ed. 3.A.M.
the largest mass boundary of our observational McDonnel), p. 155, 3ohn Wileyand sons, Chiche-
material and a local maximum just at the visual ster.
meteors (they are close to the SuperSchmidt me- 3acchia, L.G. 1958, Smithson. Contr. Astrophys.2,
teors). This local maximum at log m = -0.5 is 181.
mostly caused by the A-group bodies. They comprize 3acchia, L.C. Verniani, F., Briggs, R.E.: 1965,
a half of ail meteors in the whole Super region Smithson. Astrophys. Obs. Spec. Rep. 175.
and almost 90% at log m = -0.5. 3ones, 3., Sarma, T.: 1965, Bull. Astron. Inst.
As a check on the problem of calibration Czechosl. 36, 103.
of masses, an extreme and rather crude assumption 3ones, 3., Sarna, T., Ceplecha, I.: 1985, Bull.
on the luminous efficiency T was also introduced. Astron. Inst. Czechosl. 36, 116.
log T 0 -. 0.? log m - 18.70 McCrosky, R.E., Posen, A.: 1961, Smithson. Contr.
Astrophys. 4, 15.
To - To V
McCrosky, R.E., Shao, C.-Y., Posen, A.: 1976
and 1977, Prairie Network (PN) Fireball Data
(in c.g.s. system of units combined with 1 = 1 I.+ 11., Center for Astrophys., Prepr. 665
for 0 stellar magnitude, v is the velocity). + 721.
This is represented by curve b) in Fig. 1. The Sarma, T., Oones, 3.: 1985, Bull. Astron. Inst.
discrepancy with the visual data at the local Czechosl. 36, 9.
maximum is bigger, but from log m = -1 to log
m = -3 the visual and photographic curves are Sekanina, Z.x 1983, Astron. 3. 88, 1382.
closer. Verniani, F.: 1965, Smithson. Contr. Astrophys.
8, 141.

213
Vernlani, F.: 1967, Smithson. Contr. Astrophys.
10, 181.
Wetherill, G.W., ReVelle, D.O.: 1981a, Icarus D I S C U S S I O N
<t8, 308.
Wetherill, G.W., ReVelle, 0 . 0 . : 1981b, Relation-
ship Between Comets, Large Meteors and Meteo-
r i t i e s , i n Comets, ed. L. Wilkening, Univ. Fechtip,: I assume that the densities for your
of Arizona Press (USA). groups given in Table 1 are average numbers.
Whipple, F.L.: 1967, in Zodiacal Light and Inter- Therefore you should give ranges to inter-
planetary Medium, NASA-SP 150, p. 409. compare your results with, for example,den-
sities for Halley dust.
Table 2 Ceplecha: Certainly, I can give the ranges
Cumulative numbers. of densities from the distribution of the
Logarithms of neteoroid numbers for the whole Earth's surface values. The intervals of the densities in
per year are given. 3
g/cm' are :
larger jna s s
than m I II IIIA II1A1 All "ast" + 1 : 2.7 9
log m
(log g
•• a s t A B 01 C2 C3 D meteoroids A + II 1 .4 7
6.8 ( 1 .89) 2 .71 B 0.65 7
6 • 6 ( 2 .03'
6 .4 2 .17
2 .81
2 .92 (1 .58 2 .43
IIIA 0.55 91
3. 1 4 IIIB 0.18
6.2 2.31 3 .02 (1 . 7 4 2 .51 3.24 38
6.0 2 .45 3.12 (1 .89 2 .60 3.34
5 .a 8 .59 3.23 (2 .05 2 .68 3 .44 These intervals contain two ^inseparable
5 .6 2 .73 3 .33 (2 .20 2 .76 .55
5.4 2 . 8 7 3 .44 (2 .36 2 .84 3 .65 components superposed: the random errors
5.2 3 . 0 1 3 .55 (2 .51 2 .92 .76 of determination of the densities and the
5.0 3 .15 3 .65 2 .66 3.00 3.87 real distribution of bodies with different
4.8 3 .29 3 .75 2 .62 3.08 3 .98
4 .6 3 .42 3 .86 2 .97 3.16 4.09 densities. Inside the given intervals of
4 .4 3 .56 3 . 9 6 3.12 2.77 3 .24 4.20
4 .2 3 69 4 . 0 7 3.27 .32 4 .32
densities there lies 2/3 of the values,
2.85
4 .0 3 .82 4 . 1 7 3 .43 2.94 3 .40 4 .43 while 1/6 of the values is outside the
3.8 3 .95 4 . 2 8 3 .58 3.02 2.55 3 .48 4 .55 interval at the upper end of the distrib-
3 .6 4 08 4 . 3 8 3 .73 3.10 2.71 3 .56 4 .66
ution and 1/6 is cut off at the lower end
3. 4 4 .20 4 . 4 9 3 .89 3.19 2.88 .64 4 .78
3.2 4 .31 4 . 5 9 4 .04 3.27 3.04 3 .72 4 .89 of the distribution.
3 0 4 .43 4 . 7 0 4 . 1 9 3.35 3.20 3 .81 5 .01
2 .8 4 54 4 . 8 0 4 .34 3.43 3.36 .90 .12 Lindblad: In Table I there is a systematic
2 .6 4 .66 4 . 9 1 4 .50 3.52 3.52 4 .00 5 .24 difference between the mean orbital elements
2 4 4 77 5 . 0 1 4 .65 3.61 3.68 4 .10 5 36
2 2 of photographically determined orbits and
4 88 5.12 4 . 8 0 3.73 3.84 4 .22 5 48
2 0 4 99 5.23 4 .95 3.89 4.00 4 .34 5 60 television camera orbits, in the sense that
1 .8 5 11 5 .33 5 .09 4.08 4.16 4 .47 5 .72 the TV orbits are smaller than the corre-
1 6 5 22 5 .44 5 .24 4.30 4.32 4 .61 5.84
1 4 5 33 5 .54 3 .95 5 .37 4.55 4.48 4 .76 5 96 sponding photographic orbits. Is this due
1 2 5 • « • ) 5j .65 4 .15 5 50 4.82 4.64 4 91 6 09 to a difference in the mean mass, or what
1 0 5 56 .75 4 .36 5 .62 5.11 4.80 5 06 6 22
0 8 5 67 5 .87 4 .57 5 .73 5.39 4.97 5 21 6 36 is the explanation?
0 6 5 78 02 4.78 5 82 5.67 5.13 5 35 6 51 Ceplecha: This is due to the difference in
0 4 5 90 3 22 .99 5 91 5.94 5.29 5.50 6 67 the mass. The explanation lies most prob-
0 2 6 01 3 46 5.20 6 03 6.17 5.45 5 66 6 87
0 0 6 12 6.76 5 .41 b 17 3.40 5.61 5 B2 7 09 ably in much higher ejection velocities of
-0 2 6 24 7 .12 5 .62 6 32 5.77 5 99 7 36 smaller particles from the source, mainly
•0 4 6 35 7 53 5.83 6 49 I'.BO 5.93 6 17 7 69
-0 6 6. 47 7 95 6.04 6 66 6.9B 6.10 6 35 8 04 from comets (Hawkes et a l . , 1984; Jones
-0. 8 6 . 58 8 21 6 .25 6 85 7.15 6.29 6 54 8.29 et a l . , 1 9 8 5 ) , which changes the orbits
-1. 0 6. 70 38 6 .46 7 03 7.32 6.47 6 73 B 45
-1. 2
a quite significantly.
6. 81 8 49 6 .66 7 22 7.48 6.67 6 93 8 58
-1. 4 6 . 90
-1. 6 6 . 97
a8 5648 6.87
7 .07
7 42
7.62
7.64 6.86
7.80 7.05
7 13
7 33
8 69
8. 78
GrUn: The slope of the cumulative mass
-1. 8 7 . 04 70 7.24 7 83 7.94 7.25 7 52 8 87 distribution of 0.6 to 0.7 seems very low,
-2. 0 7 . 11
a 76 7 .39 8 05 8.08 7.44 7 72 8 . 96 at least if it is compared with the slope
-2. 2 7 . 18
a
8 81 7 .52 8 8.20 7.63
29 92 9 07 of somewhat smaller particles derived from
-2. 4 7 . 25 8 87 7.64 8.55 8.31 7.83 8 07 9 . 19
-2. 6 7 . 33 8 92 7 .75 8 . 80 8.41 8.02 8 , 17 9 . 31 lunar microcraters (Grtin et a l . , 19B5).
-2. 8 7 . 40 8. 98 7.85 9 . 03 8.52 8.21 8 . 25 9 . 45 Ceplecha: The average cumulative slope of
-3. 0 7 . 48 9 04 7 .95 9. 17 8.61 8.41 8 . 32 9 . 55
-3. 2 7 . 55 9, 10 B .05 9 25 8.71 8.60 8 . 37 9 . 64 photographic, visual and microcrater counts
-3. 4 9 . 16 .15 9. 30 8.81 8.79 8. 41 9. 71 of meteoroids are indentical in the mass
-3. 6 9 . 22 8a.25 9. 33 8.90 8.98 8 . 45 9. 78
9 . 28 8 .35 8 . 48
range from 0.05 g to 5 g. For bigger bod-
-3. a 9. 35 8.99 9.17 9. 85
-4. 0 9 . 33 8 .45 9 . 37 9.07 9.36 9 . 93 ies, the slope decreases to -0.69 in good
-4. 2 9 . 39 8 .55) 9 . 38) 9.15 9.55 1 0 . 02 agreement from three independent analyses
-4. 4 9 . 45 B .65) 9 . 4 0 ) 9.22 9.73 1 0 . 12
-4. 6 9. 51 8 .75) 9. 41) 9.30 9.91 1 0 . 23 (McCrocky: 1 9 6 8 , Distribution of Large
Meteoric Bodies, Smithson. Astrophys. Spec.
Rep. 2 8 0 ; Halliday et a l . , 1 9 8 4 ; Ceplecha, this
p a p e r ) . For bodies smaller than 0.05 g, the c u -
mulative slope decreases to - 0 . 5 , which is hold
up to at least 0.001 g. The next two orders of
smaller masses are too close to the lower bound-
ary of the whole studied interval of 12 orders
that the slope from 0 g to 10 g may be dif-
1
ferent from reality. In
In any
any case,
case, between
between 10
to 10 g one would expect an increase of the
slope again to fit the satellite data (if they
do not reflect some denser system of Earth bound
particles, because sporadic meteors used in this
paper are strictly interplanetary). I repeat
again that the advantage of photographic and Ti/
meteors lies in detailed knowledge of velocity
and mass at many points of each individual atmo-
spheric trajectory.
log m ((I

214
 Table 3
Incremental numbers and rcaoaea.
Logarithms of number3, log M, and logarithms of total masses, loglNoi), inaide each BI&BB interval
of 0.2 in log sa are given. Units: jn in grama, N . . . numbers of meteoroide for the entire Earth s
surface per year.
mass I n IIIA IIIAi ma All
interval "a3t" A B 01 C2 C3 D meteoroids
log a l o g l o g Log l a g l o g l o g log I log l o g l o g l o g l o g log iiog l o g l o g
ITom to M tin M Nm M Hm K I Bm K Ho N Nil K | Nm H Tim
6.8 6.6 (1.47 8.17 2.14 8.84 2.22 8.92)
6.6 6.4 C 1.61 8.11 2.24 8.74 2.33 8.83)
6.4 6.2 1.75 B.05 2.35 B.65 1.22 7.52 1.76 8.06 2.55 8.S5
6.2 6.0 1.89 7.99 2.45 8.55 1.37 7.47 1.64 7.94 2.66 8.76
6.0 5.8 2.03 7.93 2.56 8.46 :1.53 7.43 1.91 7.B12.77 8.67
5.8 5.6 2.17 7.87 2,67 6.37 :i.68 7.38 1.99 7.69 2.88 B.58
5.6 5.4 2.32 7.82 2.77 8.27 1.83 7.33 2.07 7.57 2.99 8.49
5.4 5.2 2.46 7.76 2.SB B.18 1.98 7.28 2.15 7.45 3.11 8.41
5.2 5.0 2.59 7.69 2,98 8.08 2.14 7.24 2.23 7.33 3.22 B.32
5.0 4.8 2.72 7.62 3.08 7.98 2.29 7.19 2.30 7.20 3.33 B.23
4.8 4.6 2.84 7.54 3.19 7.89 2.44 7.14 2.39 7.09 3.44 8.14
4.6 4.4 2.99 7.49 3.29 7.79 2.59 7.09 2.47 6.973.56 8.06
4.4 4.2 3.12 7.42 3.40 7.70 2.75 7.05 2.09 6.39 2.54 6.84 3.69 7.99
4.2 4.0 3.24 7.34 3.50 7.60 2.90 7.00 2.10 6.28 2.62 6.72 3.80 7.90
4.0 3.8 3.36 7.26 3.61 7.51 3.05 6.95 2.26 6.16 2.70 6.60 3.91 7.81
3.8 3.6 3.47 7.17 3.71 7.41 3.20 6.90 2.34 6.04 2.21 5.91 2.78 6.48 4.03 7.73
3.6 3.4 3.5B 7.08 3.82 7.32 3.36 6.86 2.43 5.93 2.37 5.87 2.87 6.374.14 7.64
3.4 3.2 3.69 6.99 J.92 7.22 3.51 6.81 2.51 5.81 2.53 5.83 2.96 6.264.26 7.56
3.2 3.0 3.80 6.90 4.03 7.13 3.66 6.76 2.59 5.69 2.69 5.79 3.06 6,16 4.37 7.47
3.0 2.8 3.91 6.61 4.14 7.04 3.81 6.71 2.67 5.57 2.85 5.75 3.18 6.08 4.49 7.39
2.8 2.6 4.02 6.72 4.24 3.97 6.67 2.76 5.46 3.01 5.71 3.30 6.00 4.61 7.31
4.13 6.63 «.35
2.6 2.4
2.4 2.2 4.24 6.V4 4.46 l:lf 4.12 6.62 2.89 5.39 3.17 5.67
4.27 6.57 3.12 5.42 3.33 5.63
3.44 5.94
3.58 5.86 fd 7.23
7.16
2.2 2.0 4.35 i.45 4.56 6.76
6.66 4.41 6.51 3.37 5.47 3.49 5.59 3.73 5.834.98 7.08
2.0 1.8 4.46 6.36 4.67 6.57 4.55 6.45 3.62 5.52 3.65 5.55 3.89 5.79 5.11 7.01
1.8 1.6 4.58 6.28 4.77 6.47 4.68 6.38 3.90 5.60 3.81 5.51 4.05 5.75 5.23 6.93
1.6 1.4 4.69 6.19 4.88 6.38 4.80 6.30 4.19 5.69 3.97 5.47 4.21 5.71 5.36 6.86
1.4 1.2 4.80 6.10 4.98 6.28 3.72 5.02 4.91 6.21 4.49 5.79 4.13 5.43 4.37 5.67 5.50 6.80
1.2 1.0 4.92 6.02 5.08 6.18 3.94 5.04 5.00 6.10 4.79 5.89 4.30 5.40 4.53 5.635.63 6.73
1.0 0.8 5.03 5.93 5.24 6.14 4.15 5.05 5.07 5.97 5.08 5.98 4.46 5.36 4.67 5.575.78 6.68
0.8 0.6 5.14 5.84 5.49 6.19 4.36 5.06 5.09 5.79 5.35 6.05 4.62 5.32 4.B1 5.515.97 6.67
0.6 0.4 5.26 5.76 5.78 6.28 4.57 5.07 5.21 5.71 5.59 6.09 4.78 5.28 4.97 5.47 6.18 6.68
0.4 0.2 5.37 5.67 6.09 6.39 4.78 5.OB 5.40 5.70 5.80 6.10 4.94 5.24 5.14 5.44 6.42 6.72
0.2 0.0 5.49 5.59 6.45 6.55 4.99 5.09 5.60 5.70 6.01 6.11 5.10 5.20 5.31 5.416.70 6.80
0.0 -0.2 5.60 5.50 6.87 6.77 5.20 5.10 5.79 5.69 6.19 6.09 5.26 5.16 5.50 5.40 7.03 6.93
-0.2 -0.4 5.72 5.42 7.32 7.02 5.41 5.11 5.99 5.69 6.35 6.05 5.42 5.12 5.69 5.39 7.41 7.11
-0.4 -0.6 5.84 5.34 7.74 7.24 5.62 5.12 6.19 5.69 6.01 5.62 5.12 5.89 5,39 7.79 7.29
-0.6 -0.8 5.55 5.25 7.86 7.16 5.83 5.13 6.38 5.68 I'.&l 5.97 5.82 5.12 6.09 5.39 7.92 7.22
-0.S -1.0 6.06 5.16 7.88 6. 98 6.04 5.14 6.57 5.67 6.82 5.92 6.02 5.12 6.29 5.39 7.96 7.06
-1.0 -1.2 6.15 5.05 7.87 6.77 6.24 5.14 6.77 5.67 6.98 5.88 6.22 5.12 6.49 5.39 7.99 6.69
-1.2 -1.4 6.17 4.87 7.83 6.53 6.45 5.15 6.98 5.68 7.13 5.83 6.41 5.11 6.69 5.39 8.01 6.71
-1.4 -1.6 6.14 4.64 7.79 6.29 6.64 5.14 7.19 5.69 7.27 5.77 fi.61 5.11 6.89 5.39 8.05 6.55
-1.6 -1.8 6.20 4.50 7.80 6.10 6.76 5.06 7.41 5.71 7.40 5.70 6.80 5.10 7.09 5.39 8.15 6.45
-1.8 -2.0 6.29 4.39 7.83 5.93 6.85 4.95 7.65 5.75 7.50 5.60 7.00 5.10 7.29 5.39 8.26 6.36
-2.0 -2.2 6.37 4.27 7.89 6.93 4.83 7.93 5.83 7.58 5.48 7.19 5.09 7.48 5.38 8.41 6.31
-2.2
-2.4
-2.4
-2.6
6.45 4.15 7.95 1:11 7.02 4.72 8.19 5.89 7.66 5.36 7.38 5.08
6.53 4.03 8.01 5.51 7.10 4.60 8.44 5.94 7.75 5.25 7.58 5.08
7.53 5.238.56
7.50 5.00 8.72
6.26
6.22
-2.6 -2.8 6.60 3.90 6.07 5.37 7.18 4.48 8.64 5.94 7.84 5.14 7.77 5.07 7.48 4.78 6.86 6.16
-2.8 -3.0 6.68 3.78 8.14 5.24 7.27 4.37 8.61 5.71 7.92 5.02 7.96 5.06 7.45 4.55 8.89 5.99
-3.0 -3.2 6.75 3.65 8.20 5.10 7.36 4.26 e.47 5.37 8.01 4.91 6.15 5.05 7.42 4.32 8.88 5.78
-3.2 -3.4 8.26 4.96 7.45 4.15 8.33 5.03 8.10 4.80 8.34 5.04 7.40 4,10 8.90 5.60
-3.4 -3.6 8.32 4.88 7.55 4.05 8.18 4.68 8.18 4,68 8.53 5.03 7.38 3.88 8.96 5.46
-3.6 -3.8 8.38 4.68 7.66 3.96 8.03 4.33 8.25 4.55 8.72 5.02 7.35 3.65 9.05 5,35
-3.8 -4.0 8.44 4.54 7.76 3.86 7.95 4.05 8.31 4.41 8.91 5.01 9.16 5,26
-4.0 -4.2 8.50 4.40 7.86 3.76 7.91 3.8i: 8.37 4.27 9.09 4.99 9.29 5.19
-4.2 -4.4 8.56 4.26 7.96 3.66 7.68 3.58: 8.43 4.13 9.27 4.97 9.43 5.13
-4.4 -4.6 8.62 4.12 8.06 3.56 7.88 3.38: 8.48 3.98 9.45 4.95 9.57 5.07

215
 ON THE INTERACTION METEOR COMPLEX

3. Rajchl
•Astronomical Institute, Czechoslovak Academy of Sciences, 251 65 Dndfejov
Czechoslovakia

An approach to the problem of a meteoric complex called the Interaction Meteor

Complex (IMC) is applied and discussed, where author's former idea of the interacti-
on layer (Rajchl 1969) is generalized. The role of an extended interaction of meteo-
roids is ephasized, both with planet surfaces and/or their satellites and with pla-
net atmospheres, elastic or inelastic in form. The dissipation and related formative
aspect are joined in one complex and compared with a topological compact. Examples
of all the above mentioned types of interaction are presented. In more detail the in-
elastic interaction with the Earth atmosphere of whole "spectrum from faint meteors
detected by TV technique to Fireball Network bolides, is considered. First results
in the form of a y structure and cross-complementarity are reported. The possibility
of the existence of another "enlarged" ^ structure is anticipated from topological
aspects and suppor- 3d for the outer planets of the Solar Planetary System by results
of Levin and Siroonenko (1982).

Introduction superrotation of upper atmosphere (i.e. fas-

ter rotation of the Earth atmosphere higher
As it is well known, the topological or geo- than 150km) by global deposition of meteo-
metrical approach, as compared with that re- roids (Mitra 1974), "cosmogonical" influence
presented by dynamical equations is conside- of meteoroids on the planetary bodies rota-
red as a more efficient one in the investi- tion (Kiladze 1986), noctilucent clouds
gation of complex systems. On the other hand, and enhanced airglow (Rajchl 198'2i» planeta-
it is the unalogy which is the other method ry rings and meteoritical craters'VThe remar-
that shows very useful in this case. Finally, ked examples are meant as possible illustra-
the relation between the dynamical and topo- tions only and we concentrate in the present
logical, ar dissipative and formative aspects paper mainly on the case of the inelastic
especially realized by the process of inte- soft interaction. As has been shown (Rajchl
raction may be of main interest. Such three 1987) some type of connection between meteo-
axioms are used in our present approach to roids as sources and noctilucent clouds
investigation of a meteor complex behaviour. and enhanced airglow as responses might exist
Especially, the extension and generalization in the form called by present author the
of author's previous idea (Rajchl 1969) on an cross-complementarity. Let us now search
interaction layer ahead of a meteor body, whether similar or analogical connections
mainly with accent on the interaction, is may be real also for individual groups cf
exploited. However, instead of atmospheric IMC members.
particles as projectiles and meteor bodies Formerly, the present author (Rajchl 1959a,
as targets, we consider the last ones as pro- b) obtained - using the relation between
jectiles and planets with their environment heights and magnitudes in the meteor bright-
in the form of their atmospheres or satel- ness maxima - that the dissipation intensi-
lites, as targets. To decide whether the mo- ty characterized by a factor 8 for both the
del used, together with achieved results are sporadic and shower meteors 1) is higher for
only superficial, or of some signification, low together with high geocentrical velocity
we compared both the results and consequences meteors (i.e. v<35km/s and v>55km/s) than
with those of the mathematical topology it- for those with velocity v = 35-55km/s. 2)
self. The different behaviour of meteors mentioned
subl) and expressed in terms of the normal
Realization (o) and abnormal (+) mean maximum brightness
M shows an opposite or inverse nature for
At first, to distinguish the widely used "Me- faint SSmeteors (i.e. photographed by Super-
teoric Complex" let us introduce the "Inte- Schmidt cameras) relatively to the bright
raction Meteor Complex" (IMC). Compared with ones (NK/SC/- photographed by normal or small
the former, IMC means rather its subset whe- cameras). Therefore, by faint meteors the
re the interaction of different meteor bo- low and high velocity ones are - in average-
dies with planets environment will be empha- normal (Bar -4 for fragmentation index
sized. The interaction may be of elastic and X = 0) and the middle velocity meteors are
inelastic nature, and may be realized either more fragmenting.
with planetary atmosphere (soft) or with To confirm these results, we enlarge the
planetary body or its satellites (hard), optically detected observational material
in full analogy with, the meteor interaction, used, on the whole, now attainable "spect-
where atmospheric projectiles interact either rum" of meteors, i.e. from TV faint ones
with meteoroid surface, or with its gaseous (Hawkes et al 1984) to very bright meteors,
or dusty coma, respectively. Therefore, we
can distinguish four fundamental types o f ubviously, the main, widely known result of
interaction: elastic soft, elastic hard, in- the soft interaction are the meteors alo-
elastic soft and inelastic hard with possible ne /elastic and inelastic in real interac-
consequences, examples of which follow: tion is present simultaneously, but one of
them is considered as prevalent/.

217
 f i r e b a l l s F N ( M c C r u o k y et a l . 1 9 7 7 ) . R e s u l t s this inversion point. For example, the unu-
are c o n t a i n e d in F i g . 1 , a n d T a b . 1. sual spectrum of a motsor 0 mg, with begin-
ning heiqht 137km (Cook et al 197}) may be
the possible candidate.
Let us call the results sub 1) shortly the
y normal 0 ^p structure (nr more precisely */* and /h or
-1 •O-for mutually inverse behaviour as sub2))
^abnormal * and the inverse connection between faint and
bright meteors, caused by the interaction
with the Earth atmosphere, the cross-comple-
mentarity. Of some importance i s , that these
results are valid also by showers: e.g. for
Taurids, Geminids and Perseids, if we select
-6 those representing the three velocity groups
(Rajchl 1959r) as for sporadics; faint Tau-
rids and Perseids show the same behaviour as
bright Geminids and vice versa. Furthermore,
the bifurcation of Geminids (Ceplecha 1957)
/, / is especially emphasized, coinciding roughly
with the double crossing pnint in Fig. 1. If
f-domain of the we wish to explain the difference between
0 normal and fragmenting groups as a result Df
•r-Geminid bifurcation their various perihelion distances,we must
/ equally accept inversion for processes lea-
ding to such difference by faint and bright
meteors (Rajchl 1974).
7
Comparison with topology
•6 T

A question may arise whether such, at the

first sight strange, results can be accepted
-1 0 1 2 3 4 as typical or even fundamental for a complex
and thus for IMC. To substanciate our results
TV ss KK/SC/ FN we direct our attention to tno topology it-
Fig.l. selft. Let us summarize these results in the
following IMC hypothesis: the interaction of
a flow (either in the form ~,i meteor showers
or in the more diffuse or "stochastic" form
Tab.l. of sporadic meteors, or of some intermediate
type) with a planetary environment leads to
an interaction structure which is of the ty
METEORS (Si ) type. Connection between various groups
of meteors (TV-FN) characterized by this in-
FN NK/SG/ SS TV
teraction structure is of a type of the
n M n H cross-complementarity. Both structures alto-
gether arr f tiridamental s of a IMC.
I 250 -l.ri 33 - 3 ' 0 .155 »*1 33 3*9 Now let us compare this hypothesis with topo-
logy: as it is well known, there exist a
whole called the topological compact (or bi-
II 50 -10*5 17 -2°1 51 1*6 16 3*2 compact) (Alexandrov 1977) and a structure
analogical to our ^ type-the so called Can-
III 18 -13*8 20 -3*7 51 1°7 28 3*3 tor discotinuum (CD) or Cantor triad (a who-
le transforms into combination
I5v<35km/sIl5v-35-55km/s III* T > 5 5 W S
(ABA)-*f\BA 1 BABlABA)-* . . .
n-number of meteors
etc. of elements A,B). Following Alexandrov
H^-mean maximum b r i g h t n e s s we can roughly say that: if an infinite se-
quence of points of a topological space con-
tains a subsequence convergent to some point
of this space, or according to Peixoto(1962),
if a motion of points is directed towards the
Instead of the factor B and the fragmentati-
so called un-wandered points, then a compact
on index X we used the mean maximum bright-
is here. This compact contains as a subset
ness M m ?•-. a common characteristics of a
the CD and vice versa, the compact is a con-
rate of n • ••.;; ipa tion for each meteor group. tinuous picture of this CD. Therefore, if we
Individual neteor groups (TV, SS ...) are now identify the sequence of moving points
characterized by log m - the mean photo- with our flow of meteoroids and the point of
metrically determined M a s s e s . The values convergence with a planet (with its environ-
(points) for SS and NK/SC/groups are ac- ment) we obtain that as a result of the flow-
cepted as starting and then optimalized in planet interaction snnnething very analogical
combination with TV and FN values to define to the compact with its CD as subset, the
together the crossing lines. The TV data show IMC can arise. We may adopt the V structure
the largest deviation. From Fig. 1 we can see as a special type of structure isomorphic
the above mentioned results as confirmed for with the CD. Furthermore, using the ideas of
the whole complex of meteor brightness used. Smale (1;67), we can obtain a more general
Among all the groups the SS meteors show to analog of our cross-complementarity in his
be the nearest to the crossing point. It may hyperbolical sets. This is a fundamental ty-
be interesting to look for such "singular" pe af connection with a very important pro-
meteors from the immediate neighbourhood of perty, well known also by CD: the crossing

218
or the so called star-shape, directly as the vidual quasishowers of all the four outer
analog of our ^ type property, are reprodu- planets (see Tab. 2) together may lead to
cing at different scale levels! Therefore, similar structure at still larger scale
we may conclude that our above mentioned re- level. Thus, the vy structure is also apparent
sults are not even in contradiction with the for a quasi-showT interaction, but for the
topological ones,but that further confronta- outer planets as a whole only.
tion m'jy be very'fruitful. However, many questions are still open here,
e.g. detailed connection between quasi-sho-
Generalization wers and planetary rings compared to the
main influence of dust particles on the pla-
Till now we presented more detailed results netary rotation in the past only for outer
of the interaction of meteoroids with the planets (Kiladze 1986).At first sight it is
Earth atmosphere only. Now, we look for how obvious that the characteristic feature of
it is by other planets of our Solar System the rings (just as that of meteor craters)
from the point of view of all the above men- is analogous to that of the CD-type. But, it
tioned results. From the topological stand- seems that on the contrary to the velocity
point, for IMC ab a compact the other structures by the Earth, such ring structu-
planets can be also convergent points for me- res - similarly as e.g. the band structures
teor flows. As shown by e.g. Levin and Simo- by nortilucent clouds or enhanced airglow
nenko (1982) there exists a substantial dif- in the Earth atmosphere - are not results of
ference between inner and outer planets in the meteor interaction alone.
the planetocentric velocity range. From
Tab. 2 Conclusion
Summarizing, we may say that the main results
Tab . 2 . in the form nf the cross-complementarity and
the \p structure, after a comparison with to-
palogical compact, show to be not only real,
Planets Entry velocity of meteors into but of a fundamental importance. They consti-
& tute together with the main axiom of interac-
Showers the atmosphere/froB-to.in k«/s / tion the supporting blocks of the IMC. On the
other hand, it is shown how can be expressed
Venus 10- the relation and connection between dissipa-
Earth 11-- F L 0 W tive and formative parts, or between dynamics
and topology in meteor problematics.The inte-
Mars raction layer regime (i.e. this one between
free-molecule and shock waves flows) seems
Jupiter 61-68 to be very intimately connected with the
Q U A S 1 crossing point region (and/or with the cros-
Saturn 37—41 sing itself ). Furthermore, several perspec-
Uran 22—28 S H O W E R S tive extrapolations can be offered:
Neptun 26-29 1) for meteor trains e.g. it follows that ac-
cording to their low brightness (smaller than
0 m g ) , their velocity structure could be of
Per s H0 M the same type as for faint meteors (i.e. of
Gem 5il the -rt- type);
Tau J30-33I W E R S 2) according to the fundamental complementa-
rity between faint and bright meteors and
thus, according to some type of connectivity
between them, the physical theory of both the
categories of meteors should obey also some
it is evident that whilst all the inner pla- type of complementarity;
nets (without Mercury) have the entry velo- 3) if the "reproduction" of the ^r and cross-
cities in the interval roughly ll-60km/s, complementarity structures toward both the
thus a very wide fluw is in action, for larger and smaller scale levels is true,
outer planets it i:- not true. Here the flow then it may be a useful tool also in the mo-
of meteoroids is somewhat between the wide re general cosmogonical considerations. In
velocity range flow of inner planets and this respect connections to general solutions
monovelocity meteor showers, i.e. something, of the cubic equation (in velocities) related
what may be called trie quasishowers. In to the two basic factors A and B, and to the
other words, the sporadic or stochastic Clifford algebra may be interesting.
component is here larger than for showers,
but smaller than by flows interacting with References
inner planets. Whilst, e.g. for a wide ran-
ge velocity sporadic flow is the V structu- Alexandrov P.S.; 1977, Vvedenije v teoriyu
re present and even if the condition mnozhestv i obshchuyu topologiyu, NauKa.
Ceplecha Z.; 1957, Bull. Astron. Czechosl.
A = vx v v =0 18,51.
+ n + n i
Cook A.F; Hemenway C.L.; Millman P.M.; Swi-
is valid (where V j , VJJ and VJJJ are the der A.; 1973; in: Evolutionary and Physi-
mean velocities of the corresponding veloci- cal Properties of Meteoroids NASA SP-319,
p. 153.
ty groups from Tab. 1 ) , the three-phase Hawkes R.L.; Jones J.; Ceplecha I.; 1984,
structures as special case of the T structu- Bull. Astron. Inst. Czechosl. 35, 46.
re may exist; by outer planets with quasi- Kiladze R.I; 1986, Sovremennoe vrashchenie
showers it is not valid. But, similarly as planet kak rezultat razvitiya okolopla-
individual showers in summation can lead to netnykh roev, Tbilisi.
something analogical to the known V struc- Levin B.J; Simonenko A.N.; 1982, in: Meteor-
ture "in large", here the summation of indi- noe veshchestvo v mezhplanetnom prostran-
stve, Moskva, p. 257.

