Asphaug et al.

: Asteroid Interiors 463

Asteroid Interiors
Erik Asphaug
University of California, Santa Cruz

Eileen V. Ryan
New Mexico Highlands University

Maria T. Zuber
Massachusetts Institute of Technology

Asteroids represent a geophysical frontier of considerable scientific importance, for these

building blocks of planets preserve a compositional and mechanical record of the solar system’s
origin. They also pose a formidable hazard to life on Earth, while offering potentially enormous
resources to benefit solar system exploration. This chapter introduces their geologic subtlety
through the theme of strength vs. gravity: Asteroids stand apart from rocks and planets be-
cause these primary forces (strength short-range and gravity long-range) achieve an intricate
mechanical balance that is only partly understood. Recent findings have turned Earth-based
intuition on its head. For example, structurally weak asteroids and comets may, through stress
dissipation, be the most highly resistant to catastrophic disruption. Perhaps more surprising,
the collisional evolution of bodies the size of a city block may be determined by their minus-
cule self-gravity. While the fundamental geophysical behavior of asteroids continues to elude
us, one idea resonates: Instead of competing for dominance, strength and gravity collaborate
over a wide spectrum of sizes and shapes to produce some of the richest structures in nature.

1. INTRODUCTION of a city block, whose escape velocities are much slower

than a page turning.
The gravity of a small asteroid can barely hold on to its This is at serious odds with Earth-based intuition. Indeed,
rocks, yet the best spacecraft images of ~10-km bodies show most early ideas about asteroids have proven wrong. The
fields of boulders, lunarlike craters with dramatic rim de- recent adoption of modern geophysical ideas (rate- and size-
posits, landscapes mantled in mature regolith, and shapes dependent strength, micro- and macroporosity), together
broadly conforming to gravity potentials (see Sullivan et al., with laboratory, numerical, and dynamical advances de-
2002). But gravity’s influence must decrease with decreas- scribed below, have led to the overturn of several fundamen-
ing mass, and asteroids smaller than some diameter are gov- tal concepts regarding asteroid geodynamics and mechanics.
erned by strength. But how small? Smaller than tiny Dactyl? Their behavior is certainly not trivial, and it is appropriate
This ~1-km satellite of Ida [the first confirmed asteroid satel- to say that the study of asteroids expands our geophysical
lite, imaged by Galileo en route to Jupiter (Belton et al., experience to include low-gravity test beds of processes that
1996)] is a spheroid possessing what appear to be central remain poorly understood on Earth. Granular flow, impact
peak craters. These characteristics indicate gravitational con- cratering mechanics, studies of wave attenuation and fault
trol, yet anything traveling faster than a half meter per sec- motion in geologic media, and the mechanics of landslides
ond will escape Dactyl’s surface. [For a nonrotating asteroid may all be advanced considerably by studying the geophys-
with bulk density ρ ~ 2 g cm–3, escape velocity (in meters ics of asteroids. Of course, they also deserve our scrutiny
per second) is about equal to asteroid radius (in kilometers). for pragmatic reasons. The common kilometer-sized aster-
If you can jump half a meter on Earth, you can leap off a oids most hazardous to life on Earth might exist in a no-
5-km-diameter asteroid.] Smaller than near-Earth asteroid man’s land where neither gravity nor strength predominates,
Castalia? The first imaged asteroid (Ostro et al., 1990), and may be stranger than ever imagined.
Castalia is believed to consist of two ~800-m lobes resting
against one another self-gravitationally. Detailed examina- 2. STRENGTH AND GRAVITY
tion of even smaller objects has just begun (see Pravec et
al., 2002; and Ostro et al., 2002), but for reasons we shall To understand the collisional evolution of asteroids and
see, gravity may control the evolution of asteroids the size comets, researchers in the 1960s began using laboratory

463
464 Asteroids III

impact experiments to determine relations between initial elasticity and fragmentation.] But hydrocodes are seldom
conditions (e.g., speed and angle of impact, structure and easy to use and the data they produce are not trivial to in-
composition of target) and outcome (e.g., kinetic energy re- terpret. As with all tools, hydrocodes are easier to misuse
quired for breakup, velocity and rotation of fragments). This than use. One common culprit is lack of resolution adequate
database (see Fujiwara et al., 1989; Martelli et al., 1994; to resolve the impact shock. The shock determines the ve-
Holsapple et al., 2002) guides our understanding of impact locities in the excavation flow, and hence the growth of a
physics, although the experiments are limited to small pro- gravity-regime crater, or disassembly following catastrophic
jectiles whose masses can be accelerated to speeds (several disruption. Other errors include the use of an inappropri-
kilometers per second) typical of asteroid collisions. The ate equation of state, application of a model beyond its
largest laboratory targets are orders of magnitude smaller designed domain, and misinterpretation of results. Further-
than any asteroid; Earth’s gravity overwhelms self-gravity, more, although these numerical techniques date back half
to be sure, and also overwhelms delicate strength effects a century (e.g., von Neumann and Richtmyer, 1950), hydro-
that may be important at large scale. Chemical and nuclear code modeling is considered by many to be an immature
explosions (Rodionov et al., 1972; Perret et al., 1967) pro- technique. Fortunately, hydrocode outcomes can be tested
vide an analogous experimental database at geologic scales, in detail against laboratory experiments for cratering and
although an explosion in a half-space is significantly differ- catastrophic disruption (Melosh et al., 1992; Benz and
ent from impact into a finite, irregular target. Despite these Asphaug, 1994, 1995; Ryan and Melosh, 1998). Thus veri-
limitations, laboratory-scale impacts and high-yield explo- fied, a code can be applied with some confidence to more
sions constitute important benchmarks against which aster- complex scenarios and much larger sizes that are typical
oid collisional models must be gauged. But as we shall see, of asteroids.
the best benchmarks are the cratered asteroids themselves. While there remains some conflict between scaling vs.
It has long been recognized (Gault et al., 1972; Fujiwara, numerical modeling (particularly in the half-space cratering
1980) that impact disruption depends upon target size, so regime), the predictions for catastrophic disruption appear
two approaches were taken to extrapolate laboratory data to to have achieved some convergence, encouraging us to
relevant scales. Hydrodynamical similarity [“scaling” (see apply laboratory-validated code models to the fundamen-
Holsapple et al., 2002, and references therein)] is a pow- tal issues of gravity, strength, and structure on asteroids.
erful approach that offers a unique ability to provide mean- Furthermore, if asteroids are complicated entities with odd
ingful relationships between key parameters, for instance, shapes, rotations, prefractures, and porosities, numerical
fragment size as a function of impact energy and momen- approaches may be the only way, short of in situ experi-
tum, or ejecta velocity as a function of rock strength. The ments, of understanding their behavior.
most significant limitation of scaling is that it presumes a
homogeneous continuum, i.e., bodies that are either mono- 2.1. Strong Asteroids
lithic or finely comminuted. Where competing length scales
exist (e.g., size of projectile comparable to or smaller than Two decades ago it was widely believed on the basis of
size of structural components in an aggregate, or crater di- scaling from impact experiments (Gault and Heitowit, 1963;
ameter comparable to target diameter) or where target struc- Housen et al., 1979) that rocky asteroids smaller than
ture and shape is important (contact binary or coarsely shat- ~70 km diameter and icy bodies smaller than ~20 km would
tered asteroids), the technique may break down. But for lack regolith (cf. Veverka et al., 1986). [Correcting for a
well-posed problems (notably half-space cratering into ho- typesetting error: A line was skipped on p. 354 of Satel-
mogeneous media) the technique has a well-established util- lites, so that it would appear that the 20-km limit applied to
ity. Scaling also has the distinct advantages of providing rock, not ice (K. Housen, personal communication, 2001).]
direct physical intuition (for instance, how crater diameter Smaller bodies could not hold onto loose material because
relates to impact speed) and requiring no major computa- their craters would form in the strength regime, with nearly
tional effort. all material being accelerated to speeds >vesc. [The two
A very different approach is to directly integrate the classical regimes of impact cratering are the strength regime
shock physics relations, together with an equation of state and the gravity regime. Other regimes can also be defined
plus the mass, momentum, and energy conservation equa- (see Housen et al., 1983), depending on the dominant force
tions of continuum mechanics. These “hydrocodes” are restricting crater growth. Craters forming in the strength
versatile and on modern computers can be run with ad- regime must break apart rock, in which case the energy of
equate resolution and fidelity to model targets with layers, fragmentation (the rock strength) is proportional to the
cores, realistic shapes, prefractures, and multiple compo- energy of ejection. For craters forming in the gravity re-
nents. [The term “hydrocode” broadly describes any explicit gime, ejection velocity scales with vesc.] Nor could aster-
continuum mechanics code capable of modeling shock oids smaller than this size retain primordial regolith, be-
physics and the behavior of solid media under high dynamic cause scaled experiments showed that any surface debris
stress. Originally applied only to extreme conditions where would rapidly erode by impacts down to bedrock. Because
rock strength can be ignored (“hydro”), these codes have regolith is a common component of meteorites (see Bunch
evolved to model distinctively nonfluid behaviors such as and Rajan, 1988), regolith breccias were believed to derive
 Asphaug et al.: Asteroid Interiors 465