219
McCrosky R.E.; Shao C.Y.; Posen A.^ 1977,
Center for Astraphys. Preprint ser. No.
721.
Mitra V.; 1974, Planet. Space Sci 22, 559.
Peixoto M.; 1962, Topology 1, 101.
Rajchl 3.; 1959a, Bull. Astron. Inst. Cze-
chosl. 10, 47.
; 19590, Bull. Astron. Inst. Czechosl. 10,
177.
; 1969, Bull. Astron. Inst. Czechosl. 20,
363.
; 1974, Bull. Astron. Inst. Czechosl. 25,
34.
; 1987, Astron. Inst. Czechosl. Acad. Sci.
Preprint No. 47.
Smale S.; 1967, Bull. Amer. Math. Soc. 73,
747.

220
 SEPARATION OP THE PARTICLES DUHING METEOR FLARES
V.S.Getmati
Institute of Astrophysics, Dushanbe, 734670, USSR.

The method of the estimate of the numbers of fragments^ to which meteor bodies
are fragmentating during the terminal flares, is offered.

The meteor flares is a rather well-known Then

phenomenon. Their appearance is usually co-
nnected with the process of the dividing of (9) n=
the body or a part of it into a large num - Or for the terminal flare
bers of small fragments. Prom one to seve - (10) n = (I<,/i^33(6/_ } 9-f)
ral flares with the duration O.02-O.06 sec
can have different meteors. where index " f means the moment of the
In this work only terminal flares,which flare. Since during the flare the body is
lead to complete distruction of the meteor fragmentating and evaporating eimultaneo -
bodies,have been inveetigated.which ia co - usly,thevalues Q f can be near to 9 f , A f
nfirmed by the fact of sharp falling of the
brightness right after the flare. And it is can be near to A ~. Then in the first app-
evident,that meteor bodies fragmentate into roximation we can put down
very email fragments otherwise,the presence (11) n = (I f /i f ) 3
of big particles would have prolonged the
visible trajectories of meteors. This fact Using the formula (11) we can estimate "n"
makes easy the estimation of the number of with the help of the light curves of the
fragments,making it possible to consider meteors. The values I~ are taken directly
them to be equal. This gives us the opportu> in the points of maximum of the luminesce-
nity of using the simple physicaly clear mo- nce of the flare. The values i f (the inten-
del of fragnentation,offered by Levin(1956). sity which a meteor would have without fra-
let the mass body "H" fragmentate in "n" gmentation) can be calculated by the meth-
equal fragments. Their sunmary section %S0 od as follows.
is more than the cross-section of the body In works by Babadzhanov and Getman(1974,
S, i.e. £ S O > S , while l l , < I. It is 1975) was picked out the class of non-fra-
known,that S and II are connected as follows gmentating meteors of the Taurid stream ,
which were loosing their mass by intensi-
CD a s = A(M<TV 3 , ve evaporation of atoms and moleculas from
3
where A=S/V' is form factor (V is the volu- the surface of the body. Thia was proved
me of the body), & is the density of the by the absence of wake and terminal blen -
meteor body. ding in the ordinary photographs and by
Then M o = Wn, the point structure of the images, obtai -
ned by the method of instantaneous eacposu-
(2) So ) re. It's well known,that during the evapo-
ration of large meteor bodies the evapora-
(3) Sn / 3 , ting moleculas and atoms are screening the
(4) n => (IS 0 /S) 3 surface of the body,giving strong influence
at heat transfer to the body,which leads to
The luminous intensity is I ' ^ S 1 C/'ia the change of the coefficient A .
atmospheric density, S' is evaporating sur- According to works by Babadzhanov and
face), that is why Getman (1974,1975),and by Bronshten(1983)
(5) n ~ (I/i) 3 , .A depends oa the product R/>v3/,( R is
where I and i is accordingly the luminous radius of the body). Since R ^ M ,we can
intensity of meteor with fragmentation and make the substitutions R 0 v for
without it. That means that "n" can be es- 1/3 3 '
timated by the ratio cf this values. wJJ> -r , In work by Babadzhanov and Getman
let's consider this case more detailed. (1975) (look also work by Bronshten (1983)
Let's put down the equation of luminescen- was obtained the empiric dependenc-3
ce for the cases of non fragmentated body (12) A/q. = C(M1/3p V 3 ) " *
(6) i => (T A s 3 For the part of trajectories from the
and of fragmentated body for "n" particles height of the meteor appearance H. till
the height of maximum light H_ wire obtai-
(7) I = (T Aspv 3 n V 3 )/(4<J) ned the constants
Here T = T O V is coefficient of luminescen- lg C = - 5.75 , <* = 0.5.
ce, A and A are accordingly coefficients of Let's put down the differential equation
heat transfer by evaporating and fragmenta- of the mass loss of the evaporated meteor
ting, a, and Q are accordingly the specific body considering (12)
energy of evaporation and fragmentation, v (13) dM A C T 3
) ! ^
is velocity of meteor.
Let's divide (7) for (6)
(8) I / i = n1/3A<2./GA Kgglacting the deceleration (v » v«, ) and

221
consiering p ft,exp(H/H
considering =ft,exp(-H/H ) ( (H is atmos-
mos The values ro , obtained in this paper,
pheric
h i scale
l heif^it),
h i ^ i t ) ddt
t = - dH/v
dH/ cosZZ (Z iis coincide with the datas of Simonenko(1967),
aenith angle of the meteor radiant),d. => 0.5, who was inclined to conclude^that particles
let's integrate (13) of a sxfce of the order of 10 cm appear to
• V2 be structural elements (or grains) of me-
ACH rjt i/2 teor bodies.
(14) 4/3
2§ cosZ
where p, is atmospheric deneity of the me-
teor appearance Hfe,index «*> refers to the in-
itial values velocity and mass of the meteor
body. Putting (12) considering <* = 0.5 into -7
the luminous equation
-2
2 dt H km
and considering (14) we'll get
(16) -2
+2
where B -5
Using the formula (I6),we can define the -1
value "i" in any point of the part of the
trajectory from H^ to H f . If necessary we
can turn to the magnitudes m. and a f , ac- -8
cording to m = - 2.5 lgi.
Four meteors with the terminal flares,
which have been photographed from two sta -
tions in Dushanbe (Babadzhanov and others -1
1966,1968) have been investigated. With the 92 84 H km
formulas (16) and (11) were found the values
"i f " and "n". The following values of the
constants have bean used: lg to • - 19.0 ,
Fig. light curves of meteors accordingly:
o - 0.3 g/cm , A = 1*21, H*= 6.5 km. The observed (solid lines) and calculated by
values of the p are taken from CIRA 1972. formula (16) (broken lines). Meteor's num-
The results of the calculation and some beres from the above: 632725,621234,
other datas are given in the following table 641701b,641623.
The editional symbols: I. is the observed
luminous intensity at the height of the me- The problem of flares is waiting for its
teor appearance, r0 is radius of fragment. decision. Its new aspect opens in connec -
Table. tion with Levin and Bronsten's (1986) sup-
position about the analogy between the
Tunguska body explosion and terminal fla -
Ho. 621234 632725 641623 641701b res and fireballs. To the auther's mind
these phenomenons are of the same nature,
v(kn/s) 19.0 64.5 24.6 24.0 but different scale.
If 6.9 398.0 1.7-1O3 75.8 REFERENCES
6.3
hi °'<
f0.66 27.0
6.9
8.1
1.9
1.4
Babadzhanov,P.B.;Getman,V.S.:1974, Dokl.
Akad.Nauk Tajic SSR,Dushanbe,17,No.9,18.
Babadzhanov,P.B.;Ge^man,V.S.:1975,Vzaimod.
n 10 3
3-1O3 9-106 1.6-1O5 meteorn.veshestva s Zemloi i otsenka
pritoka meteorn.vesheetva as Zemlu i Lu-
Kls) IO~3 3-1O"4 1.3-1O"5 1.7-1O"5 nu,Demish,Dushanbe,3.
Babadzhanov,P.B.;Getman,T.I.;Zausaev,A.P.;
re(cm)4 10 2 3-1O-2 10-2 10-2 Karaselnikova.S.A. :BJjull.Inst.Astrof iz.,
Dushanbe,49,3.
Babadzhanov,P.B.;Suelova,W.N.;Karaselniko-
From the results come out two important va,S.A.:1966,Bjull.Inst.Astrofiz.,Du -
consequences: shanbe,41-42,3.
a) For three meteors out of four 621234, Bronshten.V.A.:1983,Physics of Meteoric
641623 and 641701b the values i f can be co- Phenomena.D.Reidel Publ.Comp..Dordrecht-
mpared with the values I h , that is Holland, 38.
for the estimation of "n" can be used the CIRA 1972-Berlin:1972,Akademie-7erlag.
following: n - (Ij/I^) 3 ; levin,B.Yu.:1956,The physical theory of me-
teors and meteoric matter in the solar
b) In case of evaporation of meteor bodi- system.Moscow:Akad.Nauk SSSR,104.
es,the light curve goes up slowly (Figure) Levin.B.Yu.;BronBhten,V.A.:1986,Meteoritics
|dm/dH| 21,Ho.2,199.
Simonenko,A.N.:1967,Komety i Meteory,15,34.
i.e. during the process of evaporation M i" Simonenko,A.N.:1973,Meteoritika,No.32,50.
changes not much. Let's retained that the
classic light curve (not coneidereng the
effect of block up, -* = const) is
Idm/dHJ = 1/6

222
 PHOTOGRAPHIC DATA OF EXTREME PRECISION EVALUATED BY EXACT
SINGLE-BODY SOLUTION OF METEOR PHYSICS
P.B. Babadzhanov and Z. Ceplecha 2)

1) Institute of Astrophysics, Dushanbe, 734870, USSR

2) Astronomical Institute of the CSAV, 251 65 Ondfejov
Observatory, CSSR
The exact solution of the single-body motion and ablation of a meteoroid in the
atmosphere is applied to one of the most precise double-station records of a fire-
ball photogrrphed from Dushanbe Oct 30, 1962. The entire trajectory of 5.2 seconds
duration from 77 km to 36 km of height with 2-58 time marks corresponds to a single
value of the ablation coefficient.

1 . Observational material (3)

= C h
One of the most precise set of geome- " obs/coszR
trical data on meteor atmospheric trajecto-
ry was derived for a double-station photo-
graph of a fireball at Dushanbe, USSR, Dct <O Z-U C Q m - l obs ) = minimum ,
30, 1962, 17 n 2 8 m 19 s UT (Babadzhanov, Get-
man, 1980). The entire photographed trajec-
tory of this fireball contains 258 measura-
ble time-marks spaced by 0.D202 seconds each where c is the same constant as in equation
and covering the height interval from 77.43 (1). The parameters of the problem are: t ,
to 36.24 km. The maximum absolute brightness which defines the zero point of the relative
reached -7.3 magnitudes at 49.6 km. At each time counting; 1 the distance along the
time-mark the observations yielded the rela- trajectory at time t ; v the velocity at
tive time, t, the relative distance along the time t • v«, the initial velocity (t-*-°-);
trajectory, 1 . and the height, h . . & the ablation coefficient
The standard deviation of one measured 1 .
is - 1 meter, which is much better than
the precision induced to observations by the
(5) A
theoretical model based on "flat Earth sur- 2jr
face" (assumption of constant inclination of where A is the heat-transfer coefficient,
the trajectory to the surface: standard de- P the drag coefficient and C the energy
viation - 19 meters). The 25B measurable necessary for ablation of trie unit mass of
time-marks occupy a time interval of 5.1914 a meteoroid.
seconds . The solution of equations (1) and (2).
with c and cos z R derived from ( h) and (4)
can be performed by method of gradients of
2. Theoretical model the four unknown parameters 1 , w»- , v
i O U
The exact solution of the differential *• The velocity v at any arbitrary point
equations of the single-body theory was re- is defined by the same parameters from the
cently found by Pecina and Ceplecha (1983, velocity integral of the Gingle-body equa-
1984) in the form tions :

(1) (6)

)--
2 K e xp
Jr i dh
(c-i)cosz R
J 9
cl)c where K is the shape-densi ly coefficient
(c-lo)coszR
(7)
where Ei(x)= f u -1'exp(u) du is the exponen-
K --Pfi (f-/n
tial integral and

(2)
-1 dl C. the bulk density if the mi; tenroiri, A the
t — t. snape factor
(8)
where t is the time (independent variable), A =
1 the distance along the trajectory, v the
velocity, h the height,^ the air density,
all of them at any given arbitrary point. The m the meteoroid mass at an arbitrary point,
constant Zp is the zenith distance of the mo. the initial meteoroid mass ( t — » - — » )
radiant resulting from a linear least-squares and S the head cross-section of the mete-
correlation of 1 . and h ^ oroid .

223
 The numerical procedure compares 1 com- h) The value of Km ^ r e s u l t e d as 0.079 cin2/g.
puted from (]) and (2) with l Q b s and finds With O. = 3.7 g/cm , K =,0.5 and the
initial "dynamic" mass m^,= 250 g, which
linear gradients of the four unknown para- leads to the terminal mass nv - 31 g.
meters 1 , v w , v Q , <J so as to approach (CIRA 72 November atmosphere! .
condition (4). Thus starting with a first
suitable approximation of these four values,
each step in the direction of the gradient
of these values goes toward the final solu- REFERENCES
tion, where the linear gradient of the four
parameters is equal zero. At this point the
condition (4) is also fulfilled and the Babadzhanov, P.B., Getman, T.I.: 1980,
least-squares fit of (1) and (2) to 1 . is Meteoritika (Russ.) 39.
found. The partial derivatives necessary for Pecina, P., Ceplecha, Z.: 1983, Bull.
solution of the gradient of the parameters Astron. Inst. Czechosl. 34, 102.
are rather complicated expressions, but they Pecina, P., Ceplecha, Z. : 1984, Bull.
can be straightforwards numerically computed. Astron. Inst. Czechosl. 35, 120

3. Results
We applied the theoretical model of
chapter 2 to t'he observational material des-
cribed in chapter 1. We used CIRA 72 October
and November atmosphere for the Dushanbe la-
titude as the air density model. The results
follow:
a) The entire trajectory of the fireball can
be expressed by one single constant value
of ablation coefficient:

d= 0.0300 - 0.0003 s 2 /km 2 for CIRA 72 Oc-

tober atmosphere
'<= 0.0275 - 0.0003 sZ/km2for CIRA 72 No-
vember atmosphere

b) There are only 4 points amongst 258, which

deviate in 1 slightly more than 3 standard
deviations from 1 , . (About 1 such value
is expected under the normal distribu-
tion).

c) The two successive values of 1 deviating

by more than 3 standard deviations at
t = 4.33 seconds indicate some breakage
of the meteor body.

d) The resulting standard deviation for one

observed 1 from (1) and (2) resulted as
- 15 meters, slightly less than - 19 me-
ters, which had been computed on assump-
tion of constancy of Zn (flat Earth's
surface) from equation (4).

e)The initial velocity resulted with preci-

sion better tfian - 1 m/s:

v., = 13.6303 - 0.0009 km/s for CIRA 72 Oc-

tober atmosphere
v w = 13.6340 - 0.0009 km/s for CIRA 72 No-
vember atmosphere
f) The velocity changed during the entire
trajectory from 13.61 to 5.85 km/s. The
only method known to handle such a velo-
city change with not loosing more than
90% of -the accuracy inhibited in the ob-
servations, is the method of Pecina and
Ceplecha (1983, 1984) briefly described
in chapter 2.
2
g) The deceleration changes from -0.0352km/s
at the beginning point to -4.08 km/s at
the maximum-deceleration point (t = 4.73 s
at a height of 38.4 km) and back again to
-3.65 km/s at the terminal point. (CIRA
72 November atmosphere).

224
 SOME NEW ASPECTS IN THE POSITIONAL REDUCTION OF
THE PHOTOGRAPHS TAKEN BY FISH-EYE OBJECTIVES

P. Spurny
'Astronomical Institute of the Czechoslovak Academy of Sciences,
251 65 Ondfejov, CSSR

In this work the method used up to now for a positional reductions of the photo-
graphs is compared with other reductional formulas. It was found that the reduction
formula presently used for determination of the zenith distance is suitable, howe-
ver the formula for determination of the azimuth can be replaced by a new expression,
which essentially improves the total positional reduction.

The cameras with Fish-eye objectives (Op- The interpolation formulas (1) and (2)
ton - Distagon, f = 30 mm, a field of view were compared, along with some other inter-
of 180 , focal ratio 1/3,5) are used in the polation formulas, and the results are pre-
Czech part of the European Network for fire- sented in Table 1 and 2. This comparison was
balls already more than ten years with a performed for one specially chosen case (as
great success. large as possible range of zenith distances
Reduction of the photographs taken by ca- and azimuths of measured stars).
meras with Fish-eye objectives consists in We can see from Table 1 that the last
the finding of the most suitable unknown three interpolation formulas give better re-
parameters of the interpolation formulas sults (represented by the standard deviation
describing the dependence of the azimuth and S* ) than all the rest tested formulas, but
the zenith distance on the measured rectangu- in the interpolation formula (2) we must
lar coordinates. determine lesser number of unknown parame-
For this purpose a certain number of sui- ters. Therefore the interpolation formula (Z)
table stars (usually about 15) is chosen on is most suitable for use. The formula (1)
the photographic plate as far as possible in was used for determination of the unknown
a near environment of a meteor. The equato- parameters x Q and y (the relation (3)),
rial coordinates of stars are known from a which are necessary for interpolations for-
catalogue. We have to transform these coordi- mulas in Table 1.
nates to the horizontal coordinates - the
azimuth and the zenith distance. ThiSiWay It is evident from Table 2 that the rela-
tion
we obtain thPoi'tical coordinates a. and
z . From c measuring instrument we received
rectangular coordinates x. and y,. arctg / A
Now we need to find the most suitable in-
terpolation formulas between measured rec-
tangular coordinates x., y. and a horizontal
coordinate system a. and z. . Coordina- gives essentially better results than the
tes a c o m and z sre computed values from hitherto used formula (A, B, a , x , y
interpolation formulas. A solution of these are unknown parameters). The following for-
formulae; must fulfil the requirement that the mula from Table 2 gives rather better results,
sum of squared differences, (a, - a ) but at the cost of the determination of more
mid (i^ - zC° ) , is minimum for al^stars unknown parameters.
used. In the end the best formulas (2) and (4)
Interpolation formula hitherto used for were tested together for ten casually chosen
tir-? iprni nation of the azimuth is examples. From Table 3 it is evident that
in all cases we achieved the improvement of
com the total reduction (represented by the
arctg (1) standard deviation U ) and this improvement
makes about '5% on the average.

where n . , x , y are s m a l l unknown parameters,

f'oj dc•fceVmiRa t. i on o f the z e n i t h distance
Conclusion
l'orinu i.a
For next reductions of photographs taken
S tr-:p (I) (2) by Fish-eye objectives it will be suitable
to replace the hitherto used interpolation
formula for determination of the azimuth (1)
i.".,i;il, vilir.it-r: U , V , S , 0 a i d u n k n o w n finrame-
by the new formula (4) and to keep the inter-
P o -i;i f ! i'V i • w e h a v e
polation formula (2).

REFERENCES

We must (li;: t" i lii J ne seven unknown p a r a m e t e r s in Ceplecha, Z.: 1987, Bull. Astron. Inst. Czech.
the cornnori :".: Itrt i on . The whole meihod of solu- Vol. 38, No 4 (in print) .
tion c.f. t h i .• I::!'VK men liuned i n t e r p o l a t i o n
f o r m u l a s \.. .:i";i:ri bed in detail in C e p l e c h a
( 1 9 8 7 ).

225
 List of used symbols
n -k
cat
theoretical value of azimuth
ziat theoretical value of zenith distance
g com
computed value of azimuth tot
com
computed value of zenith distance
measured rectangular coordinates n number of stars
,y ,A,D,C unknown parameters in inter- kg number of unknown parameters in inter-
polation formulas for determination of polation formulas for determination
the azimuth of the azimuth
U,V,S,0,T unknown parameters in interpolation
k number of unknown parameters in inter-
formulas for determination of the ze- polation formulas for determination
nith distance of the zenith distance
com ,
Aa i = ( a • " - a, ;
com , all values of standard deviations are in de-
cat grees
i

x
i
yi " 1

_i/£(*3i)
V n- k

T A B L E 1

Reduction formula

sin(z,/2)= U Vr, 1.62766 0.3410

sin(z,/2)= U h Vr
i
+ Sr^ + Dr? 0.01496 0.0353
sin(z,/2)^ 2
y V r , + Sr. 3 4
U • + Dr. + Tr. 0.00869 0.0281
sin(z,/2)= U H Vr, + Sexp(Dr,) 0.00859 0.0268
z, = U + V Sr r 0.01605 0.0366
i i
z, = U + V Sr
i + Dr^ + Tr^ 0.00427 0.0197
z, = U + V SexpCDr,) 0.00418 0.0186
z, = U + Vr, , Tr
i + Sexp(Dr,) 0.00318 0.0170

226
 T A B L E 2

Reduction formula

a
i
= a
o + arctg(u) 0.00B89 0.0262

-a * arctg(Av H 2 3^
a
i 0.00296 0.015.7
0 Bv + Cv )
a
i a r c t g ( A u ^ Bu 2 ) 0.00147 0.0116

2
a
i a r c t g ( A u •> Bu + Cu 3 ) 0.00126 0.0112

T A B L E 3

. old . new old • new improvement

9 6a Z 0z ^tot <5\ot in Vtot in %

0.0302 0.0223 0.0186 0.0195 0.0253 0.0209 17.4

0.0276 0.0263 0.0118 0.0121 0.0216 0.0201 7.0
0.0381 0.0325 0.0352 0.0342 0.0368 0.0334 9.2
D.0638 D.0412 0.0307 0.0310 0.0508 0.0362 28.7
0.0333 0.0262 0.0228 0.0136 0.0288 0.0206 28.5
0.0560 0.0501 0.0227 0.0254 0.0447 0.0392 12.3
0.0586 0.0505 0.0385 0.0402 0.0500 0.0454 9.2
0.0337 0.0292 0.0313 0.0294 0.0326 0.0293 10.1
0.0310 0.0264 0.0135 0.0166 0.0249 0.021B 12.4
0.0212 0.0168 0.0132 0.0116 0.0179 0.0143 20.1

227/

/a
INTERPLANETARY DUST
 DISTRIBUTION OF INTERPLANETARY DUST
R.K. Giese and B. KneifJel

Ruhr-Universitat Bochum, Bereich Extraterrestrische Physik

4630 Bochum, F.R.G.

Simple 3D distributions of the interplanetary dust cloud derived from observations

in the visible and distributions suggested by IR investigators are compared.
Predictions of visual brightness based on 1R models are fairly compatible with
observations for large (c<70°) elongations but not close to the Sun. Some reasons
for this behaviour and first steps towards more realistic models are discussed.

1. Introduction From admittedly very preliminary statements

of infrared investigators one can get the
Attempts to derive the three-dimensional impression that the IR results are generally
(3D) Distribution of the zodiacal dust cloud consistent with previously determined
from optical observations have been made interplanetary dust distributions (Hauser et
since many years starting with models al. 1984) and that the out-of-plane
involving some scale height above the measurements are well matched with a dust
ecliptic plane or density distributions like density distribution {Murdock and Price,
the so called "Fan-models" (Divari, 1967). 1985) which is very similar to the Fan-model
The problem of all these efforts was the type of distributions as favoured e.g. by
fact, that the observed intensity at the Leinert et al., 1981. On the other hand
position of an observer is not exclusively there is agreement, that such models are
related to the number density n of dust only representing the crude overall shape of
particles along the line of sight but also the cloud and that any details need more
to the angular dependence of the scattering thorough and complicated modelling. A first
function (differential scattering cross step into details has been performed from
section) of the dust particles. Therefore it the infrared groups by deriving the plane of
was expected that infrared observations symmetry of the zodiacal cl-oud from annual
relating on the isotropic thermal emission variation of the zodiacal infrared emission
of the dust particles would avoid these (Hauser and Houck, 1986; Good et al, 1986;
difficulties and lead more easily to Deul and Holstencroft, 1987) and to compare
realistic modelling of the 3D distribution it with the results of observations in the
of interplanetary dust. Unfortunately, optical range. This led to some agreement
however, the wavelength dependent index of and also corroborated the findings of
refraction and also the size enters the optical analysis (Misconi, 1980; Schuerman,
calculations of thermal balance and 1980) that the "plane" of symmetry is
temperature. This can lead to considerable eventually warped. Another problem area,
deviations from the temperature predicted where infrared results seem to strenghten
for a black body. Therefore, either extended previous suspicions is the inhomogeneous
calculations using Mie-theory (spherical composition of the interplanetary dust
particles!) have been performed taking into cloud. Simple optical models have been
account the wavelength dependence of usually based on the assumptions that the
available indices of refraction (e.g. Lamy, physical properties of the dust particles
1974; Mukai and Mukai, 1973; Roser and are independent of location and that the
Staude, 1978; Schwehm and Rohde, 1977) or number density decreases with solar distance
reasonable assumptions were adopted about according to a power law. These assumptions
average efficiencies of absorption in the are made in order to manage the problem, to
visible or in the infrared , respectively, derive dust densities or to "invert the
as pioneered for example by Kaiser 1970. brightness integral" (Dumont 1973; Lamy and
From this it becomes evident that also Perrin 1986) in nontrivial cases.
infrared data are not a king's way to obtain Nevertheless all investigators, including
easily the distribution of dust in the solar the authors of this paper, are aware, that
system. Nevertheless, recent results such assumptions are suspect from physical
obtained by rocket experiments (ZIP: reasons since there are processes
Zodiacal Infrared Project, Murdock and (radiation, sputtering, packing effects)
Price, 1985) and by the IRAS satellite changing the dust particles while they are
(Hauser et al, 1984) are a source of spiraling into the inner parts of the solar
information which is extremely important, system due to the Poynting-Robertson-effect
since it relies on a different physical (cf. Fechtig 1984; Mukai und Fechtig, 1983).
process. Another completely different There has been also evidence from analysis
physical aspect which also helps to solve of optical (Schuerman, 1980) and infrared
the problem is a thorough analysis of the observations that particle properties (e.g.
dynamics of meteoroids and especially Albedo, Dumont and Levasseur-Regourd, 1986)
micrometeoroids using data obtained from are changing and that the number density
earthbased and space measurements. While does not follow a simple power law (Hong,
these will be treated by other papers in 1987). On the other hand Leinert et al 1981
this volume, the present review is have shown, that with the exception of
restricted to the optical ad infrared point polarization the results of HELIOS 1 and 2
of view. are surprisingly consistent with what would
be expected from the two assumptions

231
 mentioned above. Therefore such simplified adopted, a system of polar coordinates with
models are still justified as an initial the heliocentric distance r and the
step of approach, especially in the regions heliocentric latitude a will a preferable
inside 1AU. alternative.
In the following sections we shall first Unfortunately these definitions are not
present the geometric definitions and draw unambigously used in the recent literature.
attention to some bew:'dering differences of While e.g. Frazier, 1977; Giese et al. 1985;
terminology in the recent IR-1iterature. Leinert, 1975, and Weinberg and Sparrow,
Then we adopt the most simple model approach 1978 follow the definitions referred in
referred to above and compare models Fig.1, the IR papers Murdock and Price, 1985
suggested by optical observations of the or Good et al, 1986 prefer cylindrical
zodiacal light with those proposed by coordinates, i.e z and obviously the
infrared investigators. Finally some projection r • cos(liQ) of r on the symmetry
comments are presented towards the current plane. This undisputed free choice of the
and future discussion about more realistic authors turns out to become misleading if
models involving spatial changes of the dust followed by statements such as "this
properties. functional form is a generalization of that
used by Frazier" (Good et al, 1986) or by an
inconsistent set of formulae after referring
2. Basic Geometry to Leinert, 1975 (Murdock and Price, 1985.
Equ.(9) through (13)). A confusion of the
As mentioned above, the symmetry plane of definition of r has only small influence on
the zodiacal cloud and the ecliptic plane the results obtained from IRAS and the
are not identical. However, for the rocket project ZIP which both are performed
following discussion the inclination between at R=1AU and at large (> 30°) elongations.
these planes (< 3°) is neglible although it The ambiguity of definitions can however
plays an important role under other aspects become fatal as soon as investigations are
(e.g. dynamics). He shall therefore make no extended towards the regions near the Sun
distinction between the ecliptic, the (cos(B ) « 1 ) . Another source of possible
invariable and the symmetry plane unless it confusion is the difference in the
is explicitely mentioned. Under this definition of elongation as used in this
precaution Fig.1 illustrates the problem and paper and other zodiacal light work and the
defines the geometric relations referred to "elongation" measured in the symmetry plane
in the text. An observer located at 0 at (i.e. X-A Q ) referred to in the papers of the
solar distance R in the symmetry plane looks IRAS ana of the ZIP teams. Therefore care
in the direction of his line of sight LOS is necessary in comparing results and
and receives radiation scattered or emitted interpretations.
at an angle 0 within his viewing cone (solid
angle (in). The particles of volume element
dV at P are illuminated by the Sun S, where 3. Siaple 3D-Hodels
r is the distance of P from the Sun. The
direction of the LOS is defined by its Host simple models of the 3D distribution of
longitude with respect to the sun (^-*o) and interplanetary particle number density nfi-)
by its latitude ft with respect to the are based on the assumption of separability
symmetry plane, which may be approximated n into one factor depending on r only and
within our assumptions by the ecliptic another factor depending on 6 . Furthermore
plane. The angle between the observers a power law is adopted for the dependence on
viewing direction LOS and the direction OS r. This leads to n(r,IJ )=n {r/AU)"vf(8.)
towards the sun is the elongation e where n is the particle number density at
(cf. Hopkins, 1980 or Leinert, 1975). For the earth orbit (1AU) while r and B are
further discussion we define a cartesian defined in Fig.1. Examples of such models
coordinate system x.y.z centered at the Sun and their optical behaviour have been
S with z perpendicular (north) with respect revieved and extensively discussed elsewhere
to the symmetry plane. Since for all models (Giese and Kinateder, 1986; Giese et a ] ,
rotational symmetry with respect to z is 1986). Within the scope of the present paper
it is sufficient to restrict the models
HELIOECLIPTIC MERIDIAN PLANE derived from optical observations to some
markedly different examples and to compare
them with models derived from IRAS or ZIP
data by the infrared investigators. Fig.2
presents in the upper portion of each case
the isodensity lines for n=2n , m , 0.5n ,
and 0.25n , respecticely, as drafln in the
xz-plane (nelioecliptic meridian). It should
be kept im mind, that these isodensity lines
are representing isodensity surfaces due to
rotational symmetry about z in the 30 case.
The lower portion of each example presents
the deviation (in %) of the zodiacal light
as predicted by the model from the
observational tables of Levasseur-Regourd
and Dumont, 1980. Positive values indicate
that the values predicted by the model are
too bright and vice versa. The model
SYMMETRY PLANE = ECLIPTIC PLANE
calculations were performed using Leinerts
scattering function (Leinert at al, 1976 and
Fig. 1: Basic Geometry Leinert 1978) except in the case of Fig.2c
where the corresponding scattering function

232
 4 180°
a-.<fi 30* 60* POLE
HEIIOECIIPTIC MERIDIAN

Fig. 2: Isodensity lines and deviation from optical observations for 30 distributions.
Explanation see text.
 as derived by the authors (Lsmy and Perrin, (typical -25%) in the helioeclitic meridian
1986) was adopted. Fig.3 shows the towards the Sun at medium latitudes ft. From
scattering functions normalized to o=90° for reasons discussed in detail in the mentioned
comparison. The value of n was adjusted in paper a much better overall fit of the
our calculations to obtain agreement with brightness in the optical range can be
the observational tables at 90° of achieved by models, having some bulge above
elongation in the symmetry plane. The the Sun as suggested orally by Dumont at the
circles in Fig.2 present circles of the same IAU Assembly at Grenoble 1976
latitude (1 above the symmetry plane as seen ("Sombrero-Model") or by a paper of Lumme
from the observer, e.g. the outer circle and Bowell, 1985. Fig.2b shows a version of
represents the symmetry plane (eciiptic a Sombrero-type model proposed by Rittich
plane, B=Q), the center of the circles the 1986, based on the expression
(ecliptic) pole. The radial lines are the -1.3 (0.2 + 0.8 cos 44
projections of meridians at different (2) n=n Q (r/AU) <B 0 ))
longitudes ^-*0 with respect to the Sun
(left corner: solar direction). hereafter called "Cosine-Model". As can be
seen this model approximates the
observations in all directions shown in the
lower part of Fig.2b within about 10%.
Therefore this quality of approximation is
achievable with simple models which means,
that models producing deviations of the
order of, say 25%, have definitely to be
rejected as unacceptable even within the
rather modest scope of this section.

Recently Laay and Perrin (1986) derived an

unified functional approach to brightness
and polarization data from the literature
and obtained from this a 3D distribution of
interplanetary dust and a corresponding
scattering function by inversion of the
brightness integral using the methods of
Leinert et al (1976) and Dumont (1973). They
conclude that in the case of a power law
values as v =1,3 are incompatible with the
observational data and propose a density
distribution

(3) n = n 0 (r/AU)' 1 •

• ex P (-3.5|sinB o |°- 7 7 5 + 0 - 6 2 4 sin6

o)
which is shown in Fig. 2c. The corresponding
scattering function derived by the authors
from observations at 1AU is presented in
Fig. 3 for comparison. Using this scattering
function and Equ.(3) we computed the
brightness distribution predicted by the
model to compare the result with the
observational data (Fig.2c). As can be seen,
90° 180° the brightness values fit in the symmetry
plane very well but deviate at ecliptic
latitudes B > 30° markedly (about -15 to
Fig. 3: Scattering Functions o(o): -30%) from the Tables of Levasseur-Regourd
LN Leinert 1978; yo Hong 1985; and Dumont, 1980.
LP Lamy and Perrin 1986; MP Murdock
and Price 1985. 3D distribution derived from IR measurements
are shown in Fig. 2d through Fig. 2f. Most
The Fan-Model investigators arrive close to an 1/r
dependence of n in the symmetry plane while
(1) (r/AU)"vexp(-Y]sinll0|) the IR balloon measurements of Salama et al
(1987) seems to be compatible with a
with v = 1.3 and Y = 2.1 presents the Fan-model classical Fan-model ( \> = 1.3 and y> 2.1 i.e.
as adopted by Leinert et al, 1981 and Leinert's model). A Fan-aodel with =1.1 and
referred to by many investigators (Fig.2a). r=2.7 is shown in Fig. 2d. Using Leinerfs
It achieves an excellent fit (mostly better scattering function this model provides in
than 10%) in the regions towards the Sun but the visual range an excellent (3%) fit at
is very poor in reproducing the brightness the pole and an acceptable (better than
at high latitudes (0 > 60°) and at the pole about 15%) approximation of optical data all
(deviation > 3051). A much better fit at the over the sky except in the region towards
pole and in the circle A-A o =90 the Sun (x-\ < 30", a < 60°), where the
perpendicular to the helioecliptic meridian deviations become unacceptable ( -25%). This
can be achieved by an "Ellipsoid-Model" as is not surprising since this model
shown by Dumont 1976 and Kinateder 1984 or corresponds closely to a "Flattened
in an equivalent way by a "Flattened Fan-model" as shown by Giese et al, 1986
Fan-Model" with ) =2.9 as shown by Fig.2 and which shares this disadvantages with the
Table I of Giese et al, 1986. In both cases, Ellipsoid-model of Dumont, 1976. It is,
however, this has to be paid by a poor fit however, at least encouraging that this type

234
 MP
n = 0.5 n LN
Rl
LP
FF
GD

120(

1.5

Fig. 4: I s o d e n s i t y l i n e s n = 0 . 5 r\j p e r p e n d i c u l a r t o t h e s y m m e t r y p l a n e f o r
LN F a n - m o d e l : v = 1 . 3 , Y = 2 . 1 Leinert et a l . 1981; RI C o s i n e - m o d e l
Rittich 1986; LP Lamy and P e r r i n 1 9 8 6 ; DG Good e t a l . 1 9 8 6 ; MP M u r d o c k
a n d P r i c e 1 9 8 5 ; FF F a n - m o d e l : v = 1 . 1 , y= 2.7.
 of Fan-models, which is proposed in a 4. Discussion
modification also on the basis of IRAS data
(Oeul and Wolstencroft, 1987) does not lead In Fig. 4 the isodensity lines n = 0,5n. are
to unacceptable differences with respect to compared for the models referred to acove.
optical brightness at larger ( e > 70°) It is interesting to note that for viewing
elongations. directions corresponding approximately to
the scanning cones of IRAS (60°< E < 120°)
From the papers of the IRAS team it is not the isodensity lines of the best optical
clear if their "r" is the heliocentric model (RI, Cosine-model of Rittich, 1986),
distance (e.g. Hauser, 1974} or its of the ellipsoid model (not shown here), and
projection on the symmetry plane. In the of the models suggested by IR investigations
latter case the expressions "r" and "z/r" in (FF Flattened Fan-model, GD Good et al,
the paper of Good et al., 1986 ("cylindrical 1986, HP Murdock and Price, 1985) are close
coordinates") would correspond in our together. This explaines the passable
terminology to r • cosQ and tanB n , compatibility of the models derived from IR
respectively. If we adopt tnat in the model measurements with the visual data (Dumont
of Good et al, 1986 and Levasseur-Regourd, 1980) in this region
of the sky. On the other hand it is
(4) n = n 0 (r/AU)" 1 ' 1 exp(-4.2(z/r) u2 ) understandable from their low or steep
decrease of n with [ z | that Leinert's
r has the same meaning as in this paper and Fan-model (LN) or the model of Lamy and
in most zodiacal light papers we recognize, Perrin (IP) produce too high or too low
that (4) represents a modified Fan^model of brightness at large ecliptic latitudes,
the type n * r~ ' exp(-4.2 sin 8 ) . The respectively.
isodensity lines of this model are presented
in Fig. 2e and the deviations of the For further discussion it is necessary to
zodiacal brightness predicted by the model estimate how the relative contributions of
using Leinert's scattering functions are the volume elements at different locations
shown in the lower portion at the figure. (P) along the LOS depend on the relevant
The compatibility with the visual wavelength. To simplify the problem we shall
observation is moderate but acceptable restrict ourselfs to grey bodies and to
(typical better than 20%) for elongations particles which are large or at least not
E>70° i.e. in the regions where the IRAS small compared to the wavelength. This is
data come from. The model would however Justified as a first step, since the
completely fail to present the solar particles mainly contributing to the
hemisphere (£<50°) reaching deviations up zodiacal light are in the size range of
to -55X at 8=30° in the tielioecl iptic radii between 10 and 100 urn <(Giese and Griin
meridian. This would even become worse if 1976; RBser and Staude 1978). Furthermore
Good et al, 1986 used the projection for r, admitting grey and not just black bodies
since in this case the density would become allows to take into account spatial
lower close to the Sun. On the other hand at variations of physical particle properties
large elongations (IRAS) the isodensity at least in terms of an albedo depending
lines crossed by the LOS are practically the on location.
same for both cases (r or r* cosB,
respectively) yielding the same quality of As has been shown by many authors (cf.
approximation of the visual brightness as in Leinert 1975) the observable spectral
Fig. 2e. surface brightness2at.1AU I ( A - A O , B . ) of the
zodiacal light (Win m sr) can be found by
Finally we compare the model of Murdoch and integration along the LOS in the visible
Price (1985) with visual data. Since due to region as
several misprints the formulae in the
original paper are confusing we asked the /•a(Q) n(r]
authors who kindly provided us with the (6) i = F.
correct formula (Price, 1986). It is in the J (r/AU)*
terminology of this paper
Here F is the solar flux (W/m J ) at 1 All, n
(5) n = n Q (r/AU)''l-cosRo exp(-2.6-| sinaj) the numBer density of dust particles (1/m ) ,
o the differential scattering cross section
The corresponding isodensity lines are shown (m /ster) per particle, and d s. a line
in Fig. 2f. Using the Legendre-Polynomial element along the LOS. In order to keep the
approximation of the scattering function problem as simple as possible and only to
(Fig.3) published by the authors we arrive demonstrate the physical principles we will
at unacceptable deviations in nearly all handle it as if there would be just one
parts of the sky reaching even 133X at 8=30° particle size. If discussion has to be
in the helioecliptic meridian. This is due extended to the real case of a size
to the unusually strong increase of the distribution, o can be understood as the
adopted scattering function. Therefore we average scattering cross section of one
did the same calculation using the more particle of the mixture (c.f. Leinert
conservative scattering function of Leinert. 1975).
In this case an acceptable agreement with
optical observations can be achieved, except In a similar way the spectral surface
in the region of X-X <50° and especially brightness due to thermal emission of the
close to the Sun (-50S). grains in the IR region may be found (cf.
Peterson, 1963) as

(7)

236
 Here C h is the cross section for The strongest contributions per unit length
absorption at the wavelength considered, of the LOS to the observed spectral
which also can be substituted by an average brightness I stem from the inner regions of
cross section per particle for mixtures. the solar system and the contributions
BxB(A.T) is the Planck function (Wirf'sr"1). decrease systematically with increasing r.
This is true for both, the visual region
From this it is evident. that the (A=0.5ym). where practically all brightness
contribution to I of a volume element at the is due to scattered light (VES) and for the
position P(r) per unit length along the LOS IR domaine (x^Sum) where the thermal
is governed by emission (VET) is dominating. However, in
the short wave range of the IR ( =5ym) the
contributions of the hot dust inside 0.5 Alt
(8) VES are extremely preferred, while at larger
wavelengths (x>20|im) the contributions of
the inner and outer regions are not as
which will be called hereafter (cf. Dumont drastically different. Although VES (here
and Levaseur-Regourd 1986) the volume ^ r ) is due to a quite different process
elemental scattered intensity (VES). In the the contributions of dust to the integral
thermal region we use a corresponding along the LOS are biased in the visible
expression light in a similar way as in the infrared
domaine between 10 to 25 um. Roughly spoken:
The observer sees, within the limits of our
(9) VET = n C abs B{A, T) model, the same dust. Also from this point
of view the relative compatibility of the
published density distributions is
which we call the volume elemental thermal understandable.
emission (VET).
Up to now we did not take into account any
During the following discussion we adopt spatial change of the particle albedo (Lumrae
further simplifications. For particles large and Bowel 1. 1985; Fechtig, 1984). As has
compared to the wavelength having the been shown by Giese and Kinateder 1986 a
geometric cross section G and an Albedo A we change of A according to a power law A =
assume for the differential scattering cross A.(r/AU) 2 leads from a volume scattering
section a = A G / 4ir (isotropic scattering) fanction (na) ^ r" 1 to a density
and for the cross section of absorption distribution n •*• r withv = v.-v? and to
C. hc = v (1-A) G. Further we adopt flatter looking 3D distributions (see their
nifi*{r/AU)" f(6 ) as in the previous Fig.5), A decrease of Albedo A or increase
section. Then we obtain cf absorptivity {1-A) with increasing r has
been found from IR data by Dumont and
Levasseur-Regourd 1986. They arrive at a
(10) VES •A (r/AU)- ( v + 2 ) density decrease close t o n ^ 1/r or v * 1.
4TI With the HELIOS result v, * 5.3 we obtain3
correspondingly v-=0.3 0/intTA = A.(r/AU)""
and or (1-A) = (1-A ( f / A u T - 3 ) . ThiS would not
too drastically modify the values of Table
I. For example we obtain with
(11) VET (1-A)(r/AU) B(X,T) A = 0.1(r/AU)"u'° and X=0.5p at r=0.5AU or
2.5AU VES . values of 9.8 or 0.09,
respectively. For A=20ym the relative
It should be kept in mind that B(A,T) is a thermal contributions VET , are at r=0.5AU
function of solar distance r. For a black or or 2.5AU about 4.1 or 0.09, respectively.
grey body thermal balance yields
T = 2 8 0 K T ' ° ' S (e.g. Leinert, 1975).
S. Conclusions
Now we can compare VES or VET at a solar
distance r with the contributions (VES). and The 30 distributions of dust particle
(VET) at r»1AU. In the symmetry plane densities obtained from IRAS and ZIP data
(f(a_7=1) we obtain as an example with v = i are in acceptable but not in good agreement
(n^17r) and an albedo A=0.1 the relative with distributions derived from the zodiacal
values
VET
VES_ Bl = VES/(VES)n and light. This is also true for the relative
rei = VET/tVETVo as shown f8r different intensity distribution of zodiacal light as
wavelength regions in Table I. predicted from the IR models in viewing
directions at larger (e > 70°) elongations.
At low elongations (e < 40°) the density
Table I distributions proposed from IR
Relative contributions ;.er unit length of investigations are incompatible with the
the LOS in the symmetry plane for different visual data, while Sombrero type models are
solar distances r and wavelength regions X. in satisfying agreement with visual
Albedo A = 0.1, Density law n -v 1/r observations. More thorough investigations
are necessary including the regions close tc
r/AU the Sun and the near IR. These efforts have
0.5 1.0 1.5 2.0 2.5 also to take into account with increasing
complexity non grey bodies and spatial
0.5 8.0 1.0 0.30 0.13 0.06 changes of the physical properties of
5.0 40.6 1.0 0.07 0.007 0.001 interplanetary dust.
10.0 9.0 1.0 0.21 0.06 0.02
20.0 4.2 1.0 0.37 0.17 0.09

237
 F.P. Israel (ed.) Light on Dark Matter,
39-44.
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Physical Model for Thermal Emission from the function for zodiacal dust. Astron.
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Astroph.)
Hong, S.S. and Urn, I.K., 1987: Inversion of
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Hopkins, J., 1980: Glossary of Astronomy and
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238
 Murdock, T.L. and S.D. Price, 1985: Infrared Babadzhanov: What do you think about sources
measurements of the zodiacal light. The of interplanetary dust? Does the distribu-
Astronom. J. 90, 375-386. tion ot/%at dust correspond to the distri-
bution of orbital inclinations of comets
Price, S.O., 1986: private communication. or asteroids?
Giese: The most probable inclinations infer-
Rittich, U., 1986: Die raumliche Verteilung red by Hang's integral from f(/3 e ) are of
des interplanetaren Staubes: Modellrechnung- the order of i = 10 to 15 depending on the
en zur Interpretation von Zodiakallicht- model. We are, however, hesitating at the
messungen. Oiplomarbeit, Ruhr-Universitat present state to relate our results directly
Bochum. to the inclination distributions of asteroids
or comets. The following paper by B. Kneissel
Roser. S. and Staude, H.J.. 1978: The Will explain this in more details.
Zodiacal Light from 1500 A to 60 Micron, blsson-Steel:Isn't the problem of inverting
Astron. Astrophys., 67, 381-394. Ithe scattered-light data basically the same
as the computer-applied tomography? Has
Salama, A., Andreani, P., Dall'Oglio, 6., De anyone tried applying the C.A.T. algorithms
Bernardis, P., Masi, S., Melchiorri, B., to this problem?
Melchiorri, F., Moreno, G., Nisini, B. and Giese: This is a very interesting problem we
Shiranandan, K., 1986: Measurements of Near also started to think about. In computer
and Far Infrared Zodiacal Dust Emission. tomography there is the X-ray source and op-
(Submitted to The Astronom.J.) posite to it a series of sensors each mea-
suring the integral of absorption of all
Schuerman, D.W., 1980: Evidence that the volume elements (voxels) along the ray from
properties of interplanetary dust beyond source to sensor. This whole system can be
1 All are not homogeneous. In Solid Particles turned around the patient to obtain many
in the Solar System (I. Halliday and B. crossing lines of sight and a system of
Mclntosh, Eds.), 71-74, Reidel, Dordrecht. equations to solve for the density of each
voxel. In application to our problem there
Schwehm, G., and Rohde, M., 1977: Dynamical are two differences. We are not observing
Effects on Circumsolar Dust Grains J. in forward scattering (extinction) and we
Geophys., 42, 727-735. have not the choice of an optimum geometry
for the location of the sensors, especially
Weinberg, J.L. and Sparrow, J.G., 1978: without an Out-of-ecliptic spacecraft pho-
Zodiacal Light as an Indicator of tometer. However, it would be interesting to
Interplanetary Dust in: Cosmic Dust (ed. modify the method. A first step towards this
J.A.M. McDonneli), 75-122. was done by one short paper of a Spanish
group and by the thorough application of
their method of nodes of lesser uncertainty
by Dumont and tevasseur-Regourd.
D I S C U S S I O N

Ibadov.- It was very interesting. What is the

minimal heliocentric distance up to which
the power law for the number density of inter-
planetary dust holds.
Giese: The approximation by a power law seems
to be valid even surprisingly close to the
Sun. Helios penetrating to 0.3 AU and cros-
sing with its line of sight regions close
to Q.I AU did not show evidence of a dust
free zone. On the other hand, the raise of
density cannot go on in the same way inside
10 to 3 solar radii. There is evidence for
evaporation processes in these regions from 1R
measurements and theoretical calculations.
In addition we found that the polarization of
the F-corona would be much higher than the
observed inside 10 solar radii, if the power
law could be extrapolated into this region.
Grdn: The radial dependence of the spatial
density has to be stronger than n<vl/r - which
would require no source of zodiacal particles
at and inside 1 AU. As I have shown in my
paper at this meeting (TS-2) collision provide
the major source to zodiacal particles at
1 AU. Therefore a dependence n*s?T'vi\tYp} 1
is required.
Giese: The isodensity lines for^*= 0.8 shown
in one slide were an exaggerated example, how
n would change in the case of a hypothetical
albedo variatjon*r" ' . Personally, I comple-
tely agree with you expecting an albedo ef-
fect.f which might bring down JTrom 1.3 closer
to one, but still with <y> 1.
 THE DYNAMICS OF THE ZODIACAL DUST CLOUD ON ACCOUNT OF
OPTICAL AND INFRARED OBSERVATIONS

B. KneiBel and R.H. Giese

Ruhr-Universitat Bochum, Bereich Extraterrestrische Physik
4630 Bochum, F.R.G.

The method to determine the inclination distribution of zodiacal particle orbits

according to 3D- density models of zodiacal dust presented by Giese and KneiRel
(1987, this volume) is briefly discussed. The results show that models with
additional bulges at the solar poles bear an isotropic component of the inclination
distribution amounting up to 20% of all orbits, whereas infrared models show almost
no isotropic component. The existence of an isotropic component for zodiacal dust
orbits is questioned by comparison with the orbital elements of meteoroidal
particles which serve as a source for the zodiacal dusf by mutual collisions.

0. Introduction and thus the density function f(S ) should

be smooth, which is true in almost all
It was shown (Giese and Kneifiel, 1987) that cases. Furthermore, the functions f(!5Q) are
the three-dimensional distribution of dust monotonous falling ones in nearly all cases.
may be represented by a lot of different Then the solution of N(i) consists of a sum
latitude dependent density functions f(6 Q )- in which one term is N sini and the other
Recently dynamical analysis has revealed one is zero at the edges of the interval and
that models like the multilobe-model gains a maximum inside (cf. Sneddon, 1966).
(Buitrago et al., 1983) demand for an
unreasonable distribution of the As the first term is known Ln orbital
inclinations (KneiGel and Giese, 1986). Now statistics (Bandermann, 1968) as an iso-
again dynamical analysis of the 3D-density tropic distribution it might be treated as a
distribution has been involved. superposition of an isotropic part and, as
we will soon see, a part whose most probable
inclination is close to the ecliptica.1 plane
1. Method and General Result
On account of the global rotational symmetry If this interpretation is true, then the
of the zodiacal dust cloud the arguments of isotropic part should be extended to
perihelion and of the nodes of the zodiacal retrograde orbits. Thus from conservation of
dust orbits are distributed randomly. the numbers of orbits we have:
According to Opik (Opik, 1951) this should
be due to secular changes in the orbital N Q /2 s ini, 0° s i < 180°
elements from planetary perturbations. Not
only lately this has been questioned for the
small scale structures of the zodiacal dust 2. Distributions of Inclinations in Detail
cloud (cf. Gustafson, 1985).
Classical models (Ellipsoid-model: Dumont,
Assuming further that the distribution of 1976; Giese and von Dziembowski, 1969;
the semimajor axis and eccentricity may be Fan-model: Leinert et al., 1981)
separated from that for the inclinations According to the flatness of the isodensity
(cf. Bandermann, 1968; Kessler, 1981) the lines the ellipsoid-model possesses a most
relationship between the latitudinal probable inclination imax'o 10°, whereas the
dependent part of the density -f(fi ) and the fan-model has one of ^15°. Both models show
distribution of inclinations N(i) is given an isotropic component being a little less
by Haug (Haug, 1958) or more than 10% of the whole number of
orbits, demanding then for 5% of the orbits
it/2 in retrograde direction.

f(B 0 ) di Sombrero-model (Rittich, 1986, original

concept by Dumont, 1976 at the XV] IAU
B General Assembly (Grenoble))
In this case the most probable inclination
Thus the distribution of inclinations N(i) 'may * s 1 U ° - B u t > a s o n e would, expect from
is to be determined as a solution from a the bulge, -\. 20% of the orbits should be
Volterra integral equation of the first spent in the isotropic component (That
kind. As the density is the same for means, a fraction of 10% of the orbits is
prograde and retrograde orbits of the same retrograde.).
inclination the method is not capable in
discriminating both types of orbits from one Flattened fan-model (Deul and Hoistencroft,
another (N(i) e{0,ir/2)). 1987)
In comparison to a classical fan-model i
According to Dumont and Levasseur-Regourd is < 15° and the isotropic component
(Dumont and Levasseur-Regourd, 1985) the amounts < 8%.
scattering cross-section of the unit-volume

241
 Pole whole models (models by lamy and collisions should taka place in the
Perrin, 1986; Good et al., 1986; Murdock and perihelion of the particles (Dohnanyi,
Price, 1985) 1978). In the perihelion the condition for
Pole wholes models again have a most an elliptic or bound orbit is immediately
probable inclination of ^ 1 0 ° , but there is dependent on the eccentricity of the
only a negligible or no isotropic component particles (Harwit, 1963). But the particles
( < 3%). with e ^ 0 . 9 9 in the zodiacal size spectrum
(10 um - 100 urn) and Qpp/p = 1 cannot stay in
Retrograde orbits amongst zodiacal dust the solar system 1 § P R = 1 for black
particles particles, p < 1 g/cm ). This result seems
If w e d o n o t w a n t to stay with a sharp to favour pole-whole models with almost no
u n r e a s o n a b l e drop-off o f t h einclinations at isotropic component. But we have to be
90° w e h a v e t o Lake r e t r o g r a d e o r b i t s into careful, because there is a certain number
accoun.t. of meteor streams with high inclination but
Neither micro-raeteoroid impact experiments an eccentricity e < 0.99. (The famous
(Grun et a l . , 1980; Griin and Zook, 1980; Orionids (e = 0.962, i = 163,9° (Cook, 1973)
McDonnell, 1978) nor detection of the and the n -Aquarids (e = 0.958, i = 163,5°
Doppler Shifts in Fraunhofer Lines (East and
(Cook, 1973) associated with Comet P/Halley
(Kresak, 1980).) Of course Somberero-models
Reay, 1984; Fried, 1977; Hicks et a l . , and less the fan- or the ellipsoid-model
1974; James and Smeethe, 1970; Reay and have become questionable but the facts
Ring, 1968) report about retrograde orbits quoted are by far not sufficient to exclude
among the zodiacal dust cloud. these models.
There is one indication for an isotropic
distribution of dust particles in the outer
solar system (beyond Earth's orbit) by the
PIONEER 10 and 11 experiments (Humes, 1980). References
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Griin, E., Zook, H.A., Fechtig, H., and Acad., 54, 165-199.
Giese, R.H., 1985: Collisional Balance of
the Meteoritic Complex, Icarus, 62, Reay, N.K. and Ring, J., 1968: Radial
244-272. Velocity Measurments on the Zodiacal Light
Spectrum, Nature, 219, 710.
Gustafson, B.A.S., 1985: Planetary
Perturbations: Effects on the Shape of a Rittich, U., 1986: Die raumliche Verteilung
Cloud of Dust in Circular Heliocentric des interplanetaren Staubes: Modellrechnung-
Orbits, in: Properties and Interactions of en zur Interpretation von Zodiakal licht-
Interplanetary Dust (R.H. Giese and P. Lamy, messungen. Diplomarbeit, Ruhr-Universitat
Eds.), 385-388, Reidel Dordrecht. Bochum.
Haug, U., 1958: iiber die Haufigkeitsver- Schuerman, D.W., Weinberg, J.L., and Beeson,
teilung der Bahnelelmente bei. den D.E., 1977: The decrease in zodiacal light
interplanetaren Staubteilchen , Zeitschr. f. with heliocentric distance during the
Astroph., 44, 71. passage of Pioneer 10 through the asteroid
belt. Bull. Amer. Astron. S o c , 9, 313.
Harwit, M., 1963: Origins of the zodiacal
dust cloud, J. Geophys. Res., 68, Sneddon, I.N., 1966: Mixed Boundary Value
2171-2180. Problems in Potential Theory. Amsterdam New
York.
Hicks, T.R., May, B.H. and Feay, N.K., 1974:
An investigation of the motion of zodiacal
dust particles. Radial velocity measurements
on Fraunhofer Line profiles. Mon. Not. R
astr. S o c , 166, 439-448.
Humes, D.H., 1980: Results of Pioneer 10 and
11 Meteoroid Experiments: Interplanetary and
Near-Saturn, J. Geophys. Res.. 85, A11,
5841-5852.
James, J.F., Smeethe, M.J., 1970; Motion of
the Interplanetary Dust Cloud, Nature, 227,
588-589.
Jessberger, E.K., 1981: in: Zahlenwerte und
Funktionen aus Naturtvissenschaften und
Technik/Landolt-BSrnstein, Gruppe 6, Band 2,
Teilband a (K. Schaifers and H.H. Voigt,
E d s . ) , Springer-Verlag, Berlin Heidelberg
New York.
Kessler, D.J., 1981: Derivation of the
Collision Probability between Orbiting
Objects: The Lifetimes of Jupiter's Outer
Moons, Icarus, 48, 39-48.
Kneiliel, B. and Giese, R.H., 1986: The
Impact of IRAS Results on the
Three-Dimensional Models (3D) of the Global
Distribution of Interplanetary Dust. Adv.
Space Res., 6, No. 7, 79-82.

243
 D I S C U S S I O N

P. Babadzhanov: Distributions of meteors and R_. Dumont: It seems noteworthy that most of
Zodiacal Cloud are different. Do you think, the curves, both for visible and for infra-
that tha Zodiacal dust cloud and meteoroids red data, nearly cross each other at about
have different sources? 15 inclination. This could be more than
B. Kneissel: According to the results present- fortuitous, and could mean (like in the
ed here meteoroid dust has a component, which method of the "nodes of lesser uncertainty")
could originate in long period comets. This that the knowledge of the number of particles
component can't be a part of the zodiacal whose orbits are tilted by^vl5 is less
dust population as just explained. So it seems model-dependent than others,
that zodiacal dust needs sources with mean
inclinations 30 . This doesn't coincide with
the inclination distribution of asteroids
and short period comets.
H. Fechtig: Should you perhaps include dust
particles from long period comets?
B. Kneissel: If one defines the long period
comets as having a period F > 2000 then these
comets have an eccentricity 0.97 < e < 1
and an isotropic distribution of orbits over
the sky. The input of larger particles by
these comets into the solar system should be
included in the meteoroid distribution given
by Andreev and Belkovich (1985). Then the
debris in the size range of zodiacal parti-
cles originating from these larger particles
will be blown off the solar system by radia-
tion pressure.

244
 PROTON MICROPROBE ANALYSIS OF INTERPLANETARY DUST PARTICLES

R. Wallenwein, Ch. Antz, E.K. Jessberger, K. Traxel

Max-Planck-Institut fur Kernphysik

Postfach 10 39 80, 6900 Heidelberg, FRG

Comets and asteroids are thought to be the main sources of interplanetary dust par-
t i c l e s (IDPs) . IDPs with a diameter < 50 ura are able to survive tbe- entry into the
Earth's atmosphere, where they can be collected without destruction. Because of
t h e i r small size and mass, typically <10 um and <10 g, t h e i r chemical analysis i s
difficult. .

ot the proton microprobelfor the non-destructive detection of trace e l e -

ments in IDPs. Using the Heidelberg proton microprobe which provides a beam spot of
< 2x3 um , four IDPs have been analyzed and up to 26 elements,wgjfer'detected. To
quantitatively evaluate the proton-induced X-ray spectra wej^calculated ab i n i t i o X-
ray yields for the samples. Most elemental abundance r a t i o s in three IDPs agree
within a factor of two with those of cosmic abundance but with the notable excep-
tion of some v o l a t i l e elements (P, Cu, Ga, Br, and Zn) which are strongly enriched.
This i s contrasting one IDP in which Ca and the v o l a t i l e elements K, Zn and S are
depleted.

Introduction
Experimental
Comets are supposed to be the most pristine bodies in
the solar system and their detailed in-situ explo- Two IDPs, Zodiac and Bounce (#13-06-05A and #14-03-
ration would greatly enhance the knowledge on early 09A, respectively), had been prepared by P. Fraundorf
solar system processes. But because of their small for examination with different electron microscopes
size and high relative velocity access to comets i s [7], They had been compressed to a thickness of 0.5
extremely difficult and expensive. On the other hand, /jm, floated on a thin carbon foil held by Cu and Au
comets, and asteroids, are thought to be the main (Zodiac and Bounce, respectively) electron microscope
sources of the interplanetary dust [1,2] and such in- grids, and coated with 15 nm carbon. The typical size
terplanetary dust particles (IDPs) with diameters < 50 of the fragments of the IDPs i s 1 to 5 /jm. For the
/jm are able to survive the heating during entry into used 3 MeV and 4 MeV protons the compressed IDPs are
the Earth's atmosphere [3,4]. Thus IDPs from atmo- thin samples (area density < 0.15 mg/cm ) , which im-
spheric collections probably are relatively unaltered plies that deceleration of protons and absorption of
material from comets and asteroids available to the X-rays produced in the samples can be neglected.
analyst.
Two other IDPs, SP85 and SP87 (#U2-22B14 and #U2-
Because of the small size of the IDPs, typically in 22B25, respectively), were made available and were
the 1-50 /im range, microanalytical methods are neces- prepared for analysis by D. Brownlee. These particles
sary for their investigation. The application of es- with a diameters of about 10 pm are mounted intact on
tablished sensitive techniques for chemical analysis, carbon foils (- 20 nm thickness) held by beryllium
like ion microprobe and neutron activation, destroys grids. In the case of these samples deceleration of
or a l t e r s the samples [5]. The electror microprobe, protons and X-ray absorption, especially from low-Z
which i s limited in sensitivity mainly because of elements, cannot be neglected and matrix corrections
background by bremsstrahlung, provides information are necessary (see below).
only on main and some niinof elements , Since the proton The beam of the Heidelberg proton microprobe [8] can
mass is much larger than the electron mass, the back- be focussed to a minimum size of 2x3 f»m . Because of
ground of bremsstrahlung by protons i s much less. Thus the low current density of the proton beam (-10
proton induced X-ray emission spectroscopy (PIXES) al- pA//jm ) and the mounting conditions of the IDPs, no
lows the non-destructive determination of main, minor excessive heating of the samples occurs. The excited
and trace elements in very small samples [6], This is X-rays are recorded with an energy-dispersive Si(Li)
a report on our attempt to introduce the proton- detector. Beryllium or aluminium absorbers with
microprobe for the bulk chemical analyses of IDPs. different thicknesses can be placed in front of the

245
 detector to stop back-scattered protons and to avoid
pile-up from low enargy X-rays. The X-ray spectra were Ep/1000
deconvoluted and the characteristic line intensities (2)
were evaluated with the SESAMX computer routine [9].

Equation (1) can then be simplified to

z z p z (3)

•where N z is the measured X-ray intensity. To eliminate

the apparatus factors I L and an, which are difficult
to measure, and because it is not necessary to obtain
absolute atom concentrations, we normalize equation
(3) to a reference element. The abundance ratio of el-
ement z over the reference element then is given by

ef WrerRz> (4)
For normalization we choose iron and not silicon be-
cause the X-ray quanta for silicon are absorbed by the
200 jim aluminium window. The applicability and relia-
bilty of this evaluation method has successfully been
tested with two well-known, complex and thick standard
materials [121.

Figure 1: FIXE spectrum of the interplanetary dust

particle SP87. (+) Experimental counts per channel;
(—) main characteristic X-ray lines; ( ) minor
lines. Experimental conditions: 200 fim Al absorber, 4
MeV protons. Fe-esc: artificial line from the Si(Li)
detector. Results and discussion

The PIXE spectra of the four IDFs were evaluated with

Fig. 1 shows the PIXE spectrum of IDP SP87 produced SESAMX to obtain the net intensities of the main char-
during 7 hours integration by 4 MeV protons focussed acteristic emission lines. With the X-ray yields cal-
to < 10 pm. Low energy X-rays were suppressed by a 200 culated for these samples (Eqn. (2)) elemental ratios
ftm aluminium absorber. The line drawn through the data were then determined with Eqn. (4). The results are
points is the fit obtained with the SESAMX program. listed in Table 1 where upper limits are given if the
Main characteristic X-ray emissions are indicated by error exceeds 50%. The cosmic abundances [13] of the
vertical full bars and minor emissions by vertical elements detected by PIXE are also tabulated for com-
dashed bars. parison normalized to Fe.