109

6)
99
(1
108 ns

)
re

85
Ah

(19
d
an

al.
ve
Lo

et
7)

vis

)
94
99

Da

(19
(1
Q*D (erg/g)

107

n
ya

ple
House

dR
n and

p
lsa
Holsa

an
pple (1

Ho
Hols 990)

sh
apple

lo
Far (199
Fig. 1. Values for the catastrophic dis-

Me
ine 4)
lla
et a ruption threshold Q*D of asteroids vary
106 Ry l. (1
an 982
(19
92
) widely in the literature. The darker line
)
is the summary of numerical outcomes
for basalt spheres by Benz and Asphaug
Du

(1999). The general trend for all mod-

rd
a

105 els is that rocks get weaker with size

et
al

(1
because of size- and/or rate-dependent
.

99
8)
strength, and then get stronger once self-
gravity dominates. For a collisionally
evolved population, objects to the right
10 4
102 103 10 4 105 106 107 of the minimum (the strength-gravity
transition) are likely to be shattered but
Target Radius (cm) not dispersed.

from parent bodies hundreds of kilometers across, or from (1979) defined a threshold specific energy Q*D (impact ki-
primordial surfaces prior to the onset of erosive collisions netic energy per target mass) required to both shatter me-
(Chapman, 1976). chanical bonds and accelerate half the mass to escaping
A related early puzzle concerned asteroid families, trajectories. Shattering requires a lower specific energy Q*S <
whose members have orbital elements suggestive of dis- Q*D to create fragments none larger than half the target mass.
persal by catastrophic impact (Hirayama, 1923) at speeds For small rocks Q*D → Q*S, whereas for large bodies Q*S/
of hundreds of meters per second (Cellino et al., 1999). For Q*D → 0. Whenever Q*S << Q*D, the probability of a shatter-
these family members to have survived such dramatic im- ing impact becomes far greater than the probability of a
pact acceleration, it seemed that their parent rock must have dispersal, in which case an asteroid might be expected to
been strong [see Chapman et al. (1989) for a variety of evolve into a pile of rubble, unless other effects (such as
asteroid family hypotheses]. Strong targets would yield fast, melting and compaction) were to dominate.
large family members whose strength might thereafter re- Davis et al. (1979) expressed impact strength as the sum
sist catastrophic disruption over the billions of years to the of the shattering strength plus the gravitational binding en-
present day. The argument for strong asteroids was not ergy of the target, for example,
entirely satisfying to those who have seen primitive mete-
orites fall apart in their hands, but it was largely self-con- Q*D = Q*S + 4/5 π ρ GR2 (1)
sistent. [High ejection speeds are no longer required by the
orbital elements of family members, however. It has recently where R is the radius of a spherical target and ρ is its den-
been discovered that the Yarkovsky effect can perturb small sity. Equation (1) is called energy scaling; on a graph of
asteroid orbits significantly over time; see Bottke et al. Q*D vs. R (see Fig. 1) it plots as a horizontal line (Q*D ≈ Q*S =
(2002).] constant) transitioning at some size to a gravity-regime
slope of 2 (Q*D ∝ R2). The size corresponding to this break
2.2. Regolith All the Way Down in slope is known as the strength-gravity transition for cata-
strophic disruption. [The strength-gravity transition for cata-
For asteroids larger than ~100 km, another concept was strophic disruption must be distinguished from the strength-
introduced in the 1970s: the existence of gravity-controlled gravity transition for planetary cratering. An object in the
rubble piles that consist of nothing but regolith. In devel- gravity regime for disruption (Earth is one) can certainly
oping an asteroid collisional evolution model, Davis et al. have strength-controlled craters.] Subsequent analysis has
466 Asteroids III