To convert emission intensities to atom numbers one

would like to use measured yields obtained by PIXE BOUNCE ZODIAC SPSS SPS7 CQJBtic
analysis of a standard of known composition and which *toa •torn
Is similar to the sample in thickness and chemical __ _ 9.4-IO~' 40 2.B-IO" 1 40 1. 17
complexity. However, we have not yet been able to find 2 .2-10"' o.o-to-' <7S o.o-io"1 < 2.7-10 (00) 9.3-IO" 2
Al/F. 40 (55
suitable material which more over has to be chemically Si/F« 1. 1 25 1.6 35 1.4 ?5 1.6 25 1.16
homogeneous on a < 10 /jm scale. Therefore the X-ray p/r« 1 .110"= 40 2.B-10"' 30 5.4-to"3 30 . 2 . 3 - 1 0 - = (80) 9.97-IO~ 3
yields were calculated ab lnitio. The number dN of X- S/F« 4.6-IO"2 16 1.3 25 B.O-lo"' 25 5.0-10"' 17 5.6-10"'
ray quanta of a given element z produced in a layer of <a/r« 3
5 s.,0" 17 7.0-IO" 3 25 < 1.0- 1<T2 (50 < 1 . 2 - 1 0 ~ 2 (50) 5.8-10~ 3
thickness dx is given by an equation of Johannsson and
Johannsson [11]: Ca/F» < 5 7-10"' ( 7 0 6.B-1O- 2 2 0 2.2- 1O*"2 2 0 2.a-io"" z 2 5 6.9-IO~ 2
Sc/Fc < 2.3-10"' (90) «:4.0-10""* (90) < 3.0-10"* (50) ^ 7 . 4 - 1 0 ^ (50) 4.1*IO~ 5
, ..-3 -3 -3
(1) 2 5-10 20 3.9"10 IB 2.9* 10
v/r. (5O) < 2 . 4 ' I 0 " 3 (55) 3.4-IO" 4
a-,o"3 (90) (50) < 4 . 2 - I O ~ *
number of atoms of element z cr/r« 7 2-1O" 17 1.9-lo"1 I S 9 . 1 - . O - 3 17 1.5-1O" 2 19 1.6-10-=
V number of arriving protons iWr. 5 o. io" 253 2
1.0-IO" U 3.6'10" 3
IS I.Z-IO"2 19 1.010"=
F«/r« 1 1 1 1 — 1
solid angle of the detector
Co/Fe <& »• i o " 3 (50) -=1.1-10-* (50) 4.7-1O" 3 25 3.7-IO~ 3 JS 2.6-10
ionization cross-section of element z
Mi/F« 2 4-.O" 2 15 7.2-10"= 16 6.1-IO" 2 16 s.i-io"2 IB 5.6-10"=
depth-dependent energy of protons < 1 S-10'3 (50) I.2-1O" 3 3 0 J.7-JO"
3
30 5.2.1O-*
Cu/Fc —
x: penetration depth 2n/F. < 3 7-,o" (55) «: 6.9-lo* 3 (50) 3.9-IO" 3 30 7.8-10™2 4 0 I.6-IO" 3
fluorescence yield of element z G./F. — — 2.3-io"4 30 3.?-)O"4 4 0 4.0-IO" 5
transition probability of line emis- U/Fe — < 2.2.10'* (90) < 2.8-1O~* (50) < 5.6.10"* (50) 1.3-10"'
sion from element z A./r. — < 3.O-1O"5 (90) < 9.2-10"5 (90) 7.6-1O"'
transmission of X-rays from element z S./Fi _ < = . . 7 . . O - 4 <W) 7..-.O- 5 40 1.1-10-* 25 7.3-10" 5
through sample and external absorber Irltt _ _ J.6-10" 5 4 0 1.3-IO"4 35 9.3-10"*
detector efficiency for X-rays from lb/F. _ — < I . 5 I O " (60) <2.O-IO"5 (60)
5
7.4-lo" 6
element z. mtt* — — < J.5-10" 5 (Ml) < i.o-io-' (so; 7.9-1O- 7
IT/fe - — 2.0-10"' (90) 7.6-I0" 7
To obtain the total number of X-ray quanta from ele-
ment z this equation has to be integrated over the Table I; Summary of atom-ratios in ir.terplanetary dust
penetration depth x. The computer routine MACOR [10] particles obtained by proton-Induced X-ray emission
replaces the integration by summation of layers of spectrometry (PIXES). Cosmic abundances [13] are
constant thickness Ax and calculates listed for comparison.

246
 At the first glance on Table 1 one notices that quite
fewer elements - especially heavier ones - have been 100
detected in Bounce and Zodiac than in SP85 and SP87. < SP85
This is due to the superposition of the heavy element §
characteristic X-rays from the samples by those from C

the Au and Cu mounting grids excited by stray protons. o 10

After this experience IDPs SP85 and SP87 were mounted
Iou t i f
on Be grids. With this modification, 26 elements were
detected and the abundances of some 16 elements were I Ji -
quantitatively determined in the latter samples. One I T i f *
J : *
also notices that the errors quoted for major elements
like Mg, Si, and S are about as large as those for
minor and rare elements. This is due to the fact that
I- I
*
-
t i
f _| \

in this study the lower-energy X-rays were suppressed

by the Al-absorber since we were most interested in £ O.I IT -

the analysis of minor and higher-z elements. Over all o

the errors appear to be rather large (on the order of
20%). But they can be reduced by a factor of 2 when
the integration time is prolonged by a factor of 3 001
which seems to be practicable. E 0s At Sc Ir Ji V Ni Co Ft M9 s. Cr Mn As p Rb Cu K Go. CI Ge Br Se [Zn s
2 76 13 21 77 22 20 23 28 27 26 12 24 25 33 15 37 29 19 31 17 32 35 34 30 16

Figure 2 shows the PIXE results on Zodiac and Bounce 100

normaliEed to the cosmic abundance of the respective

elements and also the results from an earlier SEM-EDX
III HI <270
SP 87

study of the same particles (7). Where comparison is : \

possible the agreement is excellent. It is immediately :
f
obvious that with PIXE many more elements are quanti-
tatively determined than with electron excitation. Zo-
:

f II 1
diac overall is chondritic with notable enrichments of I II i
P and S. Bounce, on the other hand, is depleted in a T * f 4
! ;
number of elements like Ca, K, Zn and S. I
i
100 r i
BOUNCE D ' S 7M
E
- °
EOX I
i
II
-
£
. u
0.01
I
• s
E o, A l Sc Ir Ti CC! V Co ft 5 , c Mn As P Rb Cu K On CI Ge Br
f s«Zn s
Z 76 3 77 22 20 23 28 27 26 2 21 25 33 15 37 29 19 31 17 32 34 36
I 1
1 I I
condensation
temperature
volatility

r
iI ar r
i
r • Figure 3: Atomic abundances of the elements in the in-
O T3

S-5
= 0.1 :
•

I terplanetary dust particles SP85 (top) and SP87 (bot-

tom) normalized to iron and their cosmic abundance.
£E
Upper limits are marked with arrows. The elements are
II O"3 arranged according to decreasing condensation tempera-
I ture [14] .
aos Al Sc r Tr Ca V N i Co Fe Mg Si Cf As P Rb Cu K Ga CI Ge Br Se 'n S
Z 76 3 21 37 22 20 23 28 27 26 12 U 2£ 25 5 37 29 19 31 17 32 35 34 0 IE The normalized abundance patterns of the elements in
100 SP85 and SP87 are shown in Figure 3. They are rather
ZODIAC ;™« similar to each other in that most of the elements are
I DX j present in chondritic proportion (within a factor 2)
I z and in that some volatile elements are enriched rela-
tive to CI. These are P, Cu, Ga, Br, and Zn. Antz et
r
I ; |
al. (16) by SYXFA analyses of the very same particles
?
I t
found comparable overabundances of these elements.

h D
D

T
Other IDPs also exhibit enrichments of volatile ele-
ments (17,18) which have been interpreted (17) as in-
dicators of large scale elemental fractionation of the
early solar system - which seems to be a bit over-
shooting. We think that before such a far reaching
conclusion can be defended more trivial reasons for
EE r the enrichments, e.g. contamination in the atmosphere
II or in the laboratory, have to be explored experimen-
tally. Until that has been accomplished we refrain
from the detailed interpretation of the results ob-
3 0s At f Ti Co V Ni Co Fe
«B i Cr Mn Rb Cu K Ga : i G« Br Se Z s tained from only that few particles.
Z 76 3 21 77 22 20 23 28 27 26 2 L 24 13 37 29 3 31 7 32 35 34 3C 16
vololiUty The present study has shown that PIXE is a valuable
non-destructive high sensitivity method for the chemi-
cal multi-element analysis of micro-samples. It easily
Is. Atomic abundances of tl = elements in the in- can be combined with similar methods like SYXFA (16)
terplanetary dust particles Bounce (top) and Zodiac and the less sensitive, but very accurate and well es-
(bottom) normalized to iron and their cosmic abun- tablished SEM/TEM-EDX. It is essential that all this
dance. Also shown are the results from an earlier SEM- can be done prior to destructive studies with e.g.
EDX study of the same particles [7], Upper limits are SIMS. Especially in combination with SYXFA trace ele-
marked with arrows. The elements are arranged accord- ment abundances in micro-grains can be obtained rou-
ing to decreasing condensation temperature [14].
tinely with a high degree of confidence. We will fur-

247
 Cher explore this promising tool by encreasing the
proton bean luminosity and decreasing its diameter, by
installing higher resolution detectors and integrating D I S C U S S I O N
longer.

Acknowledgements Shulman: Do you claim that your p a r t i c l e s

have avoided the heating crossing the upper
We are obliged to E. Zinner for providing us vith atmosphere as well as a l l the standard me-
Bounce and Zodiac and D. Brownlee for expertedly teocoid particles?
mounting SP85 and SF87. We thank E. Bombelka for his Wallenwein: I only underlined that there is
advice with the spectra deconvolution, H. Blank and A. no depletion of v o l a t i l e s .
Janicke for help with microscopes and mlcroprobes, 0. Shulman: But the v o l a t i l e s are not free, they
Kress for drawing, and D. Krull for typing. are strongly bound to the other atoms.
Wallenwein: I agree.
Ceplecha; Micrometer p a r t i c l e s are decelerated
high in the atmosphere without any significant
heating. I want to encourage the authors in
References: continuing this highly sophisticated Lnd fine
measurements. Their r e s u l t s could help to
[1] F.L. Whipple, in J.L. Weinberg (Ed.), The Zodia-
decide, if Brownlee's p a r t i c l e s are really
cal Light and the Interplanetary Medium, NASA
of cometary origin.
SP-150, Government Printing Office, Washington
DC, (1967) 409
[2] P.M. Millman, in A. Elvius (Ed.), From Plasma to
Planet, Nobel Symp. No. 21, Wiley, New York,
(1972) 157
[3] D.E. Brownlee, in J.A.M. McDonnell (Ed.), Cosmic
Dust, Wiley, New York, (1978) 295 (and refer-
ences therein).
[4) D.E. Brownlee, Annu. Rev. Earth Planet. Sci. , 13
(1985) 147
[51 H.W. Werner and R.P.H. Garten, Rep. Prog. Phys.,
47 (1984) 221
[6] R.P.H. Garten, in W. Fresenius, H. GQnzler, I.
Luderwald, and G. Tdlg (Eds.), Analytiker
Taschenbuch, Vol. 4, Springer, Berlin, (1984)
259
[7] P. Fraundorf, Geochlm. Cosraochim. Acta, 45 (1981)
915 (and references therein)
[8] F. Bosch, A. El Goresy, W. Herth, B. Martin, R.
Nobiling, B. Povh, H.D. Reiss, and K. Traxel,
Nucl. Sci. Appl., 1 (1980) 33
[9] J.L. Campbell, W. Maenhaut, E. Bombelka, E. Clay-
ton, K. Malmqvist, J.A. Maxwell, J. Pallon, and
J. Vandenhaute, Nucl. Instrum. Methods Sect. B,
14 (1986) 204
[10] H. Blank and K. Traxel, Scanning Electron Mi-
crosc, III (1984) 1089
[11] S. Johannsson and T. Johannsson, Nucl. Instrum.
Methods, Sect. A, 137 (1976) 473
[12] E.K. Jessberger and R. Wallenwein, Adv. Space
Res.,Vol. 6, No. 7, (1986) 5.
[13] H. Palme, H.E. Suess, and H.D. Zeh, in Landolt-
Bdrnstein, K. Schaifers and H.H. Voigt (Eds),
Vol. 2, Part A, Springer, Berlin, (1981) 257
[14] J.T. Wasson, Meteorites, Their Record of Early
Solar-System History, Freeman, New York, (1985)
(15] R. Wallenwein, H. Blank, E.K. Jessberger, and K.
Traxel, Anal. Chim. Acta, 195 (1987) 317
[16] Ch. Antz, M. Bavdaz, E.K. Jessberger, A. Kndchel,
and R. Wallenwein, these proceedings
[17] C.C.A.H. van der Stap, R.D. Vis, and H. Verheul,
Lunar Planet. S c i . XVII (1986) 1013
[18] G.J. Flynn and S.R. Sutton, Lunar Planet. S c i .
XVIII (1987) 296

248
 CHEMICAL ANALYSIS OF INTERPLANETARY DUST PARTICLES WITH SYNCHROTRON RADIATION

Ch. Antz 1 , M. Bavdaz 2 , E.K. Jessberger1, A. Knochel2, R. Wallenwein1

1
Max-Planck-Institut fur Kernphysik, P.O. Box 103980, 6900 Heidelberg, F.R.G.
2
Universitat Hamburg, Institut fur Anorganische und Angewandte Chemie,
Martin-Luther-King-Platz 6, 2000 Hamburg 13, F.R.G.

Abstract:

Two 10-j*cm interplanetary dust particles collected in the stratosphere, have been an-
alyzed with X-ray fluorescence excited by white synchrotron radiation (SYXFA) at the
HASYLAB (DESY) in Hamburg. The measured abundances of the minor and trace elements
with 16 < Z < 76 are in good agreement with abundances determined by PIXE analysis
[1] of the same p a r t i c l e s .

The results demonstrate that SYXFA i s indeed a powerful non-destructive technique

for multi-element analysis of micron-sized samples. Moreover we find that the com-
bined application of two such techniques, SYXFA and PIXE, to the same valuable par-
t i c l e lends high credibility to the r e s u l t s .

Introduction: Two Interplanetary dust p a r t i c l e s

(=IDPs) SP85 and SP87 [1] have been analyzed with
white synchrotron r a d i a t i o n from the DORIS storage
ring a t DESY i n Hamburg. The aim of t h i s work was t o
t e s t the a p p l i c a b i l i t y of Synchrotron X-Ray Fluores-
cence Analysis (-SYXFA) as a non destructive method
for the chemical multielement analysis of micro-sam-
p l e s , and to combine two different microanalytical
techniques, PIXE [1] and SYXFA, on the same p a r t i c l e s .

Theoretical calculations on proton (PIXE) and photon

(SYXFA) i n t e r a c t i o n with matter, which take into ac-
count the differences of e x c i t a t i o n processes, photo-
and s c a t t e r - c r o s s - s e c t i o n s for proton- and photon ex-
c i t a t i o n y i e l d : For the elements 15 < Z < 50 primary
photons excite about 700 times more K o -transltions and
for the elements 40 < Z < 92 about 10-350 times more
L - t r a n s i t i o n s than the same number of primary protons
does [ 2 ] . The number of lonizations per unit deposited
energy in a thin sample (e.g. 1 /jra) i s by a factor of
50 to 5000 larger for photon excitation than for pro-
ton e x c i t a t i o n [3]. In the case of continuous photon
excitation the signal/background r a t i o s (-S/B) for
both, PIXE and SYXFA, should be comparable, especially
for elements with a Z > 30 [<t] . With monochromatic
photon e x c i t a t i o n , the S/B r a t i o should Increase by a
factor of -10 [ 5 ] .
For the special case of multielement analysis of mi-
cro-samples conventional x-ray tubes would not be ap- 100 1000 10000 leV)
plicable because t h e i r photon fluxes and degree of po- C.1 10
l a r i z a t i o n (- 0.3-0.5) are too low. Synchrotron radi-
ation (-S.R.). however, appears to be suitable for
chemical microanalysis because i t ' s unique properties
like high brightness (Fig. 1 ) , high degree of polar- Fig. 1: In the energy region of interest the bright-
ization (-0.9 for DORIS storage r i n g ) , and natural ness of Synchrotron Radiation from DORIS is about
collimation (emission angle in GeV-energy region i s three orders of magnitudes above the Cu-Ka char-
about 0.1 m r a d ) . acteristic radiation from a 60 kw X-ray tube.

24?
Two processes dominate when a photon interacts with an Experimental: Fig.3 shows a schematic of the ex-
atom of the sample: a) The photoelectric effect pro- perimental setup used for SYXFA at the HASY1AB (DESY)
duces an Isotropic radiation pattern and yields the in Hamburg. The S.R. from the DORIS storage ring
characteristic x-ray peaks of the elements, b) Scatter passed a Mo-slit aperture, which defined a
processes, such as coherent Rayleigh - and incoherent beam/specimen interaction area of = 10x10 /in , before
Compton-scattering, are mostly responsible for the hitting the target. The characteristic and background
background of the spectrum. X-rays were sampled with a Si(Li) detector and ana-
lyzed by a Multi-Channel-Analyzer. The data were
The differential cross-section for the scatter-process stored on a floj>j>y-disk and mainly evaluated using the
.between a relativistic free electron and a plane po- fit procedure XSPEK [13]. In order to preserve the
larized photon beam is [6,7] natural colliroation and intensity the primary beam
basses through a tube with He-atmosphere up to near
the Mo-slit. The whole experiment is placed in a small
r
2 li]"f!s i ^ | lead chamber to prevent health hazards due to high en-
ergy X-rays.

^/ith r Q the classical electron radius, vo(v') the fre-

quency of the incident (outgoing) photons, and 6 the
iangle between the electric polarization vector of the
incident and outgoing photon. By choosing a plane of
observation parallel to the plane of the storage ring
and taking into account the definition for the polar-
ization P - (I - I y )/(I X + I y ) with I - the inten-
sities of incident beam in x,y-direction, one can cal-
culate the amount of scattered intensity per unit
HE-FILLED SLIT APERTURE I»IO«10 iim 2 l
solid angle in the direction of * normalized to r Q BEAMTUBE s
and the incident intensity ($: scattering angle -•
angle of view): TARGET
\

1
T
KAPTON • EMITTED r'=
I - - - (P+l)sin * Fort
2
SYNCHROTRON-BEAM

The intensity I is minimal when 4 - 90°. Our experi-

ment was performed with $ =* 70° because of sample
mounting conditions, but in the future * - 90° can be
Fig. 3: Schematic for the experiment.
used and thus the scattered intensities will be re-
duced by a factor of <* 3 (Fig. 2)

REL INTENSITY OF COMPTON SCATTERED PHOTONS

P.DEGREE OF PULAMZATION OF INCIDENT BEAM
(ENERGY OF INCIDENT BEAM. II K£V)

Results: Fig.4 shows the SYXFA spectra of SP85 and

SP87 and for comparison a PIXE-spectrum of SP87 [1].
Full vertical lines in the spectra represent the most
intensive peaks of the elements; dotted lines are used
for secondary peaks. Kr and Ar in the SYXFA spectra
are signals from air in the lead chamber. Detection of
lowul background at <> =90°
As-K and Os -L signals are difficult because both
overlap with the Pb-L-peak from lead background radia-
tion of the chamber.
SCATTERING ANGLE 0 (DEGREE)

Fig. 2: Relative scatter intensity as a function of

scattering angle 4. In our experiment * was - 70°
whereas the lowest scattering background achiev-
able is at $-90°.

250
 10s i Atom- SPSS SP87 cosmic
ratio
* Ni

S/Fe < 1.84 8.72 • io-' ± 25 X S.58 • »"•

.0' _ K/Fe 1.12 • 10-2 ± 30 t 4.72 • t o - ' ± 20 X 4.05- 10-3
.;:* Ni
Ca/Fe 1.61 • 10-2 ± 18 X 2.57 • 10-2 ± 18 X 6.87 • 10-2
Cr Mn* (As) F«-pll*-up Sc/Fe
*•! < 1.33 • 10-3 4.07- 10-3
(Kr)
V! »•> Pb (S.> l B ,i Tl/Fe < 8.28 • 10-3 < 3.10 10-3 10-3
z
<
X
IOJ - Ai Co. TiA
f V/Fe
Cr/Fe
< 3.S0 • 1 0 " *
9.S4 • 10-3 ± 18 X
3.89 • io-*
1.24 • 10-2 ±
30 X
18 X
2.81 •
3.37 -
I.S7 •
io-«
10-2
-—1-* Mn/Fe 6.23 • 10"3 ± 16 X 1.24 • 10-2 ± 16 X 1.01 - 10-2
/I 1O!
z
t» -r'
<giound
Nl/Fe
Cu/Fe
9.13 • I D " 2 ± 15 X 1.06 • 10"' ± 15 X 5.61 • 10-2
5.23 - 10~*
§ SPflS Eci i d with White Synchi otron -Radiation 2n/Fe 5.13 • 10-3 ± 19 X S.U- 10'3 ± 19 X 1.63 . 10-3
Absorber 400 pm Ca/Fe < 2 37 • 10"*
3.95 • 10"*
10 Dote : 1,11 198 Ge/Fe 1.86 • 1 0 " * ± 44X 4.19 - io-* ± 35 X 1.32 - io-«
As/Fe s
< 6.95 • 1 0 " * < 6.80 • 10" 7.56- io-»
Se/Fe < 3.30- 10"4 2.96- io-* ± 39 X 7.32 • 10"5
Br/Fe 3
10° < 3.00- 10"* < 1.21 • t o - 9.30 • io-'
Os/Fe < 6.35 • 10-3 7.90- io-'

TABLE 1 : Atom-ratios In the IDPa SPSS and SP87 obtained with SYXFA.
Cosmic ratios are listed for comparison.

1UUU SF 85
•I with SYX FA
100 - -
T
10 ; T T -

•
• T • • f 1
1
5PB7E*it«d with Whit* Synchrotron-Radiation
Absorber 400 ^m Oc T • •
Dati : 1 11 1966 *
O.I

12 EK/KBV

0.01 -
0.001
r
Os Sc Ir Ti Ca V Ni Co e Cr As Rb K GaGe B r Sc Zn S

z 76 21 77 22 20 23 28 27 26 24 25 33 37 29 19 31 32 35 V, 30 6
volatility

IUUU
SP 87
w i t h SYXFA
o

c
-
-
T -

background
SP 87 with P I X E •
u 10 -
E(H') 4 M « V , 2 0 0 j i m Al
2631987 E 1 i
*
10° Ul
12 U 16 o
Ef/keV • i * •
o t
-a 1' f
ac T* T

Fig. 4; Spectra of SP85 (a) and SP87 (b) excited with

white S.R. Sampling time ~ 430 min. u_
o 0,1 • -
Full lines represent main characteristic X-ray
signals, dotted lines minor signals. •o
rsl

B 0,01 -
In Table 1 the atom-ratios obtained by SYXFA are
listed normalized to Fe and compared to the respective oe
cosmic ratios. In Fig. 5 the atom-ratios, normalized 2;
to cosmic abundances, are plotted. The elements are 0,001 '_
arranged according to their volatility [14]. For the Ti Ca V Ni Co -z Cr Mn As RbCu K Ga Ge Br Se Zn S
elements with a fitted relative error greater than 50% Z 22 20 23 28 27 26 2i 25 33 37 29|?9 31 32 35 3*, 30 6
(V, Se) or those overlapping with others (As-Os-Pb,
Ti-Fe-escape, Cu-Fe) we calculated upper limits, rep- » volatility
resented In Fig.5 by arrows. For both particles the
abundance patterns of the more refractory elements are Fig. 5: Atom-ratios obtained by SYXFA normalized Co Fe
almost cosmic, whereas the more volatile elements are and cosmic abundances. The elements are arranged
enriched relative to their cosmic abundances. according to their volatility. Upper limits are
represented by arrows.

251
 The spectrum sampling time for PIXE was generally five [6) 0. Klein, Y. Nishina, in "Zeitschr. f. Phys.,
times longer than for SYXFA. A comparison of the spec- (1928) 853
tra obtained with both methods shows that: [7] R.D. Evans, The atomic nucleus, New York,
Toronto, London 1955
- SYXFA has a higher integral count rate and thus a [8] H. ?alme, H.E. Suess, H.D. Zeh, Abundances of tl
better count statistic than PIXE (even in 1/5 of elements in the solar system, in: Landolt - Bon
time) stein, Bd. 2, Tell a, Springer Berlin (1981) S.
257-272
- SYXFA has a better signal/noise-ratio for the ele- [9] D.E. Bruwnlee, in J.A.M. McDonnell (ed.) Cosmic
ments with Z > 30 and is comparable for '.he other dust, Wiley, New York, 1978, p. 295 (see refer-
elements. ences therein)
[10] D.E. Brownlee, Ann u. Rev. Earth Planet Sci., 13
- S/B of SYXFA is comparable to that of PIXE. It de- (1985), p 147
creases however for elements with 15 < 2 < 30 due to [11] E.K. Jessberger, J. Kissel, H. Fechtig, F.R.
the continuous photon excitation. Krueger, On the average chemical composition of
cometary dust, In "Proceedings. Physical Pro-
cesses in Comets, Stars, and Active Galaxies, W.
A comparison of the results for SP85 and SP87 obtained Hillebrandt, E. Meyer-Hofmeister, H.C. Thomas
by PIXE and SYXFA shows that both reproduce nearly the (eds.), Springer
cosmic abundance patterns of the more refractory ele- [12] N. Gurker, X-Ray Spectrometry 14 (1985), p 74
ments as well as the enrichment of the volatiles like [13] W. Petersen, Rontgenfluoreszenzanalyse mit Hilfe
Ga, Ge, Br, Se, Zn, and S. der Synchrotronstrahlung, Interner Bericht, DESY
F41, HASYLAB 84-02, Juli 1984
[14] J.T. Wasson, Meteorites, Their Record of Early
Solar System History, Freedman, New York, 1985.

Possible interpretations: Possible interpretations of

the observed elemental patterns of the particles in-
clude

IDPs may originate from even less metamorphosed par- D I S C U S S I O N

ent bodies than Cl-Meteorites are (9,10], Cometary
dust grains show an enrichment of light volatiles
like C and N relative to Cl [11]. Thus the overbun- Henninn: Can you make any comments on the
dance of the minor volatile elements in the IDPs may mineralogical structure of IDP's with your
indicate a relation of IDPs and come;.s. new techniques?
Antz: We can only determine the average ele-
Contamination could occur during the entry of the mental ratio within '. certain error limit.
particles into the Earth's atmosphere and also dur- Ceplecha; I s '••, with my remark to the Wal-
ing laboratory processing, both, however, regarded lenwein et al. paper.
to be very unlikely but cannot be excluded.

Conclusions: The pilot experiment with SYXFA shows

that this novel technique is a powerful tool for
inulti-element microanalysis of micro-samples, e.g. it
was possible to detect in SP87 an amount of = 10"* g
Se (- 8-10 atoms) without destroying the sample.
For the future it is planned to increase the spatial
resolution to -1 /jm , using a coded irradiation tech-
nique, to allow a space-resolved analysis of micro
samples [12]. Secondly the scattered intensity will be
reduced by a factor of about 3 by choosing a view an-
gle of *-90°.

References

!1| ?.. Wallenwein, Ch. Antz, E.K. Jessberger, K.

Traxel. see these proceedings
[2] C.J. Sparks jr., F.. Ricci. S. Raman, M.0. Krause,
R.V. Centry, H.I.. Yakel and J.B. Hastings, X-Ray
fluorescence analysis with synchrotron radiation,
Anal. Chem, (1980)
[3] R.W. Shaw, Jr., and R.D. Willis, in "Electron Mi-
croscopy and X-Ray Applications to Environmental
and Occupational Health", P.A. Russel and A. E.
Hutchings (eds.)
[4] F.S. Goulding, J.M, Jaklevlc, XRF Analysis - Some
sensitivity comparisons between charged particle
and photon excitation, Nucl. Instr. and Meth.
142, 323-332 (1=177)
[5] C.J. Sparks, Jr. in "Synchrotron Radiation Re-
search. H. Winnick, S. Doniach (eds.), p. 459

252
 ON HIE SOOKCE AMD STRUCTURE OF MTERPLfiNETARy DUST PARTICLES

H. Fechtig
Max- Planck- Institut ftir Kemphysik, 6900 Heidelberg, Vfest Germany

Conetary dust grains asraeasuredby the Halley space missions show a silicate- and a light ele-
ment ccnponent. The latter mast likely represents an organic material. The densities of the
grains are mostly below 1 g/cm3. Ihe organic component slowly decays at higher temperatures
during subsequent perihelion passages. Therefore the "older" cotretary grains are different from
the "young" ccmetary grains: they show higher albedos, higher densities and orbit finally with-
in the inner solar system.

.The dust impact analyzer experiments |(c) Pioneer 10/11 dust experiments:
on Giotto and VeGa have shown that Che two dust experiments have
cometary dust generally consists of received observations which seem to
two components: contradict each other. The optical
a silicate component and a light experiment (Hanner et al., 1976) has
element component (Krueger and observed a particle number density
Kissel, 1987). This result is dependency which roughly is in
compatible with the model for dust inverse proportion to the distance
grains suggested by Greenberg from the sun until 3.3 AU.
(Greenberg, 1982). Therefore, dust Furtherout, no scattered sunlight
grains may have fluffy structures has been recorded. The penetration
consisting of submicron-sized experiment (Humes et al., 1974;
building blocks of silicate cores Humes, 1980) however, has seen a
and organic mantles. The dust impact similar depen-dence between 1 and
analyzer has directly measured the 3.3 AU, but futherout a constant
densities of cometary dust grains dust flux has been recorded until 20
ranging between 0,1 and 3 g/cm . jAU. Several authors (Cook, 1978;
Fech-tig, 1984) have tried to solve
Before discussing the evolution of this contradiction by suggesting a
cometary dust grains, some continuous decrease of the albedos
observations for the interplanetary of dust particles proportional to
dust are summarized: the distance from the sun.

(a) Lunar microcraters: it was Can the cometary particles as

possible to directly measure the measured during the Halley-missions
density of interplan-etary grains by explain all these observations?
studying the morphology of lunar
microcraters (Brownlee et al., 1974; An explanation would be easy if one
Smith et al., 1974; Magel et al., assumes the asteroids as a second
1975; Nagel et al., 1976). source for the interplanetary dust,
Simulation experiments have shown a source at least as strong as the
that the diameter to depth ratios of cometary source. If this was the
microcraters are directly corre- case, then asteroidal dust of high
lated with the densities of the albedos would populate the inner
projec-tiles (Vedder and Mandeville, solar system between the sun and the
1974; Nagel and Fechtig, 1980; asteroidal belt, and cometary
Pechtig, 1982). An analysis has particles of low albedos with
shown that less than 30% of all considerable aphelion distances
lunar microcraters are produced by would stay only temporarily in the
low density projectiles. inner solar system. In this case,
the inner solar system would be
(b) Helios dust experiment: the "dominated" by the high albedo
analysis of the dust experiment from asteroidal dust. This would fit to
the Helios space mission has shown the observations obtained by lunar
the existence of two different types micro-craters as well as by the
of particles:dust grains of normal Helios results and would explain the
densities (p = 3 to 8 g/cm 3 ) on Pioneer 10/ 11 findings.
quasi-circular orbits around the sun
(f < 0,4 ) and dust grains of low However, the asteroids are only a
densities (p < 1 g/cm 3 ) on high weak source for dust,as shown by the
eccentric orbits around the sun (e > Pioneer 10/ 11 dust experiments
0,4) (Grun et al., 1980). But again (Humes et al., 1974; Kessler, 1970):
less than 30% of all observed par- the expected increase when
ticles are in the second class with travelling through the asteroidal
fluffy type structures. belt did not occur. Also Dohnanyi
(1976) has shown that the asteroids

253
 do not produce enough dust to play a References:
role in the inner solar system.

Therefore one should neglect an 1. Brownlee, D.E.; Horz,F.; Vedder,

asteroidal source and only consider J.F.; Gault, D.E. and
the main cometary source. Let's Hartung.J.B., 197 3, Proc.
follow the possible fate of cometary Lunar Sci. Conf. 4,3197
dust from its release from the
cometary nucleus: 2. Cook, A.F., 1978, Icarus 3_3, 349
cometary dust grains of the 3. Dohnanyi, J.S., 1976, in
above mentioned properties and "Lecture Notes in Physics"
structures are released and either (eds. H. Elsasser and H.
leave the solar system immediately Fechtig, Berlin: Springer-
through the dust tail of the comet Verlag) , 48., 187
(generally the case for submicron-
sized dust grains) or they stay on 4. Fechtig, H., 1982, in "Comets",
the cometary orbit and form a p. 370, (Ed. L.L. Wilkening,
meteoroid stream (generally the case The University of Arizona
for micron-sized and larger dust Press, Tucson, Arizona.
grains)
5. Fechtig, H., 1984, Adv. Space
all grains of a meteor stream Res. 1, 5
are periodically heated up during
subsequent perihelia passages. 6. Greenberg, J.M. ; 1982, in
Therefore the following question "Comets"(Ed. L.L. Wilkening,
arises: Do the particles change The University of Arizona
their compositions and structures? Press, Tucson, Arizona), p.
It is well known that organic 131
components can not survive at
temperatures above a certain 7. Griin, E., Pailer, N., Fechtig,
threshold. They generally decay at a H., and Kissel, J., 1980,
few hundred degrees. In an earlier Planet. Space Sci. 28, 333
paper (Mukai and Fechtig, 1983), the
assumption of a decay rate of 8. Hanner, M.S., Sparow, J.G.,
approximately 10" 1 g/ cm 2 sec for Weinberg, J.L., and Besson,
Halley dust grains lead to a slow D.E., 1976, in "Lecture Notes
variation in composition and in Physics", (eds. H. Elsasser
structure. For individual grains, and H. Fechtig, Berlin:
the organic component slowly Springer Verlag) , 48., 29
decreases from the outside to the
interior. After about 10 4 to 10 5 9. Humes, D.H., 1980, J. Geophys.
years, the organic material Res. 85, 5841
essentially has disapp-eared and
only the stable silicates remain. As 10. Humes, D.H. Alvarez, J.M.,
a result, the Brownlee-particles are O'Neal, R.L., and Kinard,
evolved. Since silicates generally W.H., 1974, J. Geophys. Res.
show higher albedos, these "old" 79. 3677
cometary particles have higher
albedos compared to the albedos of 11. Kessler, D.J., 1970, NASA SP-
the "young" cometary grains (Mukai 8038
et al., 1986);
12. Krueger, F.R. and Kissel,J.,
the Poynting-Robertson effect 1987, Naturwissenschaften 74.
has changed the orbits of the 312
cometary dust grains considerably
during the time in discussion. After 13. Mukai, T., and Fechtig, H.,
4 5
1983, Planet. Space Sci. H ,
10 to 1 0 years the orbits of 655
cometary grains are much more
circle-like and hence the particles 14. Mukai, T. , F e c h t i g , H. , Griin,
orbit much longer and most of them E., Giese, R.H., and Mukai,
always within the inner solar S., 1986, Astron. Astrophys.
system. 167, 364
Thus we can conclude that almost all 15. Nagel, K. , and Fechtig, H.,
dust particles in the solar system 1980, Planet. Space Sci. 28.
are of cometary origin. In the 567
course of time there is a decrease
of the organic component which 16. Nagel, K., Neukum, G., Dohnanyi,
causes an increase in the albedos. J.S., Fechtig, H., and
Old particles with high albedos, Gentner, W., 1976, Proc. Lunar
staying essentially in the inner Sci. Conf. Zr 1021
solar system are mainly silicate
arains. 17. Nagel, K., Neukum, G., Eichhorn,
G., Fechtig, H., Miiller.O.,
and Schneider, E., 1975, Proc.
Lunar Sci. Conf. 6, 3417

254
 18. Smith, D., Adams, N.C., and
Khan, H.A., 1974, Nature 212,
101
19. Vedder, J.F., and Handeville,
J.C., 1974, J. Geophys. Res.
79,3247

D I S C U S S I O N

Qlsson-Steel: The lunar microcrater data

indicating a minority of these to be due to
low-density particles is concordant with the
meteor data: our meteor density data is
almost all from comet-related showers and
hence the meteors are low-density; the only
asteroid-related shower (the Geminids) renders
a higher density. In addition, the absence of
dust (or, at least , scattered light) at
r > 3 . 3 All is not in contradiction with the
meteoroid distribution since what is important
is where the meteoroids are disrupted to form
dust: this occurs predominantly at small
heliocentric distances, so that the source
function for the dust is v.ery different to
the meteoroid distribution and much more like
the zodiacal dust distribution.
Ceplecha: About 20% of the photograpnic meteors
have atmospheric trajectories, which can be
better explained by assuming heavy-coated
particles rather than particles of homogeneous
composition. This may be an additional support
to the model you propose.
Giese: The polarization of scattered light,
which decreases with decreasing solar distance
(cf. Leinert et al., Dumont and Levasseur-Re-
gourd) depends on both the absorption of the
material and the structure of the particles. If
fluffy particles become too compact, there
might be problems, even if absorption de-
creases. Can you say something about the
changes in structure?
fechtig: I would expect that upon the contin-
uous slow release of organic mantle material
the silicate cores remain on from Brownlee
particles. The albedos and the densities of
Brownlee particles are higher than those of
"young" cometary grains. The structure should
be more compact, too.
Hajduk: The model of particles, used in this
paper fully corresponds to the observed mass
distribution of particles, requiring the
fragmentation and evaporation of larger bodies
during their returns to perihelion.

255
'A 5(.
 DYNAMICS OF INTERPLANETARY DUST

E. Griin

Max-Planck-Institut fur Kernphysik, Postfach 10 39 80, 69 Heidelberg, FRG

The dominant forces determining the motion of interplanetary particulates are

gravitation, solar radiation pressure and Lorentz force. The latter two becoming
significant for micron- and submicron- sized particles. In situ measurements by
spaceprobes, microcrater distributions and remote observations both in the IR and
visible wavelength range have established the mass frequency and spatial distribu-
tion of dust particles in interplanetary space. Consequences of the Poynting-
Robertson effect and mu-ual collisions on these distributions and the contributions
of various sources (interstellar dust, asteroids and comets) are discussed. It is
shown that the contribution from a distributed source of large particles in the in-
ner solar system is most important. Collisions between these meteor sized particles
(m > 10~5g) produce large amounts of zodiacal light particles (10~ lo g to 10~5g) and
fS-meteoroids (m < 10" 10 g) which leave the solar system on hyperbolic orbits. At the
present time the Poynting-Robertson effect transports into the inner solar system
less than 10% of the zodiacal light particles which are produced by collisions from
bigger particles.

I. Introduction The photoelectric effect from the solar UV radi-

ation is expected to develop a net positive charge Q
Craters on the lunar surface proved that a con- (e.s.u) on interplanetary particles corresponding to a
tinuous spectrum of interplanetary particulates exists surface potential <j> of about +5 V
from km-sized boulders (small asteroids and comets) to
submicron sized dust grains. The dominant force for 10
Q - 300 - 4.8-10' Ne (3)
all particles, except for the smallest dust grains is
the solar gravitational attraction where N Is the number of elementary charges e on the
grain. Once charged, the interplanetary magnetic field
will exert a force on these particles and hence
F - 2.5 s p (1) influence their orbit. The Lorentz force F^ is given
grav
by

where 7 - 6.67-10'°g"icm"Js" is the gravitational

constant and 0^ - 1.99-1033g the solar mass. With par- F L - ^ (v x B) (4)
ticle radius s in (cm), its density p in (g cm" ) and
r - 1 AU the gravitational force is given in dynes. where v — y s w + u. Here v is the solar wind speed
Scattering and absorption of solar radiation by an in- (400 km s in the radial direction) and u is the
terplanetary particle leads to a radiation pressure orbital velocity of the particle (typically 30 km/s)
force F r a d directed almost radially outward (cf. Burns and B_ is the magnetic field strength (about 5-10"5g, at
et al., 1979). The ratio of radiation pressure to an angle of 45° with respect to the radial direction
gravitational attraction (both forces have the same at 1 AU). With these values at 1 AU equ. (4) becomes
dependence with solar distance r) has for spherical
oarticles the value (Dohnanyi, 1978) -10
- 1.4•10 [dynes] (5)

rad Comparison of (5) with (1) shows (4 - 5V and

- 5.7 10 -5 (2) p - 2.5g cm ) that for s < 10'5cm the Lorentz force
grav becomes dominant.

With Q r being an efficiency factor for the momentum

Dynamics of small interplanetary particles
transfer. Q - X for a perfectly absorbing sphere,
including gravity and radiation pressure have been
for real particles, however, Q decreases for de-
discussed by Robertson (1937); Wyatt and Whipple
creasing s below 10 cm (i.e. order of the effective
(1950); Briggs (1962); Khipple (1967), Singer and
wavelength of the solar light, Burns et al.,1979).
Bandermann (1967); Dohnanyi (1978). Electromagnetic
Therefore /J has its maximum value for absorbing
effects on particles orbiting the sun have been
particles (like carbon or magnetite) at 0 - 2 to 5 and
included by Parker (1964); Morfill and Crun (1979a);
for dielectric particles (like silicates) at /S - 0.5
Consolmagno (1979); Barge et al. (1982); Hassan and
to 1. Radiation pressure may dominate in the size
Wallis (1983). The dynamic effects on interstellar
regime from 10 to 10 cm, below that it becomes less
particles entering the solar system were treated by
important again.

257
Levy and J o k i p i i (1976) and Morfill and Grim (1979b). This interplanetary flux leads to a spatial mass
A review of the interaction of solid p a r t i c l e s with density at 1 AU of - 10 g/m , where most mass per
the interplanetary medium can be found a t Morfill e t logarithmic mass interval is in meteoroids of masses
a l . (1985). 10 g to 10" g. Measurements of the zodiacal light
(Leinert et al., 1981) provide the radial dependence
of the spatial number density n of interplanetary
II. Size frequency and spatial distribution meteoroids: n - r . The determination of the color
of interplanetary dust of the zodiacal light (Pitz et al., 1979) shows a con-
siderable reddening compared to the solar spectral
Information on :.hc> distribution of interplane- flux. This observation is compatible with the charac-
tary im-reoroids is obtained from lunar crater teristics of the flux curve, i.e. most cross-sectional
statistics, in situ spacecraft measurements, meteor area per logarithmic mass interval originates from
and zodiacal light observations. Grun et al. (1985) 8 5
derive a flux model with the following characteristics particles of masses 10 g to 10" g. The total cross-
(see Fig.l): sectional area of the interplanetary meteoroid cloud
at 1 AU is 5-10"19m2/m3.
Meteor observations (for a summary see Whipple,
1967) 1 ^ad to a dependency of the cumulative flux on III. Dynamical effects on submicron-sized
the .dteorid mass m according to m" for masses particles.
-'J S <m < 10 g. The flux of smaller particles
down to mass m - 10 g is characterized by the size For submicron-sized particles the effect of
distribution of lunar microcraters (e.g. Horrison and solar attraction is strongly reduced by radiation
Zinner, 1977). The absolute calibration of the fluxes pressure and the Lorentz force. Therefore these small
at masses 10 g and 6•10 g is obtained from measure- particles move mostly on onbound, hyperbolic orbits.
ments of the Pegasus satellite (Nauraan, 1966). At There are two types of particles which move on hyper-
13 12 bolic orbits inside the solar system: (1) Interstellar
m - 10 g and 10" g fluxes have been derived from
the HEOS 2 experiment (Grun and Zook, 1980). These dust grains which traverse the inner parts of our
fluxes are below most lunar microcrater fluxes because solar system and (2) small particles which are
the latter are dominated by secondary ejecta cratering generated from larger bodies either by collisions <^-
(Zook et al., 1984) for particle of masses meteoroids) or by emission from comets when they get
m < 10" 10 g. In the mass range 1 0 " 1 4 < m < 10'9g close to the sun and sublimation of the icy bonding
the slope of the cumulative meteoroid flux is - -0.36. material takes place (generally inside 5 AU from the
The flux of smaller particles (m < 10" g) has been sun). The latter particles are brought from bound
calculated from a collisional model assuming that all orbits of their parent bodies onto hyperbolic orbits
fragments of this size range which are produced inside by the additional significant action of radiation
1 AU are pushed out of the solar system by radiation pressure.
pressure and become ^-meteoroids (Zook and Berg,
1975). The fluxes of these different particle popula-
tions on hyperbolic orbits show quite different char-
acteristics. Interstellar dust grains in the vicinity
?7 3
cumulative flux of the solar system amount to 10 g cm or
26 3
1 1 1 1 T T 10" g cm" . The higher value Is derived from the
interplanetary flux- average interstellar extinction of 1 mag per kpc
(Greenbe*g, 1973) while the lower value assumes that
lunar flux
the solar system Is currently surrounded by low
density warm interstellar material of density
-10" g cm" , one percent of which Is in dust (Wood et
al., 1985). We will use this lower value in the
following discussion. The sun moves with respect to
this material at a speed of 20 km/s which amounts to a
17 -0 1
mass flux of 2-10" g m s" . If we assume that most
mass is in dust interstellar particles of s — o.l /jm
(m - 10" 14 g) or s - 0.01 ^m (m - 10" 17 g) then a flux
of 2 10" 3 or 2 particles m" 2 a"1, respectively, is
expected to arrive from the solar apex direction. This
18 -16 - U -12 -10 -8 -6 high flux has not been observed. There are several
reasons to explain this deficit in the flux of
interstellar particles. These small particles may have
Fig.l: Cumulative particle flux on a spinning flat ^-values in excess of 1 especially if they are made
plate at 1 AU distance from' the sun. The plate normal
out of absorbing material. For example interstellar
vector lies in and the spin axis is perpendicular to
the ecliptic plane. For an isotropic flux the stated particles with 8 - 2 (s - 0.01 /an graphite grains)
flux values for a flat plate correspond to an effec- will reach just as close as the distance of Jupiter
tive solid angle of >r sr. The fluxes In interplanetary before radiation pressure deflects them out again.
space, on the surface of the moon and the flux of fi-
meteoroids are shown (from Grun et al., 1985). Volatile icy constituents will sublimate inside 3 to

258
5 AU leaving only refractory elements to penetrate the cular orbits. Because of their radiation pressure val-
inner solar system. Electromagnetic effects may also ues /J > 0.5 these particles would leave the solar sys-
be efficient in preventing interstellar particles from tem on hyperbolic orbits just because of th» radiation
reaching the inner part of the solar system, as we pressure alone.
will discuss below.

Long period or "new" comets emit on the average IV. Dynamics of zodiacal light particles
20 t s* dust by evaporation in the inner solar system
(Delsemme, 1976). This amounts to a mass outflux of Particles which contribute most to the zodiacal
about 7-10"17g m~2 s"1 at 1 AU or 7-10"3 particles light brightness are 10 to 100 ^m in radius. The
m" s" if most mass is in s - (1.1 pm particles. This orbital evolution of these particles is dominated by
flux should be very variable in time and space. One the Poynting-Robertson drag (Robertson, 1937; Wyatt
comet per several years contributes significantly to and Whipple, 1950; Burns et al., 1979) which causes
this flux. Only once the in situ detection of such an the particles to lose orbital angular momentum by the
extended comet tail has been reported (Hoffman et al., interaction with solar photons and solar wind ions.
1976). The life time due to radiation pressure drag of a par-
A steady steam of particles on hyperbolic orbits ticle to spiral form an initial orbit (with semi-major
originates from collisions of larger meteoroids in the axis a Q and eccentricity e Q ) into the sun is
inner solar system. Grun et al. (1985) estimate that
this flux of ^9-meteoroids from the solar direction is .- 7-10° [years (6)
'PR
10" 1 and 3 1 0 " 4 particles m" 2 s"1 for particles of
s - 0.01 fim and s - 0.1 ftm, respectively, and it where r)(eo)
is a factor (t;(0) - 1) which decreases
corresponds to a mass flux of ~ 3-10" g lit" s" at with increasing e Q (Wyatt and Whipple, 1950). Solar
1 AU in the ecliptic plane which has been observed by wind ion drag reduces these life times additionally by
the dust experiments on board Pioneer 8 and 9 (Berg about 30%.
and Grun, 1973).
The inward mass flux o? micron to mm-sized par-
Levy and Jokipii (1976) studied the effects of ticles due to the Poynting-Robertson effect in the
the interplanetary magnetic field on charged inter- ecliptic plane at 1 AU is - 2.110~ 22 g cm'2 s"1 (Grun
stellar grains penetrating the solar system. They sug- et al., 1985). Because of the increase of the spatial
gested that submicron sized interstellar grains will density towards the sun (Leinert et al., 1981) the
be largely excluded from the solar system by the inward flux at the inner edge of the zodiacal cloud
sweeping action of the solar wind magnetic field. A will increase by a factor 2 to 3, depending on where
more detailed study by Morfill and Grim (1979b) showed the inner edge is assumed to be (0.1 AU or 0.03 AU)
that the unipolar field regimes at high latitudes lead and where sublimation of meteoritlc material occurs.
either to a "focusing" or "defocusing" of interstellar The evaporated atoms (mostly C, 0, Mg, Si, S, and Fe)
dust particles with respect to the solar magnetic will be ionized by photoionization and charge exchange
equator. The stochastic magnetic fluctuations in the reactions and will subsequently be convected along
equatorial region caused by the warping of the current with the solar wind and the interplanetary magnetic
sheet which separates the polar field, leads to a dif- field.
fusive transport of particles of sizes s < 10" cm.
They concluded dust that particles with radii Outside 1 AU asteroidal debris will contribute
s > 10~Jcm can penetrate deeply into the heliosphere to the interplanetary particulate cloud. Observations
if their incidence direction at the heliopause Is al- of the thermal radiation with the infrared satellite
most radially inward and close to the solar magnetic IRAS (Hauser et al., 1984) showed high intensities at
equatorial plane (i.e. approx. within 20° ecliptic wavelength of 12 to 100 jim in the ecliptic plane and
latitude). Particle trajectories coming from high in bands on both sides about 10° away from it. These
solar magnetic latitudes are focused towards the solar observations have been interpreted by Dermott et al.
magnetic equatorial plane during solar cycles of nega- (1984) as being due to Impact ejeeta particles from
tive field polarity in the northern hemisphere. During the known asteroids.
other solar cycles the inner heliosphere is shielded
from interstellar grains approaching from high lati- Measurements of the impact rate of interplane-
tudes . tary dust particles onto the Pioneer 10 spacecraft out
to 20 AU ha-> e been reported by Humes (1980). He found
Numerical trajectory calculations have been per- that outside Jupiter's orbit the particle flux stayed
formed using the code described by Morfill and Grun about constant. If this result is not just caused by
(1979a) in order to study the effects of the inter- bad statistics which is possible since the total
planetary plasma and magnetic field on /3-meteorids number of impacts was only about 30 - then there is a
(Morfill et al., 1985). The basis was a realistic problem with understanding this spatial distribution.
model of the sector structure of the interplanetary The radial drift velocity due to the Poynting-
magnetic field which extended to 15° ecliptic lati- Robertson effect is proportional to 1/r for circular
tude. As initial conditions it wai; assumed that parti- orbits. Therefore inside the source region of inter-
cles were created on orbits with inclinations i - 0° planetary particles a spatial density variation
and 30° and with the local Keplerian velocity for cir- n(r)~r~a (a—1) turns up. If the orbits are eccentric

259
or if there is a source for dust particles in that re-
gion of space then an even steeper radial dependence
(10)
(a>l) results (Leinert et al. 1983). Only if there is C(m,r)
a sink for particles in the region of space under con- Pig. 2 shows the so calculated collisional lifetimes.
sideration then a flatter slope (a<l) would be ex- At 1 AU the lifetimes are shortest (10* years), for
pected. Sublimation of water ice (Zook 1980) or sput- particles of mass 10" g to lg. Both bigger and smaller
tering and sublimation of volatile organic mantels particles have longer collisional lifetimes. For com-
(Fechtig 1987) have been proposed as loss mechanisms. parison we also show the Poynting-Robertson lifetimes.
The efficiency factor used was that for olivine
The plane of symmetry . interplanetary dust has particles and the average initial eccentricity of the
been found to deviate slightly from the ecliptic particle orbits at 1 AU is assumed to be 0.5.
plane. Inside 1 AU its ascending node and inclination Collisions dominate the lifetimes of meteoroids with
were determined hy Helios to be 0 - 87° ± 4°, masses m > 10 g. These large particles will not
i - 3.0° ± 0.V (Leinert et al. 1980), a result with change their orbits significantly due to the Poynting-
which the earthbound observations of Misconi and Robertson effect before they are involved in a
Weinberg (1978) fully agree. There is evidence that collision and fragmented into smaller particles. Only
outside 1 AU the symmetry is closer to the orbit of smaller particles (m < 10 g) will have their orbits
Mars or the invariable plane of the solar system circularized by the Poynting-Robertson drag and will
(Misconi 1980, Dumont and Levasseur-Regourd, 1987), eventually spiral in towards the sun where they will
which is also supported by the analysis of IRAS evaporate.
infrared measurements (Hauser et al., 1985).
The mass of particles in the Interval (m^.n^)
lost by catastrophic collisions per second is given by
V. Effects of mutual collision

In collisions between interplanetary meteoroids

the impact speed usually is high enough to result in -- m n(m,r) C(m,r) dm (11)
fragmentation of one or both particles. The average
Impact speed Is generally approximated by

Dohnanyi (1969) showed that an Interesting conclusion

-0.5
can be drawn from the above relations, assuming only
v(r) -
(f) (7)
conservation of mass. If the mass distribution n(m) is
steep, i.e. if there are many smaller projectiles,
much mass will be lost from a given size interval. If
with v_ 20 km/s at r Q - 1 AU. In such a collision the distribution is flat there are fewer projectiles
the smaller particle always gets destroyed, the larger which are able to fragment larger target particles.
fragments only, if the mass ratio Is not too large, Balance between production and destruction is achieved
i.e. if for n(m) - m ' , a mass distribution which was
observed for the smaller asteroids (Dohnanyi 1969). A
particle population with an index 7 > 11/6 is decaying
(8) under the influence of catastrophic collisions and an
"projectile ~ T(v) target,
extra source of particles is required to maintain
where T(v) — 250 v (km/s) was found experimentally
their distribution. This Is the case for meteoroids of
for basalt and may be typical for interplanetary par-
mass m > 10' 5 8 (Fig.3). For a population index
ticles also. If the projectile mass is smaller, the
7 < 11/6 we have to expect a build up of particles
larger particle Is eroded by the impact cratering pro-
with small masses. This is the situation for the
cess. Dohnanyi (1970) showed that for the meteoroids
with masses m < 10 g erosive collisions are much
less important than catastrophic collisions, so that life times
we limit our discussions to the latter case.

The rate of catastrophic collisions of a mete-

oroid of mass m is given by adding the probabilities
that the meteoroid will encounter a large enough pro-
jectile particle during the following second over ell
projectile masses H L :

2
C(m,r) - <r-n(m ,r v(r) dm (9) b -2 0 2
-18 -16 -14
log m (g)
m/r(v)
The cross section-is a - *(s+s ) where a and s are Fig.2: Lifetimes of interplanetary meteoroids with re-
the particle and projectile radii
d respectively. The spect to collisions Tg and Poynting-Robertson effect
r
collisional lifetime for this particle then Is PR-

260
 smaller interplanetary meceoroids. This comparison in From Fig.3 it can be seen that at 1 AU many more
terms of collisional loss and gain is shown in Ftg.3. particles are gained in the mass range 10" 10 g to 10"5g
We have also computed the radial loss due to the from collisional break-up of meteor-sized particles
Poynting-Robertson effect which is required in order
than are removed by the Poynting-Robertson effect.
to maintain a radial density distribution proportional
About 6 to 8 t/s of these particles are produced
to r"1'3.
inside 1 AU. This compares to only a total of - 0.3
t/s which are lost by the Poynting-Robertson effect
from the same region of space. This situation is not
V I . Balance between different dynamical stable but the zodiacal light particle population
effects presently increases in time (on a time scale of about
10 years at 1 AU). Time stability of this particle
Large meteor sized particles (m > 10 g) are population can only be maintained if we have
dominated by collisional fragmentation. Assuming a overestimated the meteoroid flux by more than a factor
1 1
radial dependence according r and a filling factor 10 or if the break-up laws which we have applied are
£ - 0.23 (Leinert et al., 1983) then a total of 9 t/s not at all representative for interplanetary
is lost from this size range within 1 AU. This parti- meteoroids. both alternatives are not supported by the
cle population would be depleted on a time scale of data.
- 10 years without replenishment from cometary and
asteroidal sources (Kresak, 1978). Under steady state
Small fragment particles which are generated by
conditions most meteor particles are "young", i.e.
a collision between a larger parent meteoroid and an-
they have not been fragmented by collisions and their
other meteoroid will move on unbound trajectories if
initial orbits are not much altered by radiation pres-
their reduced potential energy (gravitation minus
sure drag. Only planetary perturbations could distort
radiation pressure) is exceeded by their kinetic
the initial orbits significantly before the particles
energy which is derived from the parent particle. This
break up by catastrophic collisions. Observations of
is especially effective at the perihelion of an eccen-
meteor streams support this finding. The flow of mete-
tric parent particle's orbit, wher-. f • ,.- kinetic energy
oritic material in mass and space is demonstrated in
and the collision rate are highest . Since the eccen-
Fig.4.

The optically active zodiacal light particles

(10" g < m < 10" 5 g) are dominated by radiation Asteroidal dsbris
pressure drag and not by catastrophic disruption.
Their lifetimes due to Poynting-Robertson effect range
from 10 years to 10 years for the smaller particles.
Disintegration of Comets

The Poynting-Robertson mass flux through a

spherical shell with radius 1 AU is 140 kg/s. This
flux is the maximum contribution of debris from the - 0
asteroid belt to the zodiacal cloud inside 1 AU.
Probably its contribution is much less since
collisions among meteors also contribute to zodiacal -if
particles outside 1 AU.

-2
- 2 8 , _,. T —J ^ I 1 £
'^ zodiacal
(I-me coroids ^ tight ? meteor part id
>.-: panicles ^
-3
POYNTING ROBERTSON EFFECT
-29 - -

collisional gain ' collisional

/
-30 - / ;';" / v.. --5
:' - / -S
':'- f '..
>-'• 'Poynting- "- \
s"r ^Robertson :.
•-: / loss --
\ \
--6
-31 , 1 , >;?' , ^ i * i i r -18
-18 -16 -14 -12 -10 -8 -6 -4-2 0 2 0,01
log m (g) r(AU)
Fig.3: Net mass loss and gain rates from collisions Fig.4: Schematic diagram of dynamical effects which
and transport losses due to Poynting-Robertson effect change mass and heliocentric distance of interplane-
at 1 AU The total mass lost by collisions tary meteoroids. Sources for meteoroids are comets and
(m > lg" g) and gained as fragments (m $ 10 g) is asteroids, sinks are the ejection from the solar sys-
9-10" -g/nrs. The Poynting-Robertson effect requires a tem (/3-meteoroids which eventually become interstellar
loss of only 4 1C" g/m s in order to maintain the grains) and the evaporation near the sun (this mate-
spatial density - r~*• . rial is ionized and carried away with the solar wind).

261
trlcicies of Che parent particles are significant even Hauser, M.G., Gautier, T.N., Good, J., and Low, F.J.:
fragment particles of masses as large as m - 10 g 1985, In Properties and Interactions of
can get on hyperbolic trajectories and become ^-mete- Interplanetary dust (eds. L. Laray and R.G. Giese),
orolds (Zook and Berg, 1975). This direct injection of Reidel, Dordrecht, 43.
fragment particles into hyperbolic orbits is a very
efficient loss mechanism since the time these parti- Hoffmann, H.J., Fechtlg, H., Crun, E., and Kissel, J.
cles spend in the inner solar system is only order of 1976, in The Study of Comets (eds. B. Donn, M.
100 days. Therefore, most particles of masses Mumma, V. Jackson, H. A'Hearn, and R. Harrington),
ra < 10 g which are produced from the disruption of NASA SP-393, 949.
larger meteoroids can efficiently be removed by this
effect. Hence we conclude that the small particle Humes, D.H.: 1980, J. Geophys. Res., 85. 5841.
population is in time stability. About 1 to 3 t/s of
^-meteoroids pass the Earth's orbit. Kresak, L.: 1978, Bull. Astron. Inst. Czechosl., 2£,
135.

Leinert, C., Hanner, H., Richter, I., and Fitz, E.:

References 1980, Astron. Astrophys. 82, 328.

Leinert, C., Richter, I., Pitz, E., and Planck, B.:

Barge, P., Pellat, R., Millet, J.: 1982, Astron.
1981, Astron. Astrophvs. 103. 177.
Astrophys._115, 8.
Leinert, C., Roser, S., and Buitrago, J.: 1983,
Berg, O.E., and Grun, E.: 1973, in Space Research
Astron. Astrophys. 118. 345.
XIT.I. Akademie Verlag, Berlin 1047.
Levy, E.H., and Jokipii, J.R.: 1976, Nature 264, 423.
Briggs, R.E.: 1962, Astron. J._67, 710.
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Burns, J.A., Lamy, P.L., and Soter, S.: 1979, Icarus 1484.
40, 1.
Misconi, N.Y.: 1980, in Solid Particles In the Solar
Consolmagno, G.J.: 1979, Icarus 28, 398.
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Dordrecht, 49.
Delsemme, A.H.: 1976, Lecture Notes in Phys._48, 314.
Morfill, G.E., and Grun, E.: 1979a, Planet. Space Sci.
Dermott, S.F., Nicholson, P.D., Burns, J.A., and
27, 1269.
Houck, J.R.: 1984, Nature 312, 505.
— : 1979b, Planet. Space Sci.
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Dohnanyl, J.S.: 1969, J. Geophys. Res., 14, 2531.
: 1970, J. Geophys. Res., Z5, 3468.
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: 1978, in Cosmic Dust (Ed. J.A.M.
Sun and the Heliosphere in Three Dimensions (Ed.
McDonnell), Wiley, Chlchester, 527.
R.G. Harsden) Reidel, Dordrecht, 455.

Dumont, R. and Levasseur-Regourd, A.C.: 1987, this

Morrison, D.A., and Zinner, E.: 1977, Proc. Lunar Sci.
volume.
Conf. 8th. 841.

Fechtig, H.: 1987, this volume. Nauman, R.J.: 1966, "Thp near earth meteoroid
environment", NASA TND 3717.
Greenberg, J.M: 1973, In Evolutionary and physical
Properties of Meteoroids (eds. C.L. Hemenway, P.M. Parker, E.N.: 1964, Astrophys. J. 139, 951.
Millman and A.F. Cook), NASA-SP 319, 375.
Pitz, E., Leinert, C., Schulz, A., and Link, H.: 1979,
Grun, E. and Zook, H.A. (1980): Solid Particles in the Astron. Astrophys. 24. 15.
Solar System (Eds. I. Halliday and B.A. Mclntosh)
Reidel, Dordrecht, 293. Robertson, H.P.: 1937, Mon. Not. Roy Astron. Soc. 97.
423.
Grun, E., Zook, H.A., Fechtig, H., and Giese, R.H.:
1985, Icarus 6_2, 244. Singer, S.F., and Bandermann, L.U.: 1967, in The
Zodiacal Light and the Interplanetary Medium (Ed.
Hassan, M., Wallis, M.K.: 1983, Planet, Space Sci 31. J.L. Ueinberg), NASA SP_150, 379.
1.
Hauser, M.G., Gillet, F.C., Low, F.J., Gautier, T.N., Whipple, F.L.: 1967, in The Zodiacal Light and the
Beichman, C.A., Neugebauer, G., Aumann, H.H., Baud, Interplanetary Medium (Ed. J.L. Weinberg), NASA-SP
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262
 Wood, J.A.: 1986, in Interrelationships AmonE
It] sson-Steel : Doesn't the absence of retrn-
Circumstellar. Interstellar and Interplanetary Dust
grade dust (with a collisional lifetime nf
(Eds. J.A. Nuth III, and R.E. Stencel), NASA-CP A / 5 times less than prograde) imply some
2403. characteristic time-scale to the events oc-
curing?
Wyatt, S.}\, and Whip, ! F.L.: 1950, Astrophys. J. Grtln: We have considered only particles in
prograde orbits, because there is nu observa-
111. 134. tional evidence for retrograde orbits in
significant abundance. Therefore, the life-
Zook. H.A.; 1980, in Solid Particles In the Solar times we have calculated apply to prograde
System (Ed. I. Halliday and B.A. Mclntosh) Reidel, orbits .
Dordrecht, 375.

Zook, H.A., and Berg, O.E.: 1975, Planet. Space Sci.

21. 183.

Zook, H.A., Lange, G., Grvin, E. , and Fechcig H. : 1984,

Lunar and Planet. Sci. XV, 965.

D I S C U S S I O N

Giese; There is a debate going on whether

one can take the intensity change of zodiacal
light with location of the Helios s/c really
as a dependence of number density n/vr
on solar distance r or not. ,Since only the
product n.o can be derived (o is the average
differential scattering cross section), a
local change of <5 could make a law n/</r
acceptable. What would be in this case the
consequences for your model?
GrUn: There are reasons to believe that the
scattering does not change too much with r:
Helios did not see any change in the colour
of zodiacal light. However, polarization data
indicate some change in the particle proper-
ties which may or may not have the effect to
change the scattering properties in the sense
required to decrease the exponent of the
radial density distribution. Therefore I do
not believe that the density distribution
n « r 'has an exponent/1 a«- low as 1. But if
we assume, for an exercise, that ^" = 1, then
I can show that this leads to a contradiction.
A distribution with ?* = 1 would be set up
by Pointing-Robertson effect alone. Since we
know from the size distribution that zodiaca1
light particles are not much affected by col
lisions, no extra source for these particles
inside 1 AU is allowed, and all the zodiacal-
light particles would originate from outside
the Earth's orbit. On the other hand, we know
from our calculations of the collisional bal-
ance that zodiacal light particles are pro-
duced in great abundance from collisions of
larger particles. This contradicts sharply
the conclusion we derived from a^> = ]
value. '
Olsson-Steel: I believe that in fact the true
flux of meteoroids (masses 10- - 10 gm) is
20 or 30 times higher than we have thought
until now (paper to be presented at this
meeting). This would imply a much higher sup-
ply to the zodiacal dust cloud.
GrUn: No. We have used only the mass slope
from meteor data, not the absolute value. The
slope nicely fits the slope derived from the
lunar microcrater distribution. Because of
this close fit, I believe we have used the
right meteor flux.