changed the slopes in both regimes (the predicted transi- Lawn and Wilshaw, 1975) because of the greater likelihood
tion size varies by orders of magnitude from model to of finding large flaws in large volumes. This notion, formal-
model), but the concept was established that beyond some ized by engineers who found that it became increasingly
size rubble piles might exist. difficult to grind coal (for example) down to smaller and
Because ρQ*S has dimensions of strength and is close to smaller sizes, contributes a new power-law size-dependence
the corresponding static tensile strength of ice and rock in to asteroid mechanics. Break any brittle solid in two under
laboratory impact experiments (Fujiwara et al., 1989), ten- modest tension, and the number of available flaws decreases
sile strength was used as an easily measured proxy for ρQ*S by the weakest flaw (plus whatever neighboring flaws are
in early disruption theory. Primitive asteroids, comets, and utilized to grow the crack). Continue in this manner to de-
early planetesimals, which are presumably weak, would be duce that strength increases monotonically with decreasing
easily disrupted. This led to some notable inconsistencies, size. [The concept was originally demonstrated by measur-
the most obvious being that primitive bodies smaller than ing the force required to snap smaller and smaller pieces of
~100 km would be unlikely to survive over billions of years, thread (Weibull, 1951)].
in contrast with their abundant population. If the static failure stress s of a rock decreases with flaw
The resolution to this dilemma appears to be that im- size L as σ ∝ 1/ L (Griffith, 1920), and if the maximum
pact strength and tensile strength are not simply related, and flaw size in a target rock increases in proportion to its ra-
may even be inversely correlated. Only later did experi- dius [as postulated by Fujiwara (1980) in his argument for
ments show that loosely bonded aggregates [such as a pile size-dependent strength], then impact strength — if equated
of sintered glass beads (Love et al., 1993)] can survive a with static failure stress — depends on target size R as
projectile that would blast an equal-mass monolithic cylin-
der to smithereens. It is now believed that some of the most Q *S ∝ 1/ R (2)
fragile bodies in the solar system — porous aggregates with
little or no cohesion — can be highly resistant to cata- This same relation was derived by Farinella et al. (1982)
strophic disruption owing to their ability to dissipate and by relating impact energy to the energy required to form
absorb impact energy. Furthermore, ejection velocities from new surface area during fracture. When plotted on a graph
fragile bodies are correspondingly low, enabling them to of Q*D vs. R (Fig. 1) this has a slope of –1/2 in the strength
hold on to their pieces. Like palm trees that bend in a storm, regime: According to this relation (and neglecting strength-
weak asteroids may survive collisions that would shatter and selection effects of meteorites, which makes them stronger
disperse monolithic solids. still), a centimeter-sized meteorite is ~1000× stronger than
But prior to these and other recent insights to be explored a 10-km asteroid. This has tremendous implications for the
below, a straightforward application of laboratory-derived survival of asteroids. If strength diminishes this rapidly, self-
values for Q*S and for the partitioning of impact kinetic gravity becomes the dominant binding force at sizes smaller
energy among fragments (Fujiwara and Tsukamoto, 1980) than previously considered.
made it fairly obvious that bodies up to ~100 km diameter A problem crops up at this point: The larger asteroid is
would be strength-controlled. This fit in well with the idea only weaker somewhere, otherwise every cubic centimeter
(Housen et al., 1979; Veverka et al., 1986) that regolith of a large asteroid would be weaker than every cubic cen-
would be thin or absent on such bodies. The ~100-km tran- timeter of a small asteroid of the same material. To avoid
sition gained further support due to its consistency with two such nonsense, concepts of heterogeneity are required. In-
much simpler notions: (1) The transition should occur when stead of considering only the single weakest flaw, consider
central pressure ~2/3πGρ2R2 equals rock strength; for icy or an asteroid of volume V ~ R3 that samples a theoretical
rocky targets this transition occurs at about 100 km diameter continuum riddled with a power-law distribution of flaws.
since rock is both stronger and denser. (2) It should occur These can be grain boundaries, pores, inclusions, or cracks
when gravitational binding energy per volume equals rock opened by previous collisions.
strength Y; neglecting constants this yields Rρ = (Y/G) , Suppose the number of flaws per unit volume that be-
and R on the order of several hundred kilometers, again gin to grow at or below a stress σ is described by a simple
whether for ice or rock. power law
With four distinct ways of viewing asteroid structure con-
verging upon a transition to the gravity regime at ~100-km n(σ) = kσm (3)
sizes, the idea seemed safe that all but the largest asteroids
were monolithic. Because geochemists predict intense early The probability (Weibull, 1939) of finding a flaw in a ran-
thermal effects in bodies larger than 100 km (Scott et al., dom volume V that will begin to grow at or below σ is then
1989; McSween et al., 2002) the existence of rubble piles 1-exp[–(σ/σmin)m], where
remained a conjecture.
σmin = (kV)–(1/m) (4)
2.3. Size-dependent Strength
The threshold for failure σmin goes with the –3/m power of
Impact modelers soon began to appreciate that static radius. For reasons not yet understood, m ~ 6 may be fa-
strength is sensitive to target size (Jaeger and Cook, 1969; vored by nature (Housen and Holsapple, 1999; Asphaug,
 Asphaug et al.: Asteroid Interiors 467

TABLE 1. Weibull dynamic fracture coefficients for various rocks.

Material Reference m k (cm–3) ln(k)/m

Basalt* Melosh et al. (1992) 9.5 1.0 × 1027 6.54
Basalt* Benz and Asphaug (1995) 9.0 4.0 × 1029 7.17
Basalt† Lindholm et al. (1974) 9.5 1.59 × 1030 7.32
Granite† Grady and Lipkin (1980) 6.2 4.14 × 1017 6.54
Water Ice*,†,‡ Benz and Asphaug (1999) 9.6 1.4 × 1032 7.71
30% Sand + Water Ice† Stewart et al. (1999) 9.57 1.34 × 1030 7.25
Concrete† Grady and Lipkin (1980) 5.3 5.27 × 1012 5.53
Oil Shale† Grady and Kipp (1980) 8.1 1.70 × 1021 6.04
Limestone† Grady and Lipkin (1980) 57.0 4.26 × 10167 6.77
* Determined from simulation fits to laboratory data. The two-dimensional axisymmetric simulations
of Melosh et al. (1992) require stronger fracture parameters than the nonsymmetric three-dimen-
sional simulations of Benz and Asphaug (1995) for the same impact experiment.
† Determined experimentally through measurements of tensile strength vs. strain rate.
‡ Earlier published values of m = 8.7, k = 3.2 × 1038 (Lange and Ahrens, 1983) were later corrected

to similar values [m = 9.57, k = 1.28 × 1032 (Stewart et al., 1999)].

Although k ranges by ~150 orders of magnitude, the situation is not entirely bleak. Homogeneous
materials (such as limestone reported below) have large m, and metals are approximated by m → 8.
Because the static failure threshold (σmin) is unchanged so long as ln(k)/m remains constant (see
text), homogeneous materials of a given strength have very large k. Equation (4) shows how rocks
with large m exhibit little size dependence. While dynamic fracture coefficients have yet to be
measured for any meteorite, Housen and Holsapple (1999) propose that m ~ 6 might generally
describe “well-cracked rocks at large scale,” and hence might apply to asteroids.