263
 THE CONTRIBUTION OF PERIODIC COMETS TO THE ZODIACAL CLOUD

L. Kresak and M. Kresakova

Astronomical Institute, Slovak Academy of Sciences, 8A228 Bratislava, Czechoslovakia

The dust production rates of all the known periodic comets, calibrated by the measurements
from the 1986 apparition of comet Halley, are used to compute their dust input into the region
inside the earth orbit, and the resulting dust fluxes at R = 1 AU. The spatial distribution of
the fresh ejecta and the temporal variations of their accumulation are reconstructed. The vi-
sible release of dust is evidently insufficient to maintain the zodiacal cloud in equilibrium.
It is suggested that the progressive decay of the dark matter, including extinct cometary nuc-
lei, their fragments, and products of asteroidal collisions, represents the dominant source of
replenishment of the interplanetary dust complex.

1. INTRODUCTION and counted separately, and empirical corrections

for the instrumental effects were applied. For the
The cometary activity is the only directly ob- derivation of the relevant formulae and for the ca-
servable source of the interplanetary dust. Its ef- libration by P/Halley see Papers I and II. Here we
ficiency depends not only on the dust production shall use for the mean dust production rate D the
by individual comets but also on their revolution relation
periods. When the period is long, essentially all
the smaller dust particles are removed immediately D = C (1 - e ) 1 - 5 (1 (8- '•)

from the solar system on hyperbolic orbits by the II is the absolute total magnitude, q the peri-
solar radiation pressure and what remains, spends helion distance in AU, and e the eccentricity of
only a small fraction of each revolution within the the osculating orbit. The calibration factor C is
inner planetary region. Therefore, the share of the 1.25 x 101i* kg per century, or 3.96 x 10^ kg per
periodic comets (P -= 200 yr) should be decisive for second.
the maintenance of the zodiacal cloud, consisting Owing to the low ejection velocities of the dust
of short-lived dust particles. particles, of the order of 10"'* of the orbital ve-
The earlier estimates (Whipple, 1967; Delsemme, locities of their parent comets, one can assume
1976a; RBser, 1976; Kresak, 1980) have indicated that ohe initial orbits are identical. In fact,
that the present population of periodic comets is this approximation holds good for larger particles.
entirely insufficient to maintain the zodiacal Smaller particles are repelled by the differential
cloud in equilibrium. Various possibilities were solar radiation pressure into larger orbits of
suggested to explain this discrepancy (as summa- longer revolution period, and below some critical
rized by Delsemme, 1976b), and the long-term stabi- size lost on hyperbolic orbits. Since most of the
lity of the cloud was seriously questioned. dust release takes place around the comet's peri-
The 1986 apparition of comet Halley has made it helion, the orbits remain essentially unchanged in
possible to estimate the mass lost rates of comets this region. This effect tends to accelerate the
more reliably than before. In a previous paper dispersion oT the dust particles along the comet's
(Kresak and Kresakova, 1987a - thereinafter refer- orbit, and thereby also the operation of differen-
red to as Paper I) we have computed the mass loss tial planetary perturbations. It reduces the input
rates of all the known periodic comets over the of smaller particles, but this does not seem to
last two centuries. In the present paper we concen- play a significant role in the case of short-period
trate on their dust input close to, and inside of, cornets.
the earth orbit, where the zodiacal cloud is den- Knowing the total dust production rate D, its
sest. The evaluation of the current dust input by long-terra average contribution to any region passed
individual comets, its variability, and the recon- by the comet can be determined quite easily, being
struction of the resulting spatial distribution of proportional to the fraction of the orbital period
the fresh dust particles can be used not only to spent within it. For a heliocentric spherical shell
check their contribution to the zodiacal cloud but with inner radius R^ and outer radius R o , the con-
also to judge, by comparison, about the nature of version factor is proportional to the difference
the other sources. in the mean anomaly of the two crossing points, i
e. (Mo - MjJ/i80 0 . The mean anomalies can be compu-
2. CALCULATION OF THE DUST INPUT ted in the usual way from the true anomalies, de-
fined by the equation of the orbital ellipse as a
The estimates of the mass loss rates of indivi- function of a, «, co and H. The angular elements
dual periodic comets, as presented in Paper I, were SI, CJ and i also define the. positions of the pairs
based on some simplifying assumptions which must of crossing points, with the true anomaly as the
be reiterated. It was assumed that the mass loss variable depending on R. The flux of dust at these
rate of each object is proportional to its total points is given by the dust production divided by
brightness; that both of these quantities vary with the revolution period.
the inverse fourth power of the heliocentric dis- In order to get insight into th.. temporal varia-
tance; anrt that the gas-to-dust ratio is uniformly tions of these quantities, they were computed, fo>-
3:1. To account for the changes of the orbits by each comet, fqr three equidistant epochs : 1800.0,
planetary perturbations, the long-term integrations 1900.0 and 2000.0. All the comets of P < 200 years
by Carusi et al. (1985) were used. For the absolute observed between 1785 and 1985, with q ^ 1.1 AU at
total brightness, a list based on the maximum va- the date in question, were included. For the comets
lues in the individual comet apparitions (Kresak of Jupiter family (P -= 20 yr) , the osculating or-
and Kresakova, 1987b - thereinafter referred to as bital elements were taken from the integrations by
Paper II) was adopted. In this list, only irregular Belyaev et al. (1986). The only exceptions were
brightness bursts of limited duration were excluded P/Pons-Winnecke in 1800 and P/Grigg-Skjellerup in

265
 Table 1

Comet 1.0 0.9 0.8 0.7 0.6

3 P/Encke 3.31 0.340 8.3 1568 10994 3003 1604 1541 1485 1440 1415 1438
29 P/Grigg-Skjellerup 4.82 0.732 12 .2 5 22 6 5 5 7 10 __
21 P/Tuttle-Giacobini-Kresak 5.19 1.098 10 .4A 93 11 4 — .— __
504 P/Blanpain 5.26 0.952 8.3 86 189 104 156 189
73 P/Schwassmann-Wachmann 3 5.27 0.960 11 .8A 3 7 4 6 7
6 P/Brorsen 5.28 0.808 8.6 94 360 113 103 121 238
9 P/Pons-Winneoke 5.71 0.822 8.6 82 282 91 85 103 179 __ __
4 P/Biela 6.71 0.901 7.1 222 508 210 241 508 __
71 P/Denning-Pujikawa 9.20 0.793 13 . 1A 1 2 1 0 1 1 0
8 P/Tuttle 13.78 1.036 6 .9 8C 40 83 __
11 P/Crommelin 28.1 0.753 9 .7 7 5 2 1 1 2 2
2 P/Temp^l-Tuttle 33. r 0.974 8 12 3 2 3 3
505 P/Pons-Gambart 5".5 0.807 7,4 22 7 2 2 2 5
519 P/Dubiago J9.3 1.095 8,.7A 3 __ 0 0 __
1't P/Pons-Brooks 72.6 0.777 4,.0 443 113 39 28 32 47 33 __
27 P/Brorsen-Metcalf 73.1 0. i85 7..7 47 14 4 2 2 2 2 2 3
506 P/DeVico 75.2 0.665 6..3 76 21 6 4 4 5 6 6
1 P/Halley 76.3 0.587 2.,8E 2550 714 212 119 121 128 144 217 105
507 P/Swift-Tuttle 115.3 0.982 3..9 170 9 9 15 9 — __
517 P/Mellish 142.3 0.187 7..6 284 37 13 5 5 5 5 4 4
38 P/Herscnel-fiigollet 162.3 0.749 7..9 6 0 0 0 0 0 0
520 P/Wilk 199.3 0.633 9.,4 2 0 0 0 0 0 0 0 --
1800 - Total 5862 13287 3872 2468 2655 2103 1642 1645 1550
3 P/Encke 3.30 0.341 8.9 898 6303 1721 920 LS4 852 826 812 826
29 P/Grigg-Skjellerup 4.83 0.752 11..8 6 29 8 7 8 10 12 __
504 P/Blanpain 5.16 0.953 10. 3B 14 31 17 26 31 —
6 P/Brorsen 5.45 0.588 9. 5C 83 358 96 61 62 65 72 110 49
46 P/Honda-Mrkos-Pajdusakova 5.46 0.610 10.,8 23 99 27 18 18 19 22 40 —
73 P/Schwassmann-Wachmann 3 5.55 1.069 11. 8 2 — 3 5 — — -- — —
533 P/Tritton 5.55 1.078 10.6A 7 8 12 — — — —
9 P/Pons-Winnecke 5.83 0.923 8.9 47 113 51 65 113 — _-
24 P/Giacobini-Zznner 6.47 0.932 9.4 26 52 25 33 52 _-
17 P/Finlay 6.56 0.969 8.9 37 51 36 58 51 — — _-.
4 P/Biela 6.67 0.860 9.5C 28 73 26 26 35 37 — -- —
71 P/Denning-Fujikawa 8.83 0.748 11. 4D 5 10 3 3 3 4 5 — —
8 P/Tuttle 13.62 1.014 7.4 58 27 64 — —
11 P/Crommelin 27.5 0.739 8.8 15 11 3 2 3 3 5
2 P/Tempel-Tuttle 33.4 0.973 8.2 12 3 2 3 3 — — — —
jO5 P/Pons-Gambart 57.8 0.810 7. 4 22 7 2 2 2 4 — — —
14 P/Pons-Brooks 71.7 0.776 4.1 411 106 36 27 30 44 32
g"7 P/Brorsen-Metcaif 72.0 0.484 7.7 48 14 4 2 2 2 2 2 4
50b P/DeVico 73.9 0.664 6.3 77 22 7 4 4 5 6 6 —
1 P/Halley 76.1 0.587 2. 8B 2550 716 212 119 122 128 144 219 103
507 P/Swift-Tuttle 120.0 0.963 3.9 171 12 9 12 12 —
517 P/Mellish 145.4 0.190 7.6 265 34 12 5 5 4 4 4 4
38 P/Herschel-Rigollet 154.9 0.748 7.9 6 1 0 0 0 0 0 — —
520 P/Wi]k 187.4 0.619 9.4 2 0 0 0 0 0 0 0 --
1900 - Total 4813 8045 2335 1474 1440 1177 1131 1194 985
3 P/Encke 3.30 0.339 9.6 479 3363 919 491 471 454 440 432 439
29 P/Grigg-Skjellerup 5.11 0.996 11. 5 4 3 5 12 3 — — — —
46 P/Honda-Mrkos-Pajdusakova 5.26 0.529 11. 0 28 1£5 33 20 20 20 21 25 39
73 P/Schwassmann-Wachmann 3 5.35 0.938 11. 6 4 10 5 7 10 — — — —
21 P/Tuttle-Giacobini-Kresak 5.44 1.054 9.8D 167 19 39 — — — — —
48 P/Wirtanen 5.45 1.060 8.7 45 53 99 — — -- _-
24 P/Giai.obini-Zinner 6.61 1.034 8.9 31 30 69 — — — — —
17 P/Finlay 6.76 1.033 10. 1 10 — 10 22 — — — — —
71 P/Denning-Fujikawa 9.05 0.791 13. 1 1 2 1 0 1 1 0 — —
8 P/Tuttle 13.60 1,030 8.1 29 — 14 30 — — — — —
11 P/Crommelin 27.7 0.747 8.3 25 18 6 4 5 6 7 — --
2 P/Tempel-Tuttle 33.1 0.975 9.0 6 1 1 2 1 -- — — --
505 P/Pons-Gambart 56.4 0.822 8.4B 9 3 1 1 1 2 — — --
27 P/Brorsen~Metcalf 69.9 0.483 8. 1 34 11 3 2 2 2 2 2 3
14 P/Pons-Brooks 71.2 0.781 4.4 308 80 27 20 23 35 22 — —
506 P/DeVico 74.9 0.660 6.3B 77 21 7 4 4 5 6 6
1 P/Halley 76.0 0.587 2. 8B 2555 718 213 120 122 128 145 220 103
507 P/Swlft-Tuttle 124.6 0.959 3.9 167 12 8 11 12 — — — —
517 P/Mellish 153.9 0.197 7.6 229 28 9 4 4 4 3 3 3
38 P/Herschel-Rigollet 154.9 0.748 8.3 4 1 0 0 0 0 0 — —
520 P/Wilk 187.4 0.619 9- 4 2 0 0 0 0 0 0 0 —
2000 - Total 4214 4397 1364 957 679 656 647 689 587

266
 Table I - continued to the dust input into the region of R < 1 AU and
to the dust flux through R = 1 AU, is summarized
in Table II. OJF means comets of the Jupiter fami-
Comet 0.5 0 .4 0.3 0.2 0.1 ly other than P/Encke, and OHT comets of Halley
type other than P/Halley.
While 70 % of the dust production fall on the
3 P/Encke 1630 2045 comets of Halley type (and 50 % on P/Halley alone)
27 P/Brorsen-Metcalf 2 their long orbits make their share in the dust in-
517 P/Mellish 4 4 5 2 put inside the earth orbit and in the dust flux
through R = 1 AU much smaller, only a little over
1800 - Total 1636 2049 5 2 10 %. Their actual contribution is further reduced
3 P/Encke 938 1165 by a higher size limit for the D-particles elimi-
27 P/Brorsen-Metcalf 2 nated by the solar radiation pressure. Here comet
517 P/Mellish 4 4 4 2 Encke clearly dominates, providing 80 % of the in-
put and 77 % of the flux. The progressive fading
1900 - Total 944 1169 4 2 of this comet, accompanied by a decrease of its
3 P/Encke 496 631 dust production, results in an appreciable decline
27 P/Bro rs en-Me tcalf 1 of all of these parameters. In the total input and
517 P/Mellish 3 3 4 1 flux it makes a ratio of 3:1 over 200 years ! The
values for 2000 will be probably subject to some
2000 - Total 500 634 4 1 correction upwards by the contribution of some co-
mets so far undiscovered - and also by that of P/
Hartley 2 and P/Machholz, discovered in 1986.
2000, because these comets were passing close to
Jupiter at that time, so that their osculating ele- Table II
ments weie not representative for the perihelion
passages around which most of the mass loss occurs.
Here the elements were replaced by those for the Percentage
closest 5000-day Julian Date, according to the in-
tegrations by Carusi et al. (1985). For the comets
P/Encke OJF P/Halley OHT
of Halley type (20 yr < P < 200 yr) the osculating
elements for the nearest perihelion passage were Total dust production ]Q :
used, since otherwise the difference between the
heliocentric ami barycentrj..5 motion (Carusi et al., 1800 186 kg/s 26.7 11.5 43.5 18.3
1986) would become significant. For the absolute 1900 153 kg/s 18.6 7.0 53.0 21.4
magnitudes the same basic data as in Papers I and 2000 134 kg/s 11.4 7.6 60.6 20.4
II were used. The weighted means from all observed Mean 157 kg/s 19.8 8.9 51.4 19.9
revolutions falling at least partially within ± 50 Dust input 1(1) into R < 1 :
years of the epoch in question were adopted. Excep-
tions from this rule are marked by letters in Ta- 1800 4.21 kg/s 82.7 10.3 5.4 1.6
ble I. 1900 2.55 kg/s 78.3 10.2 8.9 2.6
The results of our computations are presented in 2000 1.39 kg/s 76.5 3.2 16.3 4.0
Table I. It lists, in succession for the three ba- Mean 2.72 kg/s 80.3 9.0 8.4 2.3
sic epochs and in the order of increasing orbital Dust flux F(1) through R = 1
periods, the following quantities : the name of the
comet preceded by its number in the catalogues by 1800 38.2 kg/s/yr 78.6 13.8 5.6 2.0
Carusi et al. (1985) and Belyaev et al. (1986); the 1900 23.0 kg/s/yr 74.9 12.6 9.2 3.3
revolution period P, in years; the perihelion dis- 2000 12.4 lcg/s/yr 74.2 3.6 17.2 5.0
tance q, in AU; the absolute total magnitude H; the Mean 24.5 kg/s/yr 76.7 11.7 8.7 2.9
mean dust production D, in 10° kg/century; the mean
dust input 1(1) into the heliocentric sphere of 1
AU radius, in 10^ kg/century; the mean dust flux F The variations of the dust input are small for
from this production through the heliocentric sphe- the comets of Halley type, the revolution periods
rical surface of radius R :> q and R < Q, in kg/s; of which are comparable with the period covered by
and the mean dust input into spherical shells be- the computations, and orbits rather stable. For
tween B = 1.1 and 1.0 AU, 1.0 and 0.9 AU, etc. The typical comets of Jupiter family a drop by a fac-
letters added to H have the following meaning : A, tor of 10 between 1800 and 2000 is indicated, with
the comet was first discovered more than 50 years the reservation mentioned above. This reflects not
after the respective epoch - H from the next epoch only the disappearance of P/Biela and P/Brorsen,
was adopted. B, the comet was lost more than 50 yr which were very active in the 19th century, but
before the respective epoch - H from the preceding also the orbital changes of other comets by plane-
epoch was adopted in the case of one missed return, tary perturbations. In fact, one half of such co-
a correction of + 1 mag applied after two missed mets has changed during each century. Integrations
returns, + 2 mag after four missed returns, and the over 800 years (Carusi et al., 1985) show that
object was cancelled after eight missed returns only three comets of P < 20 yr have remained with-
(P/Blanpain). C, an extinct comet - H fitted to the in q <; 1 all the time : the exceptional P/Encke,
fraction of the 100-yr period during which the co- the extinct P/Brorsen, and the absolutely faintest
met was active (P/Biela, P/Brorsen). D, a bursting P/Denning-Fujikawa, with spectacular intermissions
comet - H corrected for the contribution of the of activity (Kresak, 1986). Another 15 comets were
outbursts to the absolute lightcurve (P/Denning- passing through q = 1 every 150 years, on the av-
Fujikawa, P/Tuttle-Giacobini-Kresak). E, a long se- erage. For those captured into a temporary libra-
ries of earlier apparitions does not indicate any tion around the 2:1 resonance with Jupiter, like
definite trend - the mean H from the last returns P/Pons-Winnecke or P/Haneda-Campos, the passages
was adopted (P/Halley). in and out recur rather periodically.
The differences between the two types of peri-
3. THE SHARE OF INDIVIDUAL COMETS odic comets in the rate of orbital evolution imply
a substantial difference in the wandering of the
The relative contribution of different comets crossing points on the sphere of R = 1 AU. While
or comet types to their total dust production D, those of the Hallev type are relatively stable,

267
 those of the Jupiter family can suddenly skip over In Figure 1 these are comparea with the H " 1 < 3 de-
tens of degrees. This problem, essential for the pendence of the spatial density of the dust, as
recurrence of meteor showers, will be discussed in determined by Leinert et al. (1981) from the meas-
more detail elsewhere (Kresak and Kresakova, in urements on the Helios space probes. The agreement
preparation). However, one important point must be is unexpectedly good, but only thanks to the domi-
stressed here. The comets of the Jupiter family nant contribution of P/Encke. When this comet is
tend to produce strong temporary meteor showers at omitted, any dependence on R vanishes in irregular
the time when one of the crossing points passes the fluctuations, produced by local enhancements in
plane of ecliptic but, except of P/Encke, they do the ranges where the most productive comets pass
not produce permanent showers farther from the pas- their perihelia. The lower part of the figure as-
sage, like some comets of Halley type (P/Halley, sumes an oversimplified model in which the orbits
P/Swift-Tuttle, P/Tempel-Tuttle). Hence, it appears are not liable to perturbations, and each comet
improbable that any of them could have raado a sub- has the same initial dust supply (i.e., lifetime
stantial contribution to the maintenance of the inversely proportional to the dust production
zodiacal cloud in the past. rate). In spite of the minor peak at the perihe-
lion of P/Encke, the general trend, resembling an
4. THE SPATIAL DISTRIBUTION R^ dependence, is absolutely irreconcilable with
the observations. This failure underlines the im-
By summing Up the I(R) values from Table I, and portance of some effects neglected in this simpli-
dividing them by the volumes of the 0.1 AU broad fication, or all of them: the broad variety in the
spherical shells, the variations of the dust input initial dust supply of different comets; the oper-
with heliocentric distance can be reconstructed. ation of planetary perturbations, increasing the
dust production rate after each reduction of the
perihelion distance, and vice versa; the transfer
of the dust particles inwards by the Poynting-
Robertson drag; and their decay at smaller helio-
centric distances. Unfortunately f the available
data do not allow to assess the relative impor-
tance of these effects in their compound operation
resulting in the observed increase of the density
towards the Sun. For the innermost region we have
practically no observational evidence, and only
one periodic comet (P/Mellish) passes through R =
0.2 AU. Another case, not included in our computa-
tions, is the recently discovered P/Machholz.
The distribution of the dust input with respect
to the ecliptical plane can be determined from the
distribution of the points in which the individual
orbits cross the heliocentric spheres of varying
R. In Figure 2 two alternatives are compared, one
based just on the number of crossing points, and
the other with each crossing point weighted by the
computed dust flux through it. Absolute values of
the latitudes are used, since the distribution is
roughly symmetrical with respect to the ecliptic.
The two solutions are in excellent agreement, ap-
parently due to the fact that the inclination of
the orbit of P/Encke is rather typical for short-
period comets.

20 •

15 •

® o • m
*

10
O
• "e o

5
0-5 -

• i i ) i
0-0 0
0-2 0-4 0-6 0-8 VO

Figure 1. Above, the relative dust input I|t, re- Figure 2. The medians of the absolute ecliptical
ferred to the average at R < 1 Ali, as a function of latitudes B of crossing points with the sphere of
the heliocentric distance R. Below, the same assum- R = 1 AU, as a function of the heliocentric dis-
ing an equal dust production for all comets. Open tance R. Open circles, data weighted by the fluxes
circles, all comets; full circles, P/Encke omitted. F through these points; full circles, each cros-
The circled areas are proportional to the inputs sing point counted once. The circli-d areas are
on which the data are based. The full curve corre- proportional to the total fluxes, and to the num-
sponds to I R « R-1-3, the dashed one to IJJ oc R 2 . bers of points included, respectively.

268
 One half of the total dust input is concentrated
within + 12.5° of the ecliptical plane, irrespec-
tively of the heliocentric distance. This allevi-
ates the reconstruction of the distribution perpen-
dicular to this plane, as all the crossing points
can be taken together. The results are presented in
Figure 3, separately for the comets of the Jupiter
family, those of Halley type, and all comets. There
is no weighting by the dust input, but the summa-
tion of the data from three epochs and from helio-
centric spheres 0.1 AU apart makes the weights of
individual comets roughly proportional to their
average path length within H = 1 AU.
For a spherically symmetrical distribution, the
cumulative numbers of the crossing points should
follow the dashed diagonal. This is reached by ad-
justing the horizontal scale to x = sin B, and fit-
ting the vertical scale to the population at low
latitudes. The data points follow the diagonal
rather closely up to B = 14° for the Jupiter family
and up to B = 28° for the comets of Halley type.
Then a steep drop appears in both samples. A compa-
rison with the percentages on the left-hand scale
shows that the dust input into the zone around the
ecliptic is 3.6 times larger than its overall value
10 20 30 40 50 60 B for the Jupiter family, but only 1.5 times larger
for the comets of Halley type. For all the comets
taken together the ratio is 2,3, and the trend can
be tentatively reconstructed, as indicated by the
dotted line. The drop of the density is steep in-
deed: from 100 # at B = 15° to 50 % around B = 20°,
30 % around B = 30° and £0 % around B = 40° to 15 %
at B =. 90°.
The distribution in longitude is rather irregu-
lar. At R = 1 AU, P/Encke and P/Halley enhance the
density in the first and third quadrant, producing
an oblong shape of the cloud. The distribution at
smaller heliocentric distances is governed by the
perihelion arc of the orbit of P/Encke in the se-
cond and third quadrant.

5. CONCLUSIONS

The dust productions, inputs and fluxes given in

Tables I and II are still subject to considerable
uncertainties. Just the uncertainties in the abso-
lute magnitudes of individual comets may account
for differences of tens of percent in the computed
values, and the lightcurve irregularities add to
this. There may be significant departures from the
adopted H~* dependence of the brightness, and the
10 dust production may follow a different law. Recent
observations of P/Halley and other comets have de-
monstrated that the dust release tends to occur in
irregular jets, and that the dust-to-gas ratio va-
ries appreciably. The main source of uncertainty is
the limitation of observational evidence to smaller
dust particles which are not decisive for the total
mass loss. The extrapolation to higher size ranges
is still an open problem (McDonnell et al., 1986).
For these reasons our numerical data must be taken
with caution, in particular where they are given,
for the sake of conformity, to more significant di-
gits. The existing estimates of the mass of the zo-
diacal cloud and its rate of replenishment are very
approximate, too.
In spite of these limitations, the evaluation of
the present contribution of periodic comets to the
500 zodiacal cloud implies some general conclusions. In
each century, there are only about 15 to 20 active
400
comets ejecting dust at R < 1 AU, with revolution
- 300 periods less than 200 years. Their individual input

• 200 Figure 3. Cumulative numbers N of crossing points

with heliocentric spheres of radii H = 1.0, 0.9 AU
- 100 etc. as a function of their absolute ecliptical la-
titudes B. From top to bottom: comets of Jupiter
family, collets of Halley type, and all periodic co-
10 mets taken together.

269
 rates cover a range of four orders of magnitude, extinct remnants and fragments of cometary nuclei,
95 % of the total falling on about 5 objects only. to meteorite- and meteoroid-sized objects disinte-
For the last two centuries, P/Encke dominated the grating gradually into dust. Observable splitting
direct dust input into this region by 80 % of the of periodic comets occurs, on the average, once per
total, followed by P/Halley with 8 %. The next two 80 revolutions, which is only a fraction of their
comets, P/Brorsen and P/Biela with 2 to 3 % each, mean active lifetimes; and the terrestrial influx
have already disappeared more than 100 years ago, of low-density fireballs indicates an overabun-
although they were bright at their last apparitions dance of otherwise unobservable objects with sizes
and P/Biela consisted of two active components. It of the order of 10 m (Kresak, 1978). From among the
is difficult to believe that their disintegration long-period comets, those of the Kreutz group de-
into interplanetary dust has stopped at the moment serve special attention, due to their large total
when they ceased to be optically active. This lends mass, most effective splitting processes, and rela-
support to the viewpoint that the p.ocesses in co- tively short revolution periods. Products of aste-
metary comae are not the only source of dust. roidal collisions can also contribute to the input,
The calibration of the dust production rates by but their transfer closer to the Sun poses some dy-
the observations made at the 1986 apparition of P/ namical problems. The best acceptable scenario puts
Halley has not shattered the previous conclusion by the source into the outer zone of the asteroidal
Whipple (1967) and others, that the ejecta from the belt, where collisional debris of proper size may
present population of periodic comets are unable to be brought by the solar radiation pressure into the
maintain the zodiacal cloud in a state of equilib- vicinity of the orbit of Jupiter, and start there
rium. Our results point to appreciable variations orbital evolutions similar to those of the Jupiter
of their contribution on a time scale of a few cen- family of comets. The Poynting-Robertson drag alone
turies, but the input remains all the time below is hardly sufficient to maintain the zodiacal cloud
the needs. When compared with Whipple's round value in its present shape, if the evolution starts with
of IO'I kg/s, the average dust production of all pe- low-eccentricity orbits far outside, and has to
riodic comets makes 2.4 %, that of the periodic co- pass through a number of resonances with Jupiter.
mets of q < 1 All 1.6 )!, and the direct Input into We conclude that the interplanetary dust parti-
R <= 1 AU 0.03 %. cles move in orbits similar to those of short pe-
We have found that one half of the total dust riod comets, result from a stepwise fragmentation
input by periodic comets at B < 1 AU concentrates of their parent objects, and only a small fraction
within the ecliptical latitudes of ± 12.5° , drop- of the input manifests itself in the comae and
ping abruptly beyond ± 15°. Omitting P/Encke, there tails of active comets.
is no definite trend of the input with the helio-
centric distance, and the fresh dust cloud assumes
a shape consistent with a narrow single-lobe model. REFERENCES :
This is in conflict with all the observational evi-
dence, as summarized by Giese et al. (1986). When Belyaev N.A., Kresak L., Pittich E.M., Pushkarev
P/Encke is included, however, the situation changes A.N., 1986 : Catalogue of Short-period Comets
drastically. A decrease of the density with helio- (Veda, Bratislava)
centric distance, following very closely the R-1-3 Carusi A., Kresak C., Perozzi E., Valsecchi G.B.,
dependence found by Leinert et al. (1981), appears. 1985 : Long-term Evolution of Short-period Co-
This also expands the equidensity lines, pointing mets (A. Hilger, Bristol)
radially from the Sun, into a shape consistent with Carusi A., Kresak L., Perozzi E., Valsecchi G.B.,
the current models. 1986 : in Exploration of Halley's Comet, ESA SP-
So there is strong circumstantial evidence in 25O/II, 413
support of the idea, first expressed by Whipple Delsemme A.H. , 1976a : in Interplanetary Dust and
(1967) that P/Encke is the main source of mainte- Zodiacal Light, Lecture Notes Phys. 48, 314
nance of the zodiacal cloud. There are only two ob- Delsemme A.H. , 1976b : in Interplanetary Dust and
jections. First, P/Encke presents itself as a comet Zodiacal Light, Lecture Notes Phys. 48, 481
with an extremely low dust-to-gas ratio, and its Giese R.H., Kneissel B., Rittich U., 1986 : Icarus
dust production rate shows no appreciable increase 68, 395
at small solar distances, according to Newburn and Kresak L., 1978 : Bull. Astron. Inst. Czechosl. 29,
Spinrad (1985). And second, searches for records of 129 and 135
its earlier apparitions - when it should have been Kresak L., 1980 : in Solid Particles in the Solar
very bright if its secular brightness decrease is System, IAU Symp. 90, 211
extrapolated back - remained without success (see Kresak L., 1986 : in Exploration of Halley's Comet,
Whipple and Hamid, 1972). On the other hand, there ESA SP-25O/II, 433
are uniquely broad streams of larger meteor parti- Kresak L., Kresakova M., I987ab : in Diversity and
cles, some of them hardly discernible from the spo- Similarity of Comets, ESA SP-278, in press
radic background, which are apparently genetically Leinert C., Richter I., Pitz E., Planck B., 1981 :
associated with this comet (Stohl, 1986; Porubcan Astron. Astrophys. 103, 177
and Stohl, this Volume). Several larger asteroidal McDonnell J.A.M. , Kissel J. , Grtln E. , Grard R.J.L. ,
objects were found to revolve in similar orbits Langevin Y., Olearczyk R.E., Perry C.H., Zarne-
(Napier, 1983), and association with the Tunguska cki J.C., 1986 : in Exploration of Halley's Co-
impact also appears very probable (Kresak, 1978). met, ESA SP-25O/II, 25
From the dynamical point of view it is clear that Napier W.M. , 1983 : in Asteroids, Comets, Meteors I
decoupling of the aphelion of P/Encke from Jupiter (Uppsala University Press), 391
would have required a long or strong operation of Newburn R.L., Spinrad H., 1985 : Astron. J. 90,
nongravitational effects, which also points to a 2591
great original size and dust supply of the parent Rflser S., 1976 : in Interplanetary Dust and Zodia-
body. cal Light, Lecture Notes Phys. 48, 319
Whatever may be the share of P/Encke, or of the Stohl J., 1986 : in Exploration of Halley's Comet,
family of objects associated with it, in building ESA SP-25O/II, 225
up the zodiacal cloud, it appears almost certain Whipple F.L., 1967 : in Zodiacal Light and the In-
that the dark matter, not involved in the optical terplanetary Medium, NASA SP-150, 409
display of cometary activity, plays a fundamental Whipple F.L., Hamid S.E., 1972 : in The Motion,
role here. The parent bodies may range from larger Evolution of Orbits, and Origin of Comets, IAU
objects like 3200 Phaethon and cometary nuclei ex- Symp. 45, 152
periencing a dormant phase (Kresak, 1986), through

270
 D I S C U S S I O N

Shulman: I do not understand how you have Kresak: Our results are based on the assump-
estimated the dust production of comet Encke, tion of 1:3 dust-to-gas ratio, as an average
because nobody has ever seen any traces of estimate from the in situ measurements of
continuum in its spectra. P/Halley (see e.g. Whipple, ESA SP-25G7II,
Krerak: We have assumed the same dust-to-gas 2B1). The larger particles, undetectable
ratio for all periodic comets, because the due to their low optical efficiency and
present information on a great majority of low impact rate, are included in what we
such objects is very limited. Also, the size call the dark matter. The disproportion
distribution of the released dust particles between the required and observed input
may substantially differ from one comet to implies a dominant share of larger solid
another. P/Encke is indeed a gaseous object objects, liable to further desintegration.
according to optical observations. On the I think we agree on this point.
other hand, there are uniquely broad streams Hajduk: A comment in connection with Dr. Shul-
of meteoroids associated with it, which man s question: There is no doubt that large
points to a substantial contribution of the particles are released from P/Encke, as we
so'id component to the total mass loss. observe them in the huge complex of Taurid
Fechtig: I think one should also expect large showers. The contribution of these particles
particles from long-period comets, which then to dust/gas ratio depends on the mass dis-
could be the targets for .dust production by tribution index and its evolution (Porubcan
collisions. and Stohl, TS-2, this meeting; Hajduk A.
Kresak: This is certainly true, but the pro- and Kapisinski I.: ESA SP-278, in press).
portion of such objects should be very limited. Olsson-Steel: Isn t the simplest solution to
This is evidenced by their low proportion the problem of non-balance (apparently)
among the meteors - in spite of the high lu- between cometary dust production, the meteor-
minous and ionizing efficiency at their high oid flux, and the supply to the zodiacal
geocentric velocities - and also by the cloud, a hypothesis that the present complex
oblateness of the zodiacal cloud. is not in a steady-state? (i.e. many more
Grun: What do you mean by the dust production comets ,vlO - 10 years ago).
rate? We know, at least from the Halley in Kresak: I have mentioned that just within
situ measurements, that much mass is carried the last two centuries there was a change
by large particles m ^ l O " g, which are invis- by a factor of three. Certainly, temporal
ible to other methods (except meteor studies) variations of much larger amplitude may
Most of these large particles move on orbits occur, but these should be due to the
very close to the parent comet and therefore contribution of exceptional objects rather
are not lost. As pointed out by Dr. Crifo, th'- th3n to the varying number of comets involved.
uncertainty of the dust to gas mass ratio is Anyway, there is strong circumstantial
large (0,3 to 20), because of the uncertainty evidence for the dominant role of the dark
of the large particle production. matter, which we do not observe in cometary
comae and tails.
 EVOLUTION EQUATIONS FOR INTERPLANETARY DUST
1/
HI. Banaszkiewicz, I. Kapisinsky{2/

1/ Space Research Centre, Polish Academy of Sciences, 00716 Warsaw, Poland

21 Astronomical Institute SAV, 84228 Bratislava, Czechoslovakia

Kinetic equations for the distribution function of dust particles in mass and
element spaces are formulated. Erosive as well as catastrophic collisions are
taken into account. Sputtering is also included and radiative effects are consi-
dered. Initial conditions are derived from tha Interplanetary Flux Model for mass
distribution, and fan or cosine models for spatial density,,

Introduction terms in the kinetic equation.

The distribution function h(m, a, e, i,
Stability of the Interplanetary Dust Com- tn) can be found from the known space -
plex was recently considered in the very com- n(r, p ) and meas - W(m) distributions. We
prehensive review by Griin et al.,(1985). In assume that they are independent and that
the most probable evolutionary scenario that n(r, p ) generates into two distributions:
was found by comparing oollieional gain and nj(r) depending on heliocentric distance
loss rates in different mass intervals the and n 2 ( p ) which is a function of ecliptic
spatial density of small particles would in- latitude. Hence the distribution function
crease on account of fragmentation of large h(t=t 0 ) also separates:
particles. Poynting-Robertson effect is not
strong enough to compete with collisions in h(m,a,e,i,t 0 ) = U(m).f 1 (a,e>.f 2 (i) (1)
determining spatial density. It is interest-
ing to find how fast will evolve spatial den- where fj(a,e) and f2(i) are to be calculated
sities of particles of different sizes and from the integral equations (Haug, 1958):
whether the steady state could be obtained
for some distribution of sources. The second
question immediately follows: will initially
independent mass and spatial distribution
functions couple during the evolution? J±C -1 (2)
To solve this problem one has to con- 2*3 r
struct a kinetic equation for distribution
function of particles in space and mass do-
mains. Some knowledge of the initial veloci- JT/2
ty distribution function is needed. The most
important effects that should be included
into the equation ares gravitational attrac- nJp)
1 = /f . 2.z 2 ' . '2 (3)
tion of the Sun, radiation pressure, Poynt- J lsm i - sin
ing-Robertson effect, collisions: catastro- i-p
phic and erosive, solar wind sputtering. We
ignore, in this paper, Lorentz scattering
and planetary perturbations, as there is no
common agreement on the importance of these where Nip is total number of Darticles.
effects. We solved the Abel-type equation (3) for
the two commonly used distributions n2( P ) :
Kinetic equation fan model ~ exp(-2.1.lsinL,P )l) and cosine
model ~ 0.15+0.85. cos ( |J f° . The obtained
Usually a kinetic equation is formulated distribution functions f2(i) are oresented
and solved in the phase-space of coordinates on Pig. 1. The integral equation (2) has no
and velocities. In case of interplanetary unique solution. We assumed the power law
dust there are reasons to use the space of distribution in major semiaxis independent
elements. First, we can easily eliminate the on the distribution in eccentricity(Leinert
variables on which the distribution function et al.,1983)
should not depend: (J , 0 , M . These elements
are randomized due to the action of planets f l ( a , e ) — e*.f le (e) (4)
and more or less uniform distribution of sour-
ces. The attraction of the Sun and the radia- and tried to find x giving the best fit to
tion pressure force are implicitly included the observed dependence of n ^ ( r ) ~ r"-'-'3.
in the concept of Keplerian elements, while For the exponential function fi e =exp(-e) n we_
the Pojmting-Robertson effect averaged over obtained x=0.85 that gives dependence r" 1 * 2 '
orbital period is given by the well known at r=0.9 AU and r " 1 ' 3 2 at r=0.3 AU. For the
formulae of Wyatt and Whipple (1950) in the Rayleigh distribution fie(e)=e.exp(-2.e^)
(a.e) variables. The most difficult task is which has a maximum at e=0.5 and can be
to describe collisions in the space of ele- close to the distribution of sources (larger
ments. However the probability of collisions meteoroids, comets) we get x=0.9 and for
between two groups of particles with given
;
the heliocentric dependence: r" 1 * 3 3 a t 0.9
.'\, e, i) and random values of remaining ele- 1 29
AU and r" ' at 0.3 AU. leinert et al.
ments was obtained in the papers by Kessler (1983) came to a similar result for the
'I-iei) and Steel and Baggaley (1985). We will Rayleigh distribution,.
use their formulae to generate collisional Collisions between two groups of Darticles

273
 90* i

Pig. 1. Distribution functions of orbit in-

clinations obtained from two model distribu-
tions in ecliptic latitude: fan model and
cosine model. Fig. 2. Regions of motions of particles
with elements (a,e,i)i and (a,e,i)?. Torus
with elements el]=(a,e,i)i and el2=(a,e,i>2 T where collisions can take place is given
take place in a torus T with the cross-sec- by the intersection of these regions.
tion given by the following inequalities in
the (r, |3 ) coordinates (Pig. 2 ) : where t describes inelasticity of collisions
( O * E * 1). Hence, for the collisions with
ni2<!r=inl« which are the most probable ones,
we can assume that the velocities of frag-
inax{q1.q2)-P]1|in«P«rlliax-niin((J1,Q2) ments are the eame as the velocity of their
parent body - m j . If two colliding bodies
have similar sizes mn = mg, the spresd of
fragments velocities Is large. This effect
Collision probability (Steel and Baggaley, leads to mass-elements coupling in the kine-
1985) Pi2(el l t el 2 ) is described by the inte- tic equation.
gral over the torus with the integrand K(r, |3J Small fragments are removed from the sye-
proportional to the time of residence of both tem by the radiation pressure which puts
particles inside the volume element connected them onto hyperbolic orbits ( P - micromete-
with the point (r, |3). oroids effect). The probability that a frag-
ment becomes a P -micrometeoroid is equal
P 12 (el v el 2 )= JJdrdpK(r,(i) (5)
(8)
Two kinds of collisions are considered:
erosive and catastrophic, the latter one oc- oc
i
euring h
when mg. T c 5 m j dd^^.mm i being
being the
the pro-
pro
jectile
til and til;
d target masses, respectively;. ll c
is a function of the square of the relative where _ - - - -jjj- V-t
velocity of the colliding particles and of af f
the physical properties of the particles: is the gravity constant reduced by the ra-
their density and compressive strength S c diation pressure. 0 is the Heaviside func-
(Gru'n et al., 1985). Mean square of the rela-
tive velocity can be found from the formula: tion.
To simplify the equations, instead of a
/Jvr2elK(r,p)drdP continuous lrass distribution following, five
values of the particle masses have only been
(6) assumed: 10 + 2 g and 10-^g for meteoroids
10"°g for the zodiacal dust particles, 10
12 and 10"l^g for (3-micrometeoroids. Special
densities of the corresponding particles
where vfei(r, p ) is an average of four pos- calculated from the Interplanetary Flux Mo-
sible values. del (Griin et al., 1985) are as follows:
Mass distributions of the fragments are
calculated from the formulae for catastrophic 1.7xl0' 21 ,2.9xlO- l6 f 6.4a:10" 12 ,1.6xl0" 9 ,
and erosive collisions, respectively (Pujiwa-
ra et al., 1977; Dohnanyi, 1978). In the case
of isotropic distribution of the velocities * Kinetic equations for the distribution
of fragments and of the same value of the ve- functions h^Ca, e, i, t ) , n=l 5, of the
locity modulus for all the fragments we get particles are:
the following value of the fragments velocity
in the Center of the Mass System coordinates:

(7) ot 1K

274
 G
nll' h l' h k' P ^ ( l " P nll ) }"4 L nk' h n' h k^ + Kneissel: Did you only take into account
prograde'orbits?
Banaszkiewiez: Yes. They seem to be the
>?+ Sources (9) dominant population in the interplanetary
dust complex (Leinert, Space Sci. Rev. 118,
281).

where the second term on the left side de-

scribes Poynting-Rohertson effect. Dlv ope-
rator acts in ta, e, i) apace, with u n being
the velocity field
{,da ae di.,
TE< cTF' W
(Wyatt and Whipple, 1950). On the right side
following collisional terms are represented:
the gain due to catastrophic and erosive col-
lisions of particles with different masses,
the gain due to catastrophic collisions bet-
ween particles with the same mass [P(el, el-y,
elg) is the mass-elements coupling function;
el = (a, e, i)], the loss due to catastrophic
and eroeiTe collisions, the loss due to the
sputtering. G and L are functionals depen-
ding on the distribution functions of colli-
ding particles, on the collision probability
Pip and on the fragmentation function gnkl
wnich gives the number of n-type particles
resulting from collisions of particles of k
and 1 types. Mass loss per unit time due to
erosion and sputtering is transfered into
the number of particles of considered type.
Sputtered mass ratio tPV/jt^ for the (a, e, i)
orbit is calculated by Its averaging over one
orbital period.
The equations can be solved after discre-
tization in the (a, e, i) space.

REFERENCES

Dohnanyi,J.S.: 1978, In Cosmic Dust (Ed. J.A.

M. McDonnell} Chichester), p.527.
Fujiwara.A., Kamimoto,G. and Tsukamoto.A.:
1977, Icarus 31, 277.
Griin.E. , Zook.H.A., Pechtig.H. , Giese.R.H. :
1985, learn* 62, 244.
Haug.U.! 1958, Zeitachr. Astrophye. 44, 71.
Kessler.D.J.: 1981, Icarus 48, 39.
Leinert.C., Roser,S., and Buitrago.J.s 1983,
Astron. Astrophys. 118, 345.
Steel,D.I., Baggaley.W.J.: 1985, Monthly
Notices Roy. Astron. Soc. 212, 817.
Wyatt,S.P., Whipple,F.L.: 1950, Astrophys. J,
111, 134.

D I S C U S S I O N

Grtin: I commend you that you took tremen-

dous task to solve meteoroid dynamics both
in orbii space and mass space. I have one com-
ment. According to your model the zodiacal
particles are fragmentation products of
larger meteor particles. Therefore, the
orbital distribution you put in the model
should be the meteor distribution, and the
zodiacal particle distribution should result.
An important question is: how different can
be both distributions?
Banaszkiewicz: In this paper we have just
concentraced on the derivation of the method
to be used for further computations. So at
the moment I am unable to answer your inter-
esting question.
 LABORATORY CHARGING OF DUST BY ELECTRONS AND IONS

J. Svestka,
( P r a g u e O b s e r v a t o r y , P r a q u e , C z e c h o s l o v a k i a and
Max-Planck-Institut fur Kernphyailc, Heidelberg, PEG)
E. Grun, S. Pinter, S. Schumacher, (Max-Planck-Institut fur Kernphysik,
Heidelberg, FRG)

Dust p a r t i c l e s of sizes between 1 micron and 100 microns from various materials
have been contained with help of quadrupole field in vacuum chamber at pressures
from 10 to 10 mbar and charged by Ar+ ions of energies up to 3 keV as well as
by electrons of energies up to 5 keV. For damping of p a r t i c l e s motion at low
pressures the damping system with photomultipliers and feedback c i r c u i t s was
developed. By charging with Ar+ ions charge-to-mass r a t i o s up t o 4 C kg" 1 were
measured and dependence of maximum charge-to-mass r a t i o on the energy of ions was
studied . Measurements of parameters of secondary electron emission by charging
with electrons at different chamber pressures were s t a r t e d .

There are many cosmic environments where

electric charging of dust particles by electrons
and ions takes place (see e.g. review of Whipple
1981) . The value of charge can have very important t 2
consequences for the life time of dust particles
and many physical phenomena related to them (e.g.
Fechtig et s i . 1979, Grun et a l . 1984, Mendis et

V
1
al. 1984). Theoretical calculations of charging are
based on many unreliable data and therefore we
started experimental work trying to simulate char-
ging processes and improve our knowledge of them. v-u COS II) t
For charging of particles we used a vacuum
chamber similar to one used before by Vedder (1963,
1978). The containment of particles during the
charging process is achieved by the three-dimen-
sional electric quadrupole field generated by volt-
age V-Ucoswt applied to conducting hyperbolic
r i r
i \
surface given in cylindrical
y coordinates by
r^-2z -r Q , two other hyperbolic surfaces
2 2-r Q 2 , two other hyperbolic surfaces given by
rr 2 -2z
- 2 z2 --rQ
- - r 2 are
are grounded,
grounded, see
see Fig.1.The
Fig.1.The equation
equation of
of
motion of contained charge particle is then h (for Figure 1. A cross section of the conducting
details see e.g. Murker et a l . 1959) given by hyperboloids
Mathieu's differential equation and i t s charge-to-
mass ratio Q/M is given by
(1) Q/M - 72r02a,zu)/U ,
For test measurements we used particles from
f - u /2TT is frequency of motion of contained par- glass, amorphous carbon and very loosely bound
ticle in z direction. Particles are falling from a A1 2 O 3 particles with diameters of 10 to 100 /jm, 1
reservoir placed above opening in the upper elec- to 10 pm and 1 to 30 /«n respectively. Particles
trode through the ion (electron) beam. Some of the were charged by A r + ions with energies up to 3 kev
particles which are charged to a certain range of with intention to reach high values of Q/M. Maximum
Q/M are contained in the center of the suspension value of about 4 C.kg"1 was achieved with Al,0,
system. By manipulation with U, V and u is possible particles.
to separate single particle and further charging Further measurements were done with two sam-
car. be performed. Particles are illuminated by HeNe ples of spherical glass particles of average diame-
laser (radiation of which is on the opposite side ters 42 pn\ and 51 pm respectively. Their size dis-
of the chamber absorbed by a light absorber) and tributions are shown in Fig.3. These particles were
observed by low power telescope mounted outside the again charged by A r + ions of energies up to 3 keV.
chamber. For damping of particles motion, which i s The aim was to attain the maximum possible values
needed at pressures below about 10 mbar, the of Q/M and compare them with the theory. According
damping system with two photomultiplers and feed- to theory, the maximum surface electrostatic poten-
back circuits was developed. Schematic diagrams of tial of particles * raax In volts should be equal to
the suspension system are shown in Fig.2. The the energy of ions E^ in eV. (At higher surface po-
metallic cylinder below the lower electrode in this tentials ions can't overcome the electrostatic sur-
figure will enable in future to measure the charge face barrier of the particles).From this follows
of the particles. that
For the simulation of the cosmic charging
processes we have to determine the influence of (2) (Q/M) - » ?E .
strong electric fields generated by voltage U to be
able to take i t into account. This field can result P* pT
in induced charge of the particles and in com- p and r are respectively density and radius
pletely changed original energy distributions of of the particles, and £ Q is the permitivity of vac-
ion or electron beams. Furthermore, the influence uum. Typical charging curves (dependences of Q/M On
of the rest gas density, which i s by many orders of time) are shown in Fig.4. Dependences of measured
magnitude higher than at cosmic conditions, is to ( Q A O mm aa xx on ion energy for individual p particles
be determined. Electrons and ions produced by shows F ig5
Fig.5. Average values of (Q/M) as
(Q/M) m 3 x a s func
func-
c o l l i s i o n s ! ionization of rest gas by electron or tions of the ion ion energy for particles from resp
ion beams can result in significant effects. tive samples are shown in Fig.6.

277
 He-Ne-Laser
min. 25 mW
%M Teleacone

Ton- or / ^^ > ^s. \

electron / X I >^-^
beam detector

V-
Photomultiplier PhotomultiDlier

Light absorber
Figure 2^ VerCical (left) and horizontal (right) cross section of the electrostatic suspension
system

2a
.i—T^
30 31 3« 36 38 40 <2 << <E IS 50 5! 5< 56 l< 46 49 50 5! 54 56 58
Particle diameter (pm) Particle diameter (ym)
Figure 3. Size distributions of glass particles with average diameters of 42 put (left) and 51
(right).

-il Ion current: 3- ^

Ion c u r r e n t : 2,L.1G
7 Pressure : 5•10"
Pressure: ",.1O" rnbar Ion energy : 2,5 KeV
Ion energy : 2,5 KeV Particle
Particle diameter (D) : 51 jum
diameter (D) : 42 ^um

Charqlng time Charging time

4, Typical charging curves, errors of measurements are about 10*. The maximum charge is reached
after about 5 min.

278
 1500 2000 2400 1500 200G 2300
Ion energv (eV) Ton energy (eV)
gure L->. Dependences of (Q/M) niaK ° n ion energy for individual particles

6O
Theoretical curve /
for 42 jim particles /
SO / • Theoretical curve
for 51 /im particles
40 -H «o
tent

C/k.

O
_e 30
3O
s,
0) s
4J
o
a
0
01
2O (0 0 O

/A
A/ .
, «J
U-l
u
10 3
01

0 ikeV 2XeV 3k«V

Ton energy Ion energy

Figure 6, Average values of (Q/M)max as functions of the ion energy, measured for 27 glass particles of
42 fim (left) and for 31 particles of 51 fim diameter (right). The error bars represent the standard
deviation of the Q/M-values

Trying to find influence of the voltage U, we

charged particles at different U keeping it during
the charging process constant. Fig.7 shows depen-
dence of (Q/M) raax on E^ in case of a 51 jira particle
o U=1500V for different U, the theoretical curve is again on
the left. From the measurements above follows that
x U=2000V
the measured values of ( Q A O m a x are less than the
& U=3000V theoretical ones given by (2). This indicates that
"effective energy" of ions (the energy of ions in
the center of the suspension system) is equal to
tn the initial energy reduced by some factor which is
increasing with the applied voltage U.
Particles were also charged by electrons of
energies up to 5 keV with main purpose to study
r secondary electron emission from particles by
charging at different chamber pressures and also to
a determine the influence of rest gas. (At first we
wanted to find the yield at different energies of
primary electrons which is well known for many ma-
terials in case of plane surfaces, but for small
particles it has been only roughly estimated up to
now) . This could be done by determination of the
equilibrium surface potentials of particles at dif-
ferent pressures and then by solving the set of
equations describing respective equilibrium states.
Initial measurements were made with glass particles
of diameters of 40 to 50 pm and 50 to 60 »jm respec-
Ion energy tively. For the present only qualitative features
Figure 7. ( Q / M ) m a x a s Junction of ion energy
have been found (such as that surface potential is
measured with a 51 (im particle for
always positive, increase (decrease) of pressure or
different voltages U.

279
energy of primary electrons imply increase (decre-
ase) of potential, and that the potential is
independent of the flux of primary electrons. We
expect that in the future more precise measurements
with an improved suspension system will give more
definite quantitative results.

References:

Fechtig, H.; Grun, E.; Morfill, G.E: 1979,

Planet.Space Sci. 27,511.

Grun, E.; Morfill, G.E.; Mendis, D.A.: 1984, in:

Planetary Rings (Eds. R. Greenberg and A.
Brahic; Univ. of Arizona Press), p. 275.

Mendis, D.A.; Hill, I.R. ; Ip, W-H.; Goertz, C.K. ;

Grun, E.: 1984, in: Saturn (Eds. T. Gehrels and
M.S. Matthews; Univ. of Arizona Press),p. 545.

Vedder, J.F.: 1963, Rev.Sci.Instr. 34, 1175.

-: 1978, Rev.Sci. Instr. 49,1.

Whipple, E.C.: 1981, Rev.Prog.Phys. 44, 1197.

Wuerker, R.F.; Shelton.H.; Langmuir, R.V.: 1959,

J.Appl.Phys. 30, 342.

280
 THE SYMMETRY PLANE OF THE ZODIACAL CLOUD RETRIEVED FROM IRAS DATA

R. Dumont1, A.C. Levasseur-Regourd2

'Observatoire de Bordeaux, B.F. 21, F-33270 Floirac, France

2
Service d'Aeronoraie C.N.R.S., B.P. 3, F—91371 Verrieres-le-Buisson, France
and University Paris VI

The annual oscillations of the brightnesses observed at 12 and 25 \im by IRAS near the ecliptic
poles are mainly due to the inclination of the symmetry plane (SP) of the interplanetary dust cloud
upon the ecliptic, but also, secondarily, to the eccentricity of the earth's orbit.
Comparing the brightnesses at the poles and in the ecliptic (near 90° elongation) allows a
retrieval of the inclination i and ascending node tt SP/ecliptic through an inversion technique, with
very little model-dependence. The results (i = 1.5°, JJ = 90°) conflict with some of those previously
obtained from the same observations by more model-dependent approaches, but they agree with former
optical determinations from D2A satellite and from Tenerife ground-based data.

1. UNCERTAINTIES ABOUT THE SYMMETRY PLANE OF THE ZODIA- shows the apices of the perpendicular to the SP on the
CAL CLOUD celestial sphere to scatter over more than 4 square-
degrees. Part of these discrepancies, however, comes
Several determinations of the inclination, i, and from the elongation-dependence of the heliocentric
of the ascending node, Q, of the symmetry plane (SP) distance of the most contributing sections of the line-
of the interplanetary dust cloud w.r.t. the ecliptic of-sight (los) : Ref. Ib, 2, 2', 3 deal with regions
plane have been published after optical studies of (i) inner to the earth's orbit j Ref. la, 4, 5 with re-
brightness-profile asymmetries, (ii) departures of the gions near it ; Ref. 7, 8, 8', 9 with regions outer
peak from ecliptic, (iii) seasonal oscillations of to it, so that some warping of the SP seems to pxist,
brightness near the ecliptic poles. Figure 1, which as pointed out by Misconi 1980. Ref. 6, on the other
summarizes the results of the past two decades : hand, was claimed to be valid irrespective of the
sun's distance.
1 . la. Dumont and Sanchez, 1968 (ground-based observa-
tions at Tzana, Tenerife) ; Levasseur and Blamont, Also displayed on Fig. 1 are the apices relevant
1975, Levasseur, 1976 (satellite D2A) ; Misconi, to the recent infrared observations of thermal emis-
1980 (ground-based observations at Haleakala, Hawaii) sion from interplanetary dust (the satellite "IRAS"
ib. McQueen, 1968 (balloon observations) and the rockets of "ZIP"). In a preliminary study of
2 . Leinert et al., 1976 (rockets) - first model IRAS data, Hauser et al. , 1984, claimed the seasonal
2'. Leinert et al. , 1976 (rockets) - second model oscillations of brightness near the ecliptic poles to
3 .Misconi, 1977 ; Misconi and Weinberg, 1978 (ground- be in agreement with optical determinations 3 and 6.
based observations at Haleakala, Hawaii) In subsequent papers, both the inclination and the
4 . Dumont and Levasseur-Regourd, 1978 (ground-based node were found to be smaller :
observations at Izafia, Tenerife)
5 . Dumont and Levasseur-Regourd, 1978 (satellite D2A) A .Hauser and Gautier, 1984 ; Rickard et al. , 1985 ;
6 .Leinert et al., 1980 (Helios space probes) Hauser and Houck, 1985 (seasonal oscillations near
7 . Tanabe et al., 1980 (ground-based observations at the poles)
Kiso, Japan) B .Hauser et at., 1985 (same approach)
8 . Winckler et al., 1985 (ground-based observations at 1
B . Hauser et al., 1985 (departures of the peak from
Jungfraujoch, Switzerland) ecliptic)
8'. Winckler el al., 1985 (ground-based observations at B". Hauser et at., 1985 (same approach, with correction
La Silla, Chile) suggested in the following ref.)
9 . Maucherat et xl. , 1985 (satellite D2B) C . Derraott et al., 1985 (same approach)

Like in the optical case, a shift of the apex

(rightwards on Fig. 1) can be seen, as the most con-
tributing sections of the los recede iron) .• 1 AU (Ref.
A, B) to more than 1 AU (Ref. B', B", C ) .

With these IRAS apices can be compared the apex

from ZIP, which admittedly was more uncertain :

D . Murdock and Price, 1985 (asymmetries in the bright-

ness profile).

2. REDUCTION OF MODEL-DEPENDENCE IN INTERPRETATION OF

IRAS POLAR DATA

The purpose of the present work is to reconsider

the seasonal oscillations of brightness seen by IRAS
near the ecliptic poles, through an "inverting" method
which has the advantage of concentrating upon the true
level of variations, i.e. the vicinity of the SP. Con-
trary to this approach, the crude use of brightnesses
integrated along the whole los is excessively model-
fig. 1 dependent w.r.t. remote sections of the los. In addi-
tion, the non-negligible effect due to the eccentri-
city of the earth's orbit will be shown.

281
 2.1. The seasonal oscillations of brightness near the
ecliptic poles
NEP
The IRAS-Explanacory Supplement (Beichman et al. ,
1984) gives (p. VI-10) the average brightness, Bo, and
the amplitudes, B|, both in MJy sr" 1 , of the sinusoidal
fits to the seasonal variations of the brightnesses B
near the north ecliptic pole (NEP), in the four wave-
lengths of IRAS. The phase <p is given in «days before
1983 January 1, when B = B o with increasing values of
B » ; a multiplication by 360/365.25 gives the phase
<j> in degrees. The shorter two wavelengths, with lower Sun
contamination by galactic emissions, can only be used
here.
fig.3
12 pro 25 pm

13. 5 also consider then Ax > 0 ) . The extremal values of Ax

Bo 27.6
1.40 over the year are ± i (AU), those of AB are ± B].
Bl 2.30
(J> (days) 23. 8 22.3
23. 5 22.0 The point is that the proportionality coefficient
<J> (°) between AB and A>. can be easily derived from the ob-
servations of IRAS in the ecliptic. This coefficient
In this section, the eccentricity of the earth's is directly provided by the derivative of the bright-
orbit is neglected. The sinusoidal variations ofbright- ness vs. elongation, £, around e = 90°, as already
ness at the NEP are completely ascribed to the alter- emphasized in the optical case (Dumont, 1973, 1983 ;
nate location of the earth "above" and "under" the SP Dumont and Levasseur-Regourd, 1085).
(Fig. 2 ) . ("Above" means that the earth is on the nor-
thern side.) Let A and B (Fij. 4) be two positions of the earth,
for which the brightnesses observed along the same los
(i.e. the chord BA) would just differ by twice the am-
plitude seen at the poles, 2B1. Then, the angle BOA
would have to be 2i, twice the inclination (rotate
Fig. 4 by 90° around OH, to successively contain the
los in the ecliptic, and then the los toward the NEF).

IRAS data (Hauser et al. , 1984, Tahle 2) does not

give the brightnesses at the relevant elongations.
However, the elongations 81.5° and 98.4°, practically
symmetrical w.r.t. c =90°, provide another chord, wider
than the previous one but unsignificantly nearer the
sun. The new angle B0A is 16.9°. Therefore, the pro-
portionality AB : Ax can be written
2B[ _ Contribution by BA
£
fig. 2 21 16.9°
which leads us to :

2.2. First approach for the ascending node, S'i 12 pm 25 pm

Contribution by BA 16 23
Since the heliocentric ecliptic longitude of the • iMJy sr"1
Bl at the NEP 1.40 2 .30
earth on January 1 is A o £• 100°, and since the average
value Bo of the brightness B near the NEP was observed
Inclination i (°) 1.48 1.69
$ days before, then the earth must have crossed the SP
from north toward south at the ecliptic longitude of
the ascending node SP/ecl. :
a = xo - *
Therefore, fi ? 77° (76° from 12 pro ; 78° from 25
Urn data). (This is in full agreement with IRAS Ref. A
and 6.)

2,3. A retrieval of the inclination, i,with low model-

dependence

No physical model of the Zodiacal Cloud (w.r.t.

neither its heliocentric nor its off-ecliptic, rates
of decrease for the space density) is required to sa-
fely retrieve the inclination. We only have to assume
the cloud to be rotationally symmetric, sufficiently
extended off its SP, at.d moderately tilted over the
ecliptic plane, so that the space density along the
"polewards" los remains practically constant within
the dihedron of the two planes.

If so, the increment AB of brightness from its

mean B o , due to the small departure Ax = T 0 T of the fig. 4
aarth from the SP is simply proportional to Ax (Fig.
3) (AB being > 0 when the earth is "under" the SP, we

282
 These results are practically insensitive to our
poor knowledge of what occurs along remote sections of
the two los, both in the ecliptic outside the earth's
orbit, and far from the earth towards the poles. B

3. CORRECTION FOR THE ECCENTRICITY OF THE EARTH'S ORBIT

This veak eccentricity (0.0167) is tempting dis-

regard, as an apparently unefficient cause of modula-
ting the brightnesses over the year. An argument to
neglect it can even be found in the fact that an ele-
mental section of the los contributes to the bright-
ness proportionally to its length and to its density ;
therefore (Fig. 5 ) , when the earth goes away from the
sun by AR AU there is an increase of length for each
los-section in the ratio of (1 + AR), and a decrease
of density in a ratio of about (1 - AR), because of
the density widely agreed to be roughly in inverse
proportion to the heliocentric distance : at least a
partial cancellation seems to occur.
fig.6
Nevertheless, the temperature of the dust also is
heliocentric-dependent. Assuming it (classically) to
decrease as I//r, as it would be the case in a grey- plitude of the eccentricity-vector is E s 0.4 MJy sr"1
bodylike cloud, the Planck term [exp(-h/kAT) - 1]"', in both wavelengths. As already seen it increases up
which rules the monochromatic emissivity, would vary to ^ 0.5 MJy sr~l for a 1//F fall of temperature ; it
by ± 3 . 9 % of its average value between perihelion and would reach ^ 0.7 MJy sr"1 if the slightly steeper
aphelion, for T=260 K at I AU (Levasseur-Regourd and - 33 advocated by Helios coworkers
fall of density ^ rr-'-
Dumont, 1985) and for A = 12 ym. The average 12 |im- (Leinert et at. , 1978) were adopted.
brightness B o at the poles, 13.5 MJy sr" 1 , can there-
fore be expected to oscillate with about 0.5 MJy sr"1 Even with the smoother gradients r -1/3 , - 1 the
amplitude by the only effect of the eccentricity. correction for eccentricity is rather important on the
Since this is more than 1/3 of the observed amplitude ascending node, which is increased by 16° (12 um) and
Bj - 1.4 MJy sr" 1 , dearly the eccentricity is a se- by 10° (25 pm). The inclination is only decreased by a
condary but non-negligible cause of the seasonal os- few percent.
cillations observed.

Both the seasonal oscillation and its two compo- 4. RESULTS AND DISCUSSION
nents can be represented by rotating vectors, with the
vernal point y as an origin (Fig. 6). The phase of the The corrected parameters of the SP are
resultant is Xo ~ <f> 1 the phase of the modulation by
the SP/ecl. tilt is unknown Q ; the phase of the modu-
lation by the eccentricity is about 11°, i.e. the lon- 12 urn 25 ym
gitude of the earth on the day when its distance to
rh<. sun is 1 AU by decreasing values (about 4 October). Ascending node, n 92 88°
Inclination, i 1•4 1?6
The amplitude of the observed resultant is Bi ;
let B2 be the amplitude of the modulation by the tilt Admittedly, the provisional character (w.r.t. ca-
cf the two planes (proportional to the unknown incli- libration, and to residual contamination by galactic
nation, i). The amplitude E of the eccentricity-vector emissions) of Hauser et aZ.'s 1984 data induce some
depends on the heliocentric derivatives assumed for uncertainty upon these figures, and upon the apex of
the temperature and for the space density of the dust, the SP, X, as located on Fig. 1 by the means for the
as shown on above example. two A A :

The most likely value for the heliocentric de- / n s 90°

pendence of the temperature is r~1/! rather than r" " 2 t i £ 1.5°
(I.evassour-Regourd and Dumont, 1986 : Dumont and They seem, however, difficult to reconcile with
Levasseur-Regourd, 1987). With an inverse proportio- the locations A and B which correspond to the couples
nality for the radial fall of space density, the ara- (fi, i) previously published from the same IRAS obser-
vations. On the other hand, the agreement is notewor-
thy with former optical results from the satellite
D2A and from Tenerife ground-based data (Dumont and
NEP Levasseur-Regourd, 1978). This agreement is at least
partly due to the inverting methodology, and to the
correction for earth's orbit eccentricity, which were
taken into account in that work.