1993), in which case one recovers equation (2) assuming If ε is approximated as the impact speed divided by the
Q*S ∝ σmin. But values of m as high as 57 and as low as 2 impactor radius, then a 1-km-diameter impactor striking at
have been reported for rocks in the literature (Grady and 5 km/s couples at a strain rate ε ~ 10 s–1. Though undeni-
Kipp, 1980) (see Table 1) and no values of m or k have been ably dynamic, this is a far cry from the ε ~ 106 s–1 typical
reported for any meteorite. of laboratory experiments. Moreover, stress waves broaden
In some instances m may be determined by direct mea- and decay with distance, so ε drops with a steep (~4th)
surement of the flaws in a geologic specimen. However, this power of distance during hypervelocity collisions (Melosh
introduces a bias, as flaw sizes approaching the sample size et al., 1992). Strain rates responsible for shattering of ~10-
tend to be excluded, and flaws larger than the sample will km asteroids can be as small as 10 –3 to 10 –5 s–1 (Asphaug
not exist. More generally m is determined by fitting labo- and Melosh, 1993).
ratory experiments to the strength-strain rate relations de- Grady and Kipp (1980) applied Weibull statistics (equa-
scribed below, although these experiments are limited to tion (3)) to derive a dynamic fragmentation model comput-
small specimens and to the small flaws activated by dy- ing fracture stress and fragment size as a function of ε.
namic fragmentation. In most asteroid impact models, frac- Except for dynamical loads of such intensity that brittle
ture parameters for basalt, granite, or ice are assumed; the fragmentation is not the mode of failure, cracks grow at a
sensitivity of these models upon m precludes one from rate cg that is about half the sound speed (Lawn and Wil-
having robust faith in blind forward modeling. shaw, 1975). The crack tip is assumed to accelerate instan-
taneously to this velocity, when in fact it takes some finite
2.4. Rate Dependence time that depends upon the applied stress and upon crack
length. This dependence upon crack length (the integral of
The above analysis of σmin provides a static explanation crack growth velocity) makes any formal treatment of crack
for why Q*S should diminish with size. But Q*S is further tip acceleration difficult in such models. Because cracks
diminished on account of dynamical fracture mechanics: relieve stress over finite time, a dynamic equilibrium is
Rock strength is a function of the loading rate ε = dε/dt, established whereby strong flaws become active as needed,
where ε is the mechanical strain. It has long been estab- when weaker flaws cannot grow fast enough to accommo-
lished that the dynamic failure strength of rocks scales with date the accumulating stress. Therefore the weakest flaws
the ~1/4 to ~1/3 power of ε (Rinehart, 1965). Recognizing are sufficient to relieve the stress under low strain rates,
that ε decreases with the size of the collisional event, Hols- resulting in large fragments (due to the low density of weak
apple and Housen (1986) explored the implication of low flaws) and a low measured strength. At high strain rates,
strain rate collisions in a revised set of scaling models. on the other hand, stronger and more numerous flaws are
468 Asteroids III

called into play. This leads to the formation of small frag- function of target size; detailed quantitative comparisons of
ments (because of the high density of strong flaws) and at these specific experiments are in progress.
high measured strength. The resulting relationships (Grady At low strain rates, not only is strength diminished, but
and Kipp, 1980) are so is ejection velocity. Fragment ejection energy (1/2vej2)
is proportional to the energy of fragmentation (strength),
σ ∝ ε 3/(m + 3) (5) which varies inversely with target size. Thus, the fragments
from a large asteroid travel more slowly, not counting the
where exponents of 1/3 and 1/4 (Rinehart, 1965) corre- effects of gravity. This greatly reduced ejection velocity is
spond to m = 6 and m = 9 respectively, and perhaps the most significant aspect of rate-dependent
strength for asteroid collisional evolution, since as vej → vesc
L ∝ ε –m/(m + 3) (6) self-gravity begins to dominate.
Rate-dependent and size-dependent strength, together
so that fragment size L is inversely proportional to strain with the greatly diminished ejection speeds for large/weak
rate for large m. targets, combine to greatly increase gravity’s influence over
These same assumptions are the basis for numerical mod- catastrophic disruption for small asteroids. By the early
els of dynamic fracture of brittle solids (Melosh et al., 1992; 1990s, rate-dependent scaling theories (notably Holsapple
Benz and Asphaug, 1994, 1995), namely that (1) cracks and Housen, 1986) had pushed the threshold size for cata-
initiate from a Weibull distribution in accordance with the strophic disruption down to tens of kilometers diameter.
applied tensile stress, (2) the crack tip accelerates instanta- This revised threshold (soon to be pushed to even smaller
neously to half the sound speed, (3) planar cracks of radius sizes) began to erode confidence in well-established prin-
a relieve deviatoric and tensile stress in a spherical circum- ciples, and placed asteroid science at a crossroads. By 1990
scribed volume; and (4) a volume is damaged (stress-re- there was no longer any uniformly accepted conclusion
lieved) according to the ratio of cracked volume to total vol- regarding asteroid internal structure and the existence of
ume. Fully damaged rock, according to these models, is regolith. In only a few years, the first detailed views of
relieved of all stress except compressive pressure, and be- asteroids would come along, without science having con-
haves as a fluid. [A straightforward modification would be verged upon even the basics of what they are.
to have fully damaged rock behave as a cohesionless Mohr-
Coulomb material, where shear stress is still resisted accord- 3. CONCEPTS
ing to the applied normal stress according to the material’s
angle of internal friction (angle of repose).] Differences in 3.1. Structural Nomenclature
these models depend primarily upon implementation, with
Grady and Kipp (1980) assuming ε = constant to derive Before proceeding, it is useful to introduce various ar-
closed integrals, Melosh et al. (1992) allowing integration chetypes for asteroid interiors (see Richardson et al., 2002).
over time-varying strain rate, and Benz and Asphaug (1994, Simplest is the monolith, which is any rock of low porosity
1995) introducing an explicit flaw distribution plus three- and significant strength. A monolith is a good transmitter
dimensional hydrodynamics in addition to time-varying of elastic stress. By definition, monoliths tend to be smaller
strain rate. [In these numerical models, the total stress tensor than the nominal strength-gravity size transition. Since this
is rotated into principal axis coordinates and the maximal transition is likely to be dependent upon fracture parame-
value (most tensile) is taken as the stress σ that activates the ters and ρ (at least), any theoretically abrupt transition
Weibull flaws.] Without explicit flaws (assigned at random would be smoothed out over a population. Monoliths formed
from equation (3) to all discretized volume elements) large by impact ejection from a parent body must be stronger than
rock volumes are modeled as homogeneously weak every- the acceleration stress; kinetic energy densities and angu-
where, when in fact rock strength is approximately fractal. lar momentum densities (speeds and rotation rates) should
Experimental verification of rate dependence in cata- therefore be high.
strophic collisions was obtained by Housen and Holsapple Monoliths are fractured by impact bombardment, in
(1999) in a series of experiments involving cylindrical gran- which case their tensile strength is compromised and may
ite targets ranging from 1.9 to 34.4 cm diameter. These be reduced to zero (shattered). A fractured or shattered
targets, identical except for size, were impacted by propor- monolith might transmit a compressive stress wave fairly
tional diameter Al cylinders at uniform speed (~0.6 km/s), well, provided pore space has not been introduced between
with Q* held constant at ~1.0 × 107 erg/g for each event. the major fragments. (Tensile stress, however, is not sup-
The remarkable outcome is shown in Fig. 2. The smallest ported across a fracture.) A rubble pile includes any shat-
target is merely chipped by the bullet, while the largest tered body whose pieces are furthermore translated and
target (everything held constant but size) is catastrophically rotated into loose packing (e.g., Chapman and Davis, 1975).
demolished. Housen and Holsapple (1999) found agree- Stress waves of any sort are poorly transmitted across a rub-
ment between this granite test data and hydrocode estimates ble pile, although intense shocks may propagate by crushing
(Ryan and Melosh, 1998) for critical specific energy as a and vapor expansion. This category also includes primor-
 Asphaug et al.: Asteroid Interiors 469