Even various earlier determinations of the SP at

the 1 AU-level (listed in la in Section 1 : see apex
1 on Fig. 1), which invoked a rough coincidence with
the invariable plane of the solar system (ft = 106°,
i = 1.6°) turn out to agree better with the present
result than the previous IRAS determinations do.

1+AR ACKNOWLEDGEMENTS• We are indebted to J.L. Weinberg and

N.Y. Misconi for helpful information. This work was
fig.5 supported by "A.T.P. Planetologie" of the french INSO.

283
REFEFENCES

Beichman, C , et at. (13 authors) : 1984, IRAS Cata-

logues and Altases, Explanatory Supplement
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"Asteroids, Comets and Meteors" II, Upsala
Dumont, R. : 1973, Planetary Spaoe Soi. 1\, 2149
Dumont, K., Levasseur-Regourd, A.C. : 1978, Astron.
As trophys. 64, 9
Dumont, R., Levasseur-Regourd, A.C. : 1985, Planetary
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phys. 3±, 293
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J. 2T±, L-15
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573
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Res. ^, 87
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119, 27
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1484
Murdock, T.L., Price, S.D. : 1985, Astron. J. 90, 375
Rickard, L.J., Dwek, £., White, B.A., Hauser, M.G. :
1985, BAAS 17, 591
Tanabe, H, TakechT, A., Miyashita, A. : 1980, IAU
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Astron. Astrophys. 143, 194

284
OTHER BODIES
 PROBABLE PERIODICITIES OF THE JOVIAN ATMOSPHERIC ACTIVITY
1 2 1
J. Xanthakis' \ C. Banos^ ', B. Petropoulos^ '
(1) Research Center for Astronomy and Applied Mathematics, Academy of Athens, Anagnostopou-
lou U , T.T. 106 73, Athens, Greece.
(2) Astronomical Institute, National Observatory of Athens 11 810, P.O.Box 2004.8, Greece.

Probable periodicities of 22,8 and 4 years have been found in the Jovian
atmospheric activity measured between 1965-84.

1. Introduction
High resolution images of Jupiter obtained 1961. Combining these results with the re-
by the Voyager 1 and 2 flyby spacecraft on sults from aprevious paper of one oftihan(19&)
5/3/1979 and 10/7/1979 respectively, show with they concluded that Jupiter presents a "calm"
remarkable details a complex cloud system, on every 20-22 years.
the horizontal structure of the Jupiter atmo- Banos (1966) studying the activity of Jupi-
sphere. These layers of clouds are probable ter for the time period 1964-66, and combi-
composed by ammonia crystals in the upper at- ning these results with previous of 1964
mosphere, located above an ammonia hydrosulfi- noticed a period of 4-5 yeaj's of the coeffi-
de (KH, SH) cloud and deeper a water ice cloud cient of activity. Later (1972) using 160
as Lewis (1969) and Weidenschilling et al., plates in three wave lengths taken at the New
(1973) have predicted. The evolution of the Mexico State University Observatory, for the
above cloud layers depend on the vertical ther- period 1964-67 found that the photcmetric coeffi-
mal structure and the ohter physical parame- cient of activity is more intensive in the
ters, of the Jupiter atmosphere, which have North hemisphere and presents a probable pe-
recently computed using Voyager data by Pet- riodicity, bigger than 3 months. Focas (1971)
ropoulos and Banos (1984.) . The mechanism of studied the activity in Jupiter atmospheric
long term changes in these cloud layers de- belts between 1904-1963 using 64 negative pla-
pends on the variations of the energy sources tes at the Lowell Observatory of Flagstaff in
internal or external, as well as on the varia- Arizona and found a periodicity of 17-20 years.
tion of the atmospheric opacity resulting frcm He also noticed that " Correlations with so-
a variation of the co osition of the clouds. lar activity (expressed by the Wolf number ) ,
The cloud layers have •nen observed by gound are not striking ". Prinz (1971) using plates
based telescopic obsei /ations of the planet obtained with the 30 cm. cassegrain reflector
and appear as belts a. i zones parallels to the of the Public Observatory in Munich for the
equatorial zone of different colours in the vi- period 1964-1968 studied the atmospheric ac-
sible surface of Jupiter. Observational data tivity of the planet Jupiter in the yellow
are summarized by Peek (1958), Michaux (1967) light. Using graphs from the work of Focas
Gehrels (1976). (1971), Prinz concluded that the activity pre-
sents two long periodicities of 17 and 20
2. Measuring the activity years for the maxima and 5-6 years for the mi-
nima and a small periodicity of 3 months.
Focas and Banos in 1964 introduced a coef- Short time periodicities have been also de-
ficient "R" measuring the activity on Jupiter tected in the activity of the atmosphere of
which is resulting by the photometric analy- Jupiter by Aksenov (1967), who noticed a three
sis of photographic plates. This coefficient months period, which agrees with Prinz (1971)
"R" is given by the relation: who found 92-93 days (three months) period in
the green and red light and a 1 04 days perio-
dicity in the blue range. Banos (1971) noti-
R= ( 1 - I (o) !dfo ced that a periodicity bigger that 3 months
can exist in the activity of Jupiter.
-45" More recent interest studies of the atmos-
pheric activity of Jupiter have been c&rried
where : R : the photometric coefficient of out by Petrova and Sorokina (1973), Banos-
activity. Sarris (1985) and Wid'manchesco (1985). In
<t> : the zenographical latitude (1973) Pokorny studying the evolution of the
C : the constant reference area with activity during the period (1964-1968) con-
limits +45°. cluded that the intensity of the Jovian belts
:
is probably affected by the occurence of so-
— the ratio between the innten- lar protons and similar events.
sities Bg of a point of the po-
lar diameter and B c of the brigh- 3. Data
test point with limits 0 to 1 . In the present work we use the values of R
resulting from the photometric analysis of
Using this coefficient of activity R and plates taken by Banos mainly during the pe-
photographic plates taken in yellow light with riod 1962-1984. The values of R are calcula-
the 16" and 25" refractors of the National ting with the method Focas-Banos (1964,1971)
Observatory of Athens, Focas and Banos studied and the plates used are taken in the National
the activity on Jupiter during the period 1952-
1963 (1964). Observatory of Athens with the 16", 25 ref-
ractors and the 48" telescope.
Among the differs it results given in that For the period 1904-1962 we use the results
work (1964.) by Focas and Banos is the the
activity on Jupiter reached a minimum in 1960 published by Focas (1971).

287
 In figure 1 we give the evolution of the ac- Spectrum analysis Mitchel (1966) has been
tivity of the atmosphere of Jupiter for the used in order to ^nmnni.e the more significan

i i [ m i | i n 111 • I I J I 1 1 1 1 1 1 1 1 j 11 i i i i i i
BIO 1S2O 1930 1940 1950
Fig. 1. Top: Coefficient ft of the activity -on Jupiter
Botton : Solar activity
time period 1956-1985, connected with other periodicity of Ro(t)> which is of 4 years wit>
results obtained by Banos (1971) Banos-Focas an accuracy of 95%. The time intervals and
(196-4) for the latitude zone +4-5°, and Sarris the amplitude of this periodicity are given
(1975). by the analytical expression.

4. Mathematical analysis of the coefficient T+C n sin^Hr

4 (5)
of activity.
We have used the method of analysis in tri- where the values of b n C , T are given in
gonometric series in order to represent ana- Table 1.
lytically time variation of the coefficient
of activity R(t)« «+2h+1
Mean valjjs, computed by the — ^r—- moving TA L E
averages method of the measured coefficient of
activity are given in the curve (a) of figure
2.
The analytical expression of R(t) can be 1913-27
given by the following relation. +0.0,v 1928-32
-0.040 1938-42
+0.040 1964-68
n^( +0.050 1979-88
191-4-1938 1937-1959
Cn T
-O.O40sinM(T-1964) (2)
-0.015 1955-82
1964-1986
After the above we now computed the analy-
tical expression of R ( ^ N .
which gives the time period of 20 years while The computed values by this relation arf
the 8 and 4 years period is given by :
compared to the observed ones in Table 2.
The standard deviation, between the obser-
R ved and computed values is :
o(t) = 0 ' 3 0 s i n |^( T - 1 9U)-0,010sin|L(T-1925)-
1916-1927 1923-1932 0 = +_O.OO43

with an accuracy A = (1- )100%=9S,1%

-0, 40s in2l(T-1 938)+0,040sinl!l(T-1964) 0,240
8 8
1938-1942 1964-196S
The above analysis has 31 parameters and
38 degrees of freedom.
+0 , C K 0 s i n | f l ( T - 1 9 6 9 ) - 0 , 5 0 s i n M ( T - 1 9 7 - 1 ) -
8
1964-1973 1979-1935
Results and Discussions
-O,Oi6sin|_(T-1955)
u
(3)
1958-1962 The following periods have been found for
the coefficient of atmospheric activity of
Jupiter.

In Figure 2, curve (a), gives the periodi- (1) 22 years period for the time interval
19U-86.
cal term of 22 years while, curve (b) gives
the periodical terms of 4 and 8 years.
(2) Small periodicities of 4 years and 8
In the same figure curve (c) represents dif- years.
ferences of the computed values R ( t ) c o m P from
the measured values given by curve a in the
same figure. The periodicity of 20-22 years has been
suggested by Focas-Banos (1964).
Ro(t) (4) The 22 years period, could be interpreted
as a result of the solar a.ctivity, Balasubra-

288
husanuyan and Vernkatesan (1970), and Krisky years which we have found in the index of tie
et al (1972) shot; that the variations of solar atmospheric activity of Jupiter.
activity caused by the fluctuacting occuranos Solar wind streamers have as sources coro-
of proton events on the Sun can also be obser- nal holes or solar flares and their number
ved on the planet Jupiter at 5A.U di^'ance. have been recently studied by Xanthakis et
Pokorny (1972), using superposition ir.ethod, al (1986) who found for the time period 1969
studied relationship between Jupiter's pho- -1984 11 years and 1 year periodicities for
tometric coefficient R and proton events for the solar wind streamers, which have flares
the period 1904.-1968, and concluded that the as sources and 14 years 2 and 1 year periods
analysis of the coefficient R yielded a two- for the solar wind streamers provided by co-
maximum relationship over the 11 year cycle. ronal holes. Then it is probable that the
In fact recently Voyager I and 2 spacecrafts 22 years period (Hale period) for the number
detected plasma waves beyond 12 A.U. during of sunspots Rg and for the flares, modulates
the time period 1982-1984. (Lanzerotti, et al the solar wind and interacts with the global
1985). These plasma waves could be associa- circulation of the winds, while the shorter
ted with turbulance expected at the heliopause. time periodicities interact with the clouds
Energetic protons have been also measured by morphology of Jupiter.
Voyager I about the same time intervals.(Lan- From figure 1 in which we give the evolu-
zerotti et al 1985). Then it is probable that tion of the coefficient of activity R for
solar wind streamers, active the Jupiter mag- the period 1904-1984 comparing it with the
netosphere, which interacts with the global Wolf number we can notice that an anticor-

1915 19; O '950 I960 1970 19(10

300
290
280
270
260
350
240
230
220
2>0
200
190
180

300
290
itm
im

-rr\A vA
MO

230
220
211
200
190
180
—fib—'•

Fig.2. Curve (a) gives the periodical terra of 22 years.

Curve (b) gives the periodical terms of 4 and 8 years.
Curve (c) represents the differences of the cor.puted values
^ c o n F froE the Pleasured values given by curve a.

circulation of the winds in Jupiter atmosphe- relation of the tw^ curves is presented for
re, with periodicity in the cloud morpho- the interval 1965-84. These measurements of
logy time of Jupiter which has been found, R are very accurate based on photographic
about six years ± three years. Beebe (1985) observations made by C. Banos.
is in agreement with the periods of 6 and 8 The two minima of R correspond to the two

289
maxima of Wolf number for the 20th and 21 s * Series I, Astron. No 22.
solar cycles respectively. The second maxi- Beebe, R., Suggs, R. : 1985, The Jovian At-
mum of the 20th cycle appears in 1972 and mosphere Proceeding or a conference
coincides with the second maximum of the gresi held at the NASA Goddars Space Studies
T A B L E

leaps R Years
(t) Comp. R^)0bs. Rr ^\Co(ap. R
(t) Obs
- Years R(t)Ccip. R t t ) 0b3

1916 0.240 0.230 1941 0.194. 0.192 1966 0.271 0.273

17 .247 .242 42 .220 .212 67 .238 .240
18 .254 .257 43 .220 .212 68 .189 .194
19 .254 .262 44 .222 .224 69 .200 .207
1920 .242 .251 45 .225 .228 1970 .243 .244
21 .235 .242 46 .229 .230 71 .244 .239
22 .244 .244 47 -234 .237 72 .223 .219
23 .263 .260 48 .240 .252 73 .218 .225
24 .280 .286 49 .246 .250 74 .229 .230
25 .284 .29C 1950 .251 .250 75 .240 .240
26 .268 .261 51 .255 .250 76 .251 .249
27 .240 .235 52 .258 .250 77 , .262 .270
28 .233 .232 53 .260 .263 78 .285 .293
29 .233 .235 54 .260 .266 79 .276 .276
1930 .231 .233 55 .258 .251 1980 .230 .241
31 .224 .223 56 .240 .234 81 .230 .230
32 .215 .212 57 .251 .248 82 .256 .251
33 .215 .206 58 .261 .267 83 .270 .261
34 .217 .214 59 .240 .244 84 .297 .288
35 .242 .245 1960 .225 .220 85 .301 .307
y .256 .265 61 .240 .244
.254 .254 62 .255 .243
' .234 .229 63 .240 .240
3? .201 .199 64 .225 .220
1940 .185 .181 65 .257 .258

line intensity of the corona. (Xanthakis 1934) N.Y. NASA Conference Publication 2441,
which is well correlated with the number of p.32.
proton flares. A second minimum appeared Basu, D. and Banos, C.J.: 1975, Astrophysical
also in the activity for the 21 " cycle in Letters V. 16, 97-98.
1982 which corresponds also to the second ma- De Pater, I.M.E. : 1986, Icarus, 68, 2, 34.4..
ximum of the green lim (Xanthakis et al 1TBO. Focas, J.H., Banos, C.J.: 1964, Annales d'
It seems therefore that the suggestion of Astrophysique 27, 36.
Pokorny (1973) in which proton flares inte- Focas, J.H. : 1962, Mem. de la Societe' Royale
ract with the activity of Jupiter is veryfied des Sciences de Liege, t. VII, 535.
for the 20th and 2 1 t h solar cycles. Banos arri Focas, J.H. : 1971, (Communicated by A. Dol-
Basu (1976) have also studied probable rela- lfus ) Icarus 15, 56-57.
tions between Jupiter's decametric radio e- Gehrels, I. : 1976, Jupiter. The University
mission and it's activity. They found signi- Arizona Press, Tucson Arizona.
ficant correlation between the peculiar acti- Lewis, J. F. : 1969, Icarus, 10, 365.
vity in the equatorial area of the planet Michaux, C M . : 1967, Handbook of the Physi-
and the Jovian decametric radiation at 18.0, cal Properties of the planet Jupiter
22,2, 27,6 MH3. NASA SP 3031.
According our opinion relationships ought Mitchel, J.M. Jr. : 1966, Climatic Change W.
to exist between solar wind streamers of so- M.0. No 195, TP 1000, 33-47.
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Vol. 24, No 2.
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U.A. Bronshten. Nebesn. Tel. Tom 1, No 5, p. 91.
Balasu, Bramayan, V.K Venkatesan, D. :1970 Xanthakis, J.,Poulakos, C , Petropoulos, B.:
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Banos, C.J. flarris, E.N. : 1985, Memoirs of
the National Observatory of Athens,

290
 A REFERENCE MODEL FOR THE ATMOSPHERE OF TITAN
B. Petropoulos, A.A. Georgakilas
Research Center for Astronomy and Applied Mathematics,
Academy of Athens, 14 Anagnostopoulou Street- Athens (136) Greece

We have computed the following physical parameters for the atmosphere of Titan,
using Voyager's measurements: 1) Temperature, 2) Pressure, 3) Density, 4) Speed of
sound 5) Density scale, 6) Number Density, 7) Mean free path, 8) Viscosity,9)Pressure
scale, 10) Mean particle velocity, 11) Mean collisional frequency, 12) Columnar mass

I. INTRODUCTION from Voyager radio occultation measurements

assuming that the satellite is spherical
Titan has been observed by ground based (Lindal et al, 1983). The indicated altitude
telescoping observations (Kuiper et al,1952) of the main haze level on Titan corresponds
and by the recent missions of Voyager space- to the elevation of its optical limb as
crafts. The satellite of Saturn appears from measured by Voyager's imaging (Smith et al,
Voyager 1 cameras (1980) as surrounded by a 1981).
dens uniform haze. Its atmosphere consists Bond albedo is derived from the effective
mainly from Ng and it is fild with aerosols. temperature , estimated by Lindal et al (1963)
II. BASIC ASTRONOMICAL DATA assuming that the internal heat source is
negligible.
Properties of Titan are given in Table I
(Allison et al, 1986). TABLET I
The mean solar distance R (or semimajor axis) Surface radius r s 2575 Km 26
and the orbital eccentricity are specified Mass M 1346X10 gr=0.022XEarth
as the (rounded) values for the oscultating Mean <g> 135.4±0.Icm/sec2
elements tabulated in the Astronomical Alma- GM 8.976X10lBcm3s-2
nac (1986). Distances are given in Astronomi- Rock:ice ratio(by mass) 52:48 ,
cal units with 1 A.U. = 1.49598X10° K m ) . Distance from Saturn 1.226X105Km=20R.
The oscultating mean distance change by as Mean Solar distance 9.546 A.U.
much as a few tenths of a percent. Orbit period around Saturn 15.945 days
Its eccentricity mostly change, no more than Orbit period around Sun 30 years
ten percent of its tabulated value. Axial inclination 26.7 6
The orbital period is taken from Allen's Bond albedo 0.22
Astrophysical Quantities (1973). Solar flux LUXEarth
The Southern solstice dates are compiled or Southern Sunnier Solstice 2002.6
extrapolated from data in Allen (1973) and Effective emission temperature 85 K
the Astronomical Almanac. As also the obliquity Effective emission pressure 1 bar
which is the inclination of a planet's equator Dry adiabatic lapse rate 1.3 KKm"]
to its orbital plane. Static Stability 0.7 KKnf'
The siderial rotation period is taken to Scale height 20 Km
be the same as its orbital period about Emission level Pe 7.5
Saturn (as reported by Davies et al 1980) Surface (or H 2 0) Ps 8.4
assuming that its rotation is tidal ly locked Meridional thermal gradient -1 K/103 Km
to the planet. Radiative time constant Pe 2X10^9 sec
Titan's equatorial radius has been derived Ps 3X10 sac

SO 120 40 80 120 WO iOO 240

A IT I T U B E A L T I TUOE (KM)

FIGURE 1. Temperature versus altitude. FIGURE 2. Pressure versus altitude.

291
 80 120 ISO 200 40 60
A I T I TUDE ( K M ) ALTITUDE (KM)

FIGURE 3 . Density v e r s u s a l t i t u d e FIGURE 4 . Speed of sound v e r s u s a l t i t u d e

5*1

« •

80 120 1S0
80 ' 120
ALTITUDE (KM)
AITI TUDE
FIGURE 5 . D e n s i t y s c a l e versus altitude FIGURE 6. Number density versus altitude
3
Vertical eddy mixinc; coefficient < 10 cm-' s-1
Coriolis parameter ?.561X10'° TABLE II
Characteristic weather length 3000 Km GASEOUS CONSTITUENTS OF THE ATMOSPHERE OF
I I I . CHEMICAL COMPOSITION TITAN
Formula Name Abundance Reference
Atmospheric c o m p o s i t i o n of T i t a n below No
0.1 bar i s g i v e n i n Table I I . (Sagan and Nitrogen "85-77* 4,8,9
3BAr Argon -12-17% 4,9,
Thomson, 1 9 8 4 ) . CH 4
A l l v a l u e s a r e d e r i v e d d i r e c t l y cr indirectly Methane ~3-6% 1,4,6,7
from Voyager d a t a . Hydrocarbons and n i t r i l e s "2 Hydrogen 0.1-0.4% 4,6
are formed on t h e s t r a t o s p h e r e from dissociation H,C-CH3 Ethane 20 ppm
H o C - C H g - CHo Propane 20-5ppm 10
of CH4 and N 2 ( G a u t i e r e t a l ) .
HCSCH Etnyne(acetylene) 2 ppm
A c r u c i a l q u e s t i o n i n T i t a n concerns possible
H2C=CH2 Ethene( Ethyl ene) 0.4 ppm
i m p l i c a t i o n s of t h e d i s c o v e r y of HCH, HC3N
and c2t>2 n i t r i l e s i n t h e Upper atmosphere. HCSN Methanenitrile
HCN i s a Key i n t e r m e d i a t e i n t h e s y n t h e s i s (hydrogencyanide) 0.2 ppm
HC=C-CSCH Bytadiyne 0.03 ppm
of amino a c i d s . L a b o r a t o r y e x p e r i m e n t s have
demonstrated t h a t once HCN has been produced (diacetylene)
HjC-CSCH Propyne
more and more complex n i t r i l e s are e a s i l y
f o r m e d . Sagan and Thomson (1984) have g i v i e n , (methylacetylene) 0.03 ppm 2
HCMC-CSN •Propynenitrile
on t h e b a s i s o f l a b o r a t o r y e x p e r i m e n t s of
i r r a d i a t i o n s o f s i m u l a t e d T i t a n i a n atmospheres (cyanoacetylene) 0.1-0.01ppm 2
NEC-C=N Ethanedinitrile
an i m p r e s s i v e l i s t o f complex o r g a n i c solids
which c o u l d have been formed i n T i t a n . (cyanogen) 0.1-0.01ppm 3
CO? Carbon dioxide 0.01 ppm 5
CO Carbon monoxide 60 ppm 11

292
 80 ' 120 160 200 240 *0 80 120 160 200
ALTITUOE (KM) A I Tl T UDE (KM)

FIGURE 7. Mean free path versus altitude FIGURE 8. Viscosity versus altitude

Is-
- M

z .

80 ' 120 ' 160 200 240 "0 40 80 120 160 2O0 240
ALTITUDE (KM) A L T I TUOE (KM)

FIGURE 9. Pressure scale versus altitude FIGURE 10. Mean particle velocity versus altitude

' o.

a
m
h

' 4b ' «'O ' 120 ' .60 ' 200 ' 240 T" T" -r-
*o 80 ' IJO ' 160 ' 200 ' ?40
A L Tl T UDE (KM) A I T I TUOE (KM)

FIGURE 11. Collisional frequency versus altitude FIGURE 12. Columnar mass versus altitude

293
References: (1) Hanel et a 1,1981; {2}Maguire et V. CONCLUSIONS
a 1 ,1981 ; (3) Kunde et al,1981, (4)Samuelson
et al,1981;(5) Maguire et al,1982,(6) Thomson We give a reference model for the atmo-
and Sagan,1984; (7)Smith etal,1982;(8)Broad sphere of Titan, as a first attempt inorder
foot etal,1981, (9)0wen,1982; (10) Samuelson, to study this atmosDherp. Lumine (1983)
1983; (11) Lutz etal, 1983; suggest that the surface 1 of Titan i s covered
by an ocean of 7v% Ci-.j and 25% C H 4 and
IV. TEMPERATURE PROFILES 5% N 2 and the vapour? of these components
forme clouds of " H . crystals at altitudes
Temperature profiles of Titan's atmosphere 20-40 Km.
measured by Voyager with two methods:
1) By radioccultation at 7 N,258°E and at If we compare the computed pressures and
8°S, 76°E (Lindal e al 1983, Tyler et al 1981) temperatures with the liquifying temperatures
2) By infrared spectroscopy at 7°N and at 68° 3f CH4 which is probably abundunt in 3-6%
N (Hanel et al 1981). in the atmosphere of Titan, we can derive
A tropopause lapse which is subadiabatic at that probably the surface of Titan is covered
all levels appear adiabatic for the lowest with oceans of CH4 and other hydrocarbons.
three to four Km that applies that the vertical The computed physical parameters can be used
thermal structure is windly convert by radiative in laboratory experiments in order to study
process and that convection is predominant the evolution and the meteorology of Titan's
at the lower boundary of the atmosphere. atmosphere.
Temperature profiles measured by radiocculta- REFERENCES
tion data are given in figure 1.(Lindal etal ALLEN, C.N. (1973). Astrophysical Quantities,
1983) There is a little difference between (Third Edition),The Athlone Press, London.
measurements obtained in North hemisphere ALLISON M. and L.D. TRAVIS (1986). The
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altitudes above 100 Km. 2441.
BROADF0OT,A.L. ,B.R. SANDEL, D.E. SHEMWSKY,
V. INPUT DATA AND RESULTS J.B. HOLBERG.G.R. SMITH, D.F. STROBEL, J.C.
in uraer to compute the physical parameters MCCONNELL, S. KUMAR,D.M. HUNTEN, S.A.ATREYA
v;u resolved the hydrostatic equation by as- T.M. DONAHUE, H.W. MOOS, J.L. BERTAUX, J.E.
suminc that'. BLAMONT, R.B. POMRHREY, AND S.LIN1CK (1981)
the atmospheric gas behaves as a real gas ana Science 212, 206-211.
follows the equation of state (Lindal etall, DAVIES,M.E., V.K. ABALAKIN, C . A.CROSS , R . L.
1983) DUNCOMBE.H.MASURSKY.B. MORANDO,T.C.OWEN,P.K.
p = P_J (1) SEIDELMANN, A.T. SINCLAIR ,G.A.WILKINS, AND
R (T/Fc) Y.S. TJUFLIN (1980). Celestial Mech.22,205-
Where, p is the density,p is the pressure, 230.
W, is the mean molecular weight, T is the GAUTIER,D.,W.B. HUBBARD AND H. REEVES(1984)
temperature, R is the universal gas constant In Planets, 1 4 ^ Advanced Course Swiss Society
and for N2 Fc is given by the formula: of Astronomy and Astrophysics.
HANEL. R.B., CONRATH.F.M. FLASAR,V.KUNDE,
(2) W. MAGUIRE,J. PEARL, J. PIRRAGLIA, R. $A:4JS_"r*l,
Ti L. HERATH,M.ALLISON,D.GRUIKSHANK,D.GAUTItR,
where, for Si-units, the constants A and B P.GIERASCH,L.HORN, R . KOPPANY , AND C. POMiiA-
are A=0.0563, 8=2.75 (Lindal et al 1983) and MPERUMA (1981).Science 212, 192-200.
Ti is the ideal gas temperature. KUIPPER G.R. and B.M. MIDDLEHURST (1952).
The following input data have been used for The solar system.
the computations: KUNDE,V.G. ,A.C. AIKIN, R.A. HANEL,D.E.
1) The radius of the satellite measured by OENNIGS.W.C.MAGUIRE, AND R.E. SAMUELS0N(1981).
Voyager, R=2575 Km {Lindal et al, 1983) Nature 292,686-688.
2) The chemical composition of the atmosphere LINDAL.G.F.,G.E.WOOD,H.B.HOTZ,D.N.SWEETNAM
No: 100% (Lindal et al , 1983) V.R.,ESHLEMAN AND G.L.TYLER (1983). Icarus 53
3) The mean molecular weight computed by taken 348-363.
into acount the above chemical composition MAGUIRE,W.C.,R.A. HANEL,D.E. JENNIGS.V.G.
and considered to be constant from 0 Km to KUNDE, AND R.E. SAMUELSON (1981).Nature 292,
200 Km, m=28.02 683-686.
4)The pressure and temperature at zero altitude MAGUIRE, W. C. ,R. HANEL, D. JENN INGS , R .SOTJELSCN
a) Po = 1497.59 mb and To=93.9 K for radioculta- A.AIKIN, AND Y. YUNG ,(1982). Presented at the
tion experiment at 8° South and 76 East Saturn Conference, Univ.of Arizona, 14 May
longitude in the morning atmosphere. 1982.
b) Po=1495.26 tab and Jo=94. K for radiocculta - LUTZ.B.L.C. DE BERGH.AND T.OWEN (1983).
tion experiment at 6 North and 258° East Science 200, 1374-1375.
longitude in the evening atmosphere (Lindal OWEN T. (1982).Planet Space Sc i . 30,839-848.
et al, 1983). SAGAM C. AND W.R. THOMPSON (1984)Icarus 59
5) The two different temperature profiles 133-161.
versus altitude measured by radioccultation SAMUELSON,R.E.(1982) Icarus 53,364-387.
which we mention in section V.{Lindal etal, SAMUELSON.R.E.R.A. HANEL,V.G.KUNDE, AND K £
1983). The physical parameters which we have MAGUIRE (1981) .Nature 292, 688-693.
computed are: 1) Temperature (fig.1), 2)Pres- SMITH,B.A..L.SODERBLOM, R.BEEBEI,J.BOVCE,
sure (fig.2), 3) Density (fig.3), 4) Speedof C.BRIGC-S, A.BUNKER,S.A. COLLINS,C . J.HAHSEN,
sound (fig.4), 5) Density scale (fig.5), 6) T.V.JONSON ET AL. Science 212, 163-190.
Number density (fif. 6) 7) Mean free path SMITH,G.R.,D.F. STROBEL,A.L. BR0ADF001,B.R
(fig.7), 8) Viscosity (fig. 8) 9) Pressure SANDEL, D.E.SHEMANSKY, AND J.B.HOLBERG( 19(52)
scale (fig. 9) 10) Mean particle velocity 0. Geophys.Res.87,1351-1360.
(fig. 10) 11) Mean collisional frequency(fig. THOMSON,W.R.AND C.SAGAN(1984) Icarus.
11) 12) Columnar mass (fig. 12) (Dashed lines TYLER.G.L. ,V.R. ESHLEMAN, J.D. ANDERSON,
represents the computed values for 6 latitude G.S.LEVY.G.F. LINDAL, G.E. WOOD, T.A. 'JROFT
and 258° E longitude, Solid lines represents (1981). Science 212, 201-206.
computed values for 80 S latitude and 76 t
longitude).

294
 INDEX OF A U T H O R S

Aliyev S.A. 55 Limboz F. 83

Andrienko D.A. 95 Lindblad B.A. 201
Antz Ch. 245,249 Mamadov O.M. 71
Babadzhanov P.B. 141,189,223 Mishchishina I.I 95
Banaszkiewicz M. 273 Mohlmann D. 67

Banos C. 287 Napier W.M. 13

Bavdaz M. 249 Obrubov Yu.V. 141

Carusi A. 21,29 Olsson-Steel D. 125,157,193
Cellino A. 121 Padevet V. 33
Ceplecha Z. 139,211,223 Paolicchi P. 101
Cevolani G. 179 Pecina P. 183,205
Crifo 3.F. 59 Perozzi E. 29
Di Martino M. 121 Petropoulos B. 287,291
Dumont R. 281 Pfau W. 91
Elford W.G. 193 Pinter S. 277
Esin-Yllmaz F. 83 Pittich E.M. 87
Falciani R. 79 Porubcan V. 163,167
Farinella P. 111 Rahe 3. 1

Fechtig H. 253 Rahmonov A.A. 55

Festou M. 79 Rajchl 3. 217

Froeschle C. 151 Rickman H. 37

GeorgakiUs A.A. 291 Scholl H. 151

Getman V.S. 221 Schumacher S. 277

Giese R.H. 231,241 Simek H. 199

Griin E. 257,277 Smaldone L.A. 79
Hajduk A. 177,179 Sole M. 47

Hajdukova M. 173 Spurny P. 225

Hsiung P. 47 Stecklum B. 91
Ibadinov Kh.I. 55 Stohl 3. 163,167

Ibadov S. 51 Svestka 3. 277

Jessberger E.K. 47.245,249 Svoren 3. 75

3ovanovic B. 107 Tammann G.A. 83

Kapisinsky I. 273 Tozzi G.P. 79
Kissel 3. 47 Traxel K. 245

Kneissel B. 231,241 Valnicek B. 7

Knezevic Z. 107 Valsecchi G.B. 21,29
Knbchel A. 249 Vashchenko V.N. 95
Konovalova N.A. 189 Wallenwein R. 245,249
Kresak C. 111,29,265 Xanthakis 3. 287
Kresakova M. 265 Zappala V. 101,121
Kristensen L.K. 131 Zioikowski K. 133
Kubacek D. 67 Zosimovich I.D. 95

Levasseur-Regourd A.C. 281 Zvolankova 3. 87

295
 ASTRONOMICKV OSTAV CSAV
Publikoce c. 67
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