Fig. 2. In a controlled series of impact experiments using a unique ballistics facility at Boeing Aerospace, Housen and Holsapple
(1999) impacted granite targets ranging from 1.9 cm to 34.4 cm diameter, otherwise identical, with proportional Al bullets fired at
~0.6 km/s, so that Q* = 1.0 × 107 erg/g for each event. The recovered bullet is the “fried egg” next to the first three targets. Because
strength is sensitive to both the loading rate and the target size, the mass of the largest remnant drops by a factor >8 between the
smallest and largest impacts. Analysis of the fragment size distributions leads to a Weibull exponent m ~ 6 for this material, in agree-
ment with thin-section examinations of the target rock’s flaw structure. This change of outcome happens across little more than an
order or magnitude in size; imagine the outcome for an ~10-km granite cylinder floating in space. Because rocks get weaker with the
~3/m power of size (see text), asteroids as small as ~1 km are now believed to be gravity-dominated entities.

dial rubble piles, those objects that accreted as uncompacted appear to be samples of the crust and upper mantle of as-
cumulates. These objects (e.g., Whipple, 1949; Weissman, teroid Vesta (Drake, 1979; Binzel and Xu, 1993; Asphaug,
1986) may have formed heterogeneously from grains into 1997; Keil, 2002; Burbine et al., 2002). Vesta is the only
clusters, clusters into larger aggregates, and so on hierar- known survivor of the original “onions” (basalt or related
chically into comets and asteroids (e.g., Weidenschilling and partial melts on the outside, and presumably olivine and
Cuzzi, 1993). then Fe on the inside), so the remainder of the original dif-
ferentiated asteroids — dozens of parent bodies judging by
3.2. Onion Shells and Cosmic Sediment the number of distinct classes of iron meteorites — have
been catastrophically disrupted (see McSween et al., 2002).
Many asteroids trace their lineage to differentiated proto- In contrast to differentiated asteroids and their monolithic
planets, and this remains the conceptual model for family- fragments are the rubble piles, which either accreted as
related asteroids (Hirayama, 1923; see also Zappalà et al., cumulates but never metamorphosed, or which reaccreted
2002). Meteoriticists have strong evidence for disrupted in the aftermath of a collision when Q*S < Q < Q*D. Indeed,
parent bodies; the H and L chondrites can be convincingly disruption and reaccumulation of planetesimals is likely to
reassembled (Keil et al., 1994) as “onion shells” of increas- have been a common and ongoing process in the early so-
ing metamorphic grade with depth, and HED achondrites lar system. In a terrestrial context we would call such an
470 Asteroids III

object sedimentary, of local or transported origin — this voirs in the deep interiors of primitive asteroids, with their
may be a more appropriate paradigm for asteroids since the mantles depleted through sublimation (Fanale and Salvail,
igneous “onions” appear to be mostly gone. Indeed, obser- 1990) or impact (see Rivkin et al., 2002). For gravity as low
vation and modeling no longer support the idea of simple as on a typical asteroid, frost or other fragile bonds can be
parentage for most surviving asteroids. For example, M- critical to long-term survival during impact or tidal events.
type spectra are no longer thought to be indicative of me- Comet Shoemaker-Levy 9, for example, could never have
tallic composition (see Rivkin et al., 2002). S-type asteroids, disrupted during its 1992 tidal passage near Jupiter (a nearly
apparently primitive in composition (Trombka et al., 2000), parabolic encounter with periapse of 1.3 jovian radii) had
appear in some cases (e.g., Gaspra) to derive from much the tensile strength across the comet exceeded ~1000 dyn/
larger parent bodies that one might expect to have under- cm2 (Sekanina et al., 1994), weaker than snow. Asphaug
gone extensive metamorphism. Strangest of all is the quan- and Benz (1994b, 1996) calculated a maximum tensile
dary that olivine-rich materials, representing mantle rocks strength of only ~30 dyn/cm2 for Shoemaker-Levy 9 in order
from the dozens of disrupted original companions to Vesta, for it to fragment from a coherent body into ~20 pieces,
is unaccounted for in the meteorite collection (see Burbine and therefore proposed a rubble-pile structure for this comet
et al., 2002), despite the fact that mantle rock should rep- and gravitational clumping (as opposed to fragmentation)
resent at least half of each disrupted parent body’s mass. as the cause of its “string of pearls” postperiapse structure.
It matters a great deal whether a body is truly strengthless
3.3. Meteorites or only extraordinarily weak: Volatile inventory is critical,
and poorly known.
Samples of asteroid interiors exist on Earth. However,
meteorites remain for the most part “samples without geo- 3.5. Fast and Slow Rotation
logic context” (McSween, 1999), and any connections be-
tween meteorite class and asteroid taxonomy are tentative. Recent discussion regarding monolithic asteroids has
To further obscure the asteroid-meteorite relationship, me- centered around a simple but profound observational result
teorites are small, highly selected specimens whose me- by Pravec and Harris (2000; see also Pravec et al., 2002).
chanical (and perhaps compositional) properties are seldom None of the ~1000 asteroids larger than 150 m with reli-
representative of asteroidal parents, as the latter are certainly ably measured spin periods rotates fast enough to require
weaker and more porous (Flynn et al., 1999). global cohesion. Specifically, for reasonable density esti-
Selection effects prevail when a meteorite is blasted from mates none rotates faster than ωo2 = 4πGρ/3, where ωo is
a parent body. Because strong rock fragments are ejected at the frequency at which material on a sphere’s equator be-
the highest speed, strong meteoroids are most likely to leave comes orbital. The corresponding minimum rotation period
their parent body at sufficient speed to encounter Earth at is Pcrit = 3.3 hrs/ ρ , with ρ in g/cm3. The most dense common
1 AU. Fragments must furthermore survive a long and con- asteroids (S type) appear to have ρ ~ 2.7 g/cm3 (Belton et
voluted journey through space, including the threat of cata- al., 1996; Yeomans et al., 2000); thus an S-type gravitational
strophic disruption by smaller meteoroids (Greenberg and aggregate can spin no faster than Pcrit ~ 2.0 hrs [see Holsapple
Nolan, 1989; Burbine et al., 1996) and must finally survive (2002) for a more detailed analysis of rotational breakup].
passage through Earth’s atmosphere and then residence From the Pravec-Harris asymptote at 2.2 hrs one might infer
upon our planet. They must also wind up in a meteorite col- a common maximum density ρ ~ 2.3 g/cm3, but as few as-
lection, although the Antarctic search plus direct followup teroids are spherical the corresponding density is probably
of fireballs has removed much of the bias against finding greater: Equatorial speeds are faster on an elongated body
extraterrestrial stones that may look like terrestrial rocks. and the mass distribution is noncentral.
Only one meteorite parent body to date has been vis- The easiest interpretation is that nearly all asteroids larger
ited with a sample return mission: A comparison of lunar than ~150 m lack cohesion. There are other plausible inter-
meteorites with Apollo samples (Warren, 1994) reveals that pretations. Larger asteroids might be internally coherent but
lunar meteorites are on the average much stronger than what possess thick regolith, shedding mass into orbit whenever
the astronauts gathered and brought home. Martian mete- random spinups [or spinup by the Yarkovsky effect (Rubin-
orites are also highly selected, almost all of them being rela- cam, 2000)] cause them to transgress the 2.2-hr rotation pe-
tively young basalts, whose high strength and wave speed riod, and then transferring angular momentum to this orbit-
may have facilitated their acceleration to escape velocity ing material. In this case the ~150-m transition may be the
during a cratering event (Head and Melosh, 2000). minimum size required for a body to retain regolith, and may
have less to do with asteroid internal structure.
3.4. Cohesion Another possibility is angular momentum drain (Dobro-
volskis and Burns, 1984). Angular momentum is lost when-
A volatile-rich aggregate is more cohesive than a dry ag- ever prograde ejecta (that launched in the direction of an as-
gregate because of the facilitation of mechanical bonding, teroid’s rotation) preferentially escapes while retrograde
either directly (e.g., van der Waals forces) or indirectly dur- ejecta remains bound. This is a good explanation for the
ing episodes of sublimation and frost deposition (Bridges relatively slow rotations of ~50–100-km-diameter asteroids,
et al., 1996). Some propose the existence of volatile reser- but for this process to apply to ~150-m asteroids the ejecta
 Asphaug et al.: Asteroid Interiors 471

mass-velocity distribution must have a significant component al. (2001a) proposed that the extraordinarily high spatial
slower than vesc ~ 5–10 cm/s. Such slow ejection speeds are densities of blocks on Eros (Chapman, 2001) represent the
typical of gravity regime cratering; for craters on ~150-m bod- migration of large blocks through size-sorting dynamics
ies to be governed by gravity, the target must be strengthless. towards the surface. Because size-sorting (e.g. the Brazil-
A final possibility is that small asteroids are simply colli- nut effect) may work best in low gravity (Jiongming et al.,
sion fragments with more angular momentum per unit mass 1998), it is even possible that the shapes of rubble-piles
than the larger remnants. In that case one would anticipate a might be governed by the very largest blocks working their
smooth transition from fast, small rotators to large, slow rota- way out towards the lowest gravitational potential.
tors, whereas the observed transition appears to be abrupt. A different view of particulate dynamics in rubble piles
Furthermore this does not explain the absence of anoma- leads to the stacked block model of Britt and Consolmagno
lous fast-rotating asteroids larger than 150 m. In summary, (2001), whereby regolith drains inwards only until small
the rotation rate data appear to require that asteroids larger grains clog the gaps between large blocks. Thereafter a
than 150 m are either strengthless or else mantled in deep mantle of fine material settles over an interior of large
regolith; perhaps future rotation rate surveys around this blocks and voids: a body with fairly high bulk density near
transition size will constrain our explanations. the surface, and significant interior porosity. These and other
An even bigger mystery is that only one asteroid smaller ideas regarding size-sorted asteroid structure will remain
that 150 m diameter (out of ~25 total) with measured rota- conjecture until the sciences of granular dynamics and of
tion rate rotates slower than this limit. [These statistics asteroid geology make significant advances.
change on a monthly basis and are by the time of reading 3.6.2. Microporosity vs. macroporosity. One must dis-
out of date; see Pravec et al. (2002)]. While no asteroid tinguish between macroscopic and microscopic porosity in
larger than ~150 m shows evidence for global cohesion, aggregate materials. An asteroid consisting of quintillions
almost all asteroids smaller than this must be cohesive. One of tiny grains might exhibit considerable cohesion and per-
might suppose that every larger asteroid is a gravitational haps support a fractal-like porosity. The total energy of con-
aggregate of smaller pieces, whereas every smaller aster- tact bonds divided by the total mass of a granular asteroid
oid is a fast-rotating collisional shard. But the term “mono- (its overall cohesional strength) is inversely proportional to
lith” for these smallest asteroids is misleading. Consider a grain diameter, so that a coarse aggregate is weaker than a
spherical object of uniform density ρ rotating with a fre- fine one. On the other hand a highly porous, finely com-
quency ω; the mean stress across its equator is ~R2ρω2. For minuted body can be crushable: cratering on microporous
the well-studied fast rotator 1998 KY26 (Ostro et al., 1999), asteroids might be a strange event involving compaction
self-gravity is not capable of holding it together; however, (Housen et al., 1999) rather than ejection.
its ~11-min period and ~30-m diameter requires only a ten- A coarse rubble pile by contrast would have far fewer
sile strength of ~300 dyn/cm2 (presuming ρ ~ 1.3 g/cm3 for contact surfaces distributed over the same total mass, and
this C-type), orders of magnitude weaker than the tensile would therefore behave much differently. Asphaug et al.,
strength of snow. (1998) used a coarse rubble pile as a starting condition for
impact studies, and found that the impact shock wave gets
3.6. Regolith and Structural Porosity trapped in the impacted components, with few pathways of
transmission to neighboring components. Whether an as-
Besides the rotationally induced regolith loss just con- teroid is macroporous or microporous, stress wave trans-
sidered, a number of fundamental processes can take place mission is hindered due to the great attenuation of poorly
in the components and regoliths of shattered and fractured consolidated rock, making the survival of porous asteroids
monoliths and rubble piles. during impact more likely, as demonstrated by the experi-
3.6.1. Grain sorting. Horstman and Melosh (1989) ments of Ryan et al. (1991) and Love et al. (1993) and as
proposed that regolith might drain into the interior of the illustrated below.
martian satellite Phobos in response to block motion dur-
ing the collision responsible for its large crater Stickney. 3.7. Overburden Pressures
Over time this process would expose large crustal blocks
to the surface as impact-comminuted materials work their Small asteroids have correspondingly low internal pres-
way down (Asphaug and Melosh, 1993). Sears and Akridge sures. Because our geophysical intuition of monoliths and
(1998) proposed that grains might become compositionally rubble piles is based upon our familiarity with terrestrial
sorted in a regolith rendered dynamic by volatile outflow or landforms, it may be helpful to consider the equivalent
meteorite gardening, resulting in iron-silicate fractionation depth zeq of a planar stack of the same material, under Earth
on an unmelted parent body. gravity, for which overburden pressure ρgzeq is equal to the
Indeed, an asteroid’s regolith or a rubble pile’s entire central pressure in an asteroid of radius R. Solving, this
mass might be expected to undergo dynamical granular gives
processes (reviewed by Jaeger et al., 1996) on a variety of
timescales in response to a variety of perturbations such as zeq(R) = 23 π Gρ2 R2/ρg = 1.4 × 10 −10 ρR2 (7)
impact excavations, vibrations, tides, differential expansion
and electrostatic repulsion (Lee et al., 1996). Asphaug et in cgs units, where g = 980 cm/s2. For Phobos zeq ~ 3 m with
472 Asteroids III

a central pressure of about 2/3 bar. For Mathilde, zeq ~ 13 m. dence that the ~150-m Pravec-Harris transition is due to
For Vesta, zeq ~ 3 km. One might anticipate analogous con- structure, for it appears to hold true for target materials of
ditions within rock and soil masses at depths on Earth cor- dissimilar density, thermodynamical behavior, and flaw dis-
responding to equal applied pressure. It is food for thought tribution. Then again, these hydrocode outcomes are for
that the 150-m-diameter transition observed by Pravec and near-threshold disruption of spherical monoliths, whereas
Harris (2000) corresponds to a zeq of less than a millimeter, actual asteroids have less-pristine original states and more
and to a central pressure of less than 100 dyn/cm2 — one- intricate collisional histories. In particular, a detailed analy-
millionth the tensile strength of rock. It is therefore easy to sis of the impact evolution of primordial rubble piles (or a
appreciate the continued resistance to ideas of gravity domi- population evolving through myriad hypervelocity colli-
nance at such small scales. sions) has yet to be conducted. In an initial exploration (see
The importance for asteroid geology is considerable, as below), Asphaug et al. (1998) find that simple variations
already discussed. For spacecraft exploration these details in target structure (a crack down the middle, for instance)
are also critical: The maximum shear stress supportable by yields dramatically different disruption outcomes. [For low-
asteroid regolith will be miniscule, in proportion to this impact velocities (~10 m/s) typical of planetesimals in the
vanishingly small normal stress. The behavior of materials “cold disk” before planet formation, Benz (2000) and Lein-
at exploration landing sites is likely to be strange compared hardt et al. (2000) find that rubble piles are easily dispersed.
with the operational test beds here on Earth. This suggests a problematic bottleneck at the initial stage
of planetary accretion.]
4. COLLISIONAL EVOLUTION Given that small impacts are more common than large
ones, an event of Q*S < Q < Q*D is expected before cata-
The physical geology of asteroids is largely the after- strophic dispersal (Q > Q*D). This means that shattering is
math of several global-scale collisions plus a fusillade of expected before catastrophic disruption. The end state of
smaller impacts; accretion itself is nothing but collisions of collisional evolution of asteroids larger than a few hundred
a gentler sort. Tides and surface process play a secondary meters is, by this logic, a gravitational aggregate. Those
role, at least in the present solar system. As is now believed primitive bodies that are rubble piles from the start (e.g.,
to be the case for planet formation (Wetherill, 1985), accre- Weissman, 1986) probably follow a different disruption
tion and cratering of asteroids may be dominated in terms of scaling than the monolithic rocks simulated by Ryan and
energy, mass, and angular momentum contribution by the Melosh (1998) and Benz and Asphaug (1999), with shat-
largest events. For planets, the largest event might trigger tering energy Q*S actually greater for a rubble pile with
core formation (Tonks and Melosh, 1992); for asteroids it modest cohesion than for a monolithic rock (Ryan et al.,
may determine the interior structure of the body and hence 1991; Love et al., 1993). It remains unclear how the en-
its response to future collisions. If rubble-pile asteroids are ergy for dispersal, Q*D, will change for rubble piles, but it
resistant to further disruption (Love et al., 1993; Asphaug, appears this, too, will be greater than for monolithic rock.
1998) then the first noncatastrophic (Q < Q*D) impact ex- The two current models for impact into porous asteroids
ceeding Q*S might therefore determine an asteroid’s long- differ fundamentally in this regard (Asphaug and Thomas,
term survival. 1999; Housen et al., 1999) (see below), yet both conclude
As discussed by Richardson et al. (2002), the 150-m thres- that aggregate bodies resist disruption and dispersal in the
hold discovered by Harris (1996) and Pravec and Harris hypervelocity regime.
(2000) had been deduced by hydrocode simulations of as- While there is much to be done in understanding the
teroid collisions. Love and Ahrens (1996), Melosh and Ryan behavior of shattered monoliths and rubble piles, it would
(1997), and Benz and Asphaug (1999) applied a variety of appear that such aggregates are the natural end state of as-
code and analytical techniques to explicitly derive the values teroids larger than ~1 km.
of Q*D for asteroids as a function of size. The most detailed
of these studies (Benz and Asphaug, 1999) applied a labora- 5. SIMULATING THE GIANT CRATERS
tory-derived size- and rate-dependent explicit fragmentation
model (Benz and Asphaug, 1995) together with a postim- Asteroids suffering catastrophic disruption have lost at
pact search for the largest surviving clump, whether bound least half their volume and bear little sign of their previous
by self-gravity or strength. All these approaches derive a incarnation. Those suffering giant craters, by contrast, still
strength-gravity transition, for initially coherent spherical exhibit their original shape minus a huge divot or two, and
bodies of rock or ice, at a few hundred meters diameter. may tell us how their interiors responded. It is hardly a
Benz and Asphaug (1999) further found an abrupt transi- coincidence that most asteroids imaged to date exhibit cra-
tion in the structure of the largest remnant after a disruption. ters with diameters comparable to their own mean radius;
For targets smaller than ~1 km (whether rock or ice) suffer- this simply reflects that asteroids are capable of surviving
ing catastrophic disruption, the largest surviving remnant enormous blows with relative impunity, perhaps owing to
consists of a single monolith in their models. For targets their unconsolidated interior structure.
larger than ~1 km, on the other hand, the largest surviving Giant craters probe the brink of catastrophic disruption
remnant is a gravitationally bound aggregate of pieces all and thereby elucidate impacts at geologic scales — a pro-
much smaller than the target. This is taken as further evi- cess masked by gravity on Earth. With three-dimensional
 Asphaug et al.: Asteroid Interiors 473

hydrocodes including rate-dependent strength running on

powerful computers, one can model the details of their for-
mation. Indeed, because one must resolve both the target
and the impactor, large craters are actually easier to model
than small ones for a finite target.
Most importantly, impact models can now be tested
against targets of asteroidal composition and asteroidal
scale. Rather than relying on blind extrapolation from labo-
ratory experiments, we can match the outcomes of detailed
impact models against existing giant craters on asteroids.
This begins with an asteroid shape model transformed into
a simulation grid [for modeling specifics, see Asphaug et
al. (1996)]. For a giant crater, one must then reconstitute
the shape so as to fill in the volume deficit, hopefully leav-
ing a good approximation of the preimpact target. One then
makes initial guesses as to interior structure and composi-
tion, as these are to be tested. For the impactor, one can
assume nominal incidence angle and impact velocity and
adopt some value [perhaps that predicted by gravity scal-
ing (Housen et al., 1983)] for the mass. Craters larger than
about ~1 km diameter appear to form in the gravity regime
for ~10-km monolithic asteroids (Asphaug et al., 1996), so
this is frequently a good starting assumption. One can then
iterate upon interior geology, and if required, upon the mass
and velocity of the impactor, until one arrives at a satisfac- Fig. 3. A photomosaic of Phobos by the Viking Mars orbiter (see
Thomas et al., 1979). The large crater Stickney is visible at the
tory fit to observables: distribution or absence of crater
upper left, and a number of grooves are prominent. Groove geom-
ejecta, global or regional fractures associated with the event, etry has been shown (Fujiwara, 1991) to correlate with impact
boulder distributions, etc. stress. Phobos is approximately a triaxial ellipsoid with dimen-
Because high-fidelity modeling remains computationally sions 19 × 21 × 27 km; Stickney’s diameter is ~10 km. Phobos is
expensive, and data analysis is not yet automated for this mysterious for its subsynchronous unstable orbit about Mars, its
kind of inversion, only rough iterations have been per- low density, and the fact that Stickney did not disrupt a satellite
formed to date for a handful of asteroids, as presented here. inside the Roche limit.

5.1. Phobos

Phobos, the ~22-km-diameter innermost satellite of Mars, stroyed Phobos (exceeded Q*S) and launched most of the
was the first small planetary body observed at high resolu- impacted hemisphere into orbit, turning Phobos inside-out.
tion (Veverka and Thomas, 1979). Its ~10-km crater Stick- This was in stark contrast to the satellite’s state of preser-
ney was a major curiosity until giant craters were found to vation. Using instead a gravity-scaled impactor [230 m di-
be the norm. Indeed, the smaller martian moon Deimos has ameter at 6 km/s, from Housen et al. (1983)], they found
an even larger crater in proportion to its size (Thomas, that this fragmented more than enough bedrock (whether
1998), although it took decades for this to be acknowledged. for icy or rocky targets) to allow an ~10-km crater to evolve
Its prevalent fracture grooves (Fig. 3), probably correlated into shock-fragmented material. This greatly diminishes the
with Stickney (Thomas et al., 1979; Fujiwara, 1991), pro- effect of strength control over crater excavation (see Nolan
vide an ideal application for strength models. et al., 1996).
Using a two-dimensional hydrocode in axisymmetry Equally significant, the flow field behind the shock in
(Melosh et al., 1992), Asphaug and Melosh (1993) attempted their model had particle velocities consistent with gravity
to model Stickney as a strength-regime event; i.e., they used scaling’s predictions, with mean flow of a few meters per
Housen et al. (1983) to predict the impactor mass required second throughout the rubble, and an excavation timescale
to yield an equal-sized crater in a geologic half-space, and of an hour. Asphaug and Melosh (1993) concluded that
applied this same impactor to Phobos. Not knowing any Stickney was a gravity-regime event, and showed that huge
parameters other than shape and bulk density [~1.95 g/cm3 craters on asteroids as small as a few kilometers in diam-
was assumed from the recently concluded Phobos 2 flyby eter should be gravitationally determined. At slow excava-
(Avanesov et al., 1989)], they adopted Weibull fracture con- tion speeds, however, dynamic grain friction begins to play
stants and equations of state for basalt and for water ice, the role envisioned by Housen et al. (1983). This is not yet
hoping to span the range of possibilities. They first discov- included in any model. Neglecting friction and the influence
ered that a strength-scaled impactor (730 m diameter at of Mars, Asphaug and Melosh (1993) found that Phobos
6 km/s, for the size-dependent strength of 0.1 kbar) de- should be covered by hundreds of meters of Stickney ejecta,
474 Asteroids III

(a) in agreement with observation (Thomas et al., 2000; Horst-

man and Melosh, 1989). Stickney’s formation in the gravity
regime was dramatically unlike the millisecond-scale labo-
ratory experiments upon which asteroid evolution models
had thus far been derived.
Fujiwara (1991) pioneered an important structural geo-
logical technique, correlating fracture geometry on small
(b)
bodies (Phobos) with the responsible impact, thereby con-
straining elastic mechanical properties of the target rock.
More detailed fracture modeling became possible with
three-dimensional strength hydrocodes at high resolution,
resulting in a kind of asteroid seismology. Asphaug and
Benz (1994a) performed the same calculations as Asphaug
and Melosh (1993), but using three-dimensional smooth
particle hydrodynamics (SPH), explicit flaws, and an ellip-
soidal target (see Fig. 4) so that the actual fracture pattern
could be discerned in the model outcome. The modeled
Phobos, being a low-density (ρ = 1.95 g/cm3) elastic solid,
transmits stress energy well, and fractures open up radial to
the crater and also around the antipode (Fig. 4a). Figure 4b
shows ejecta evolution 12 s after impact in this gravity-re-
(c) gime event. One difference between two-dimensional and
three-dimensional hydrocode models is that the crater in
three dimensions (for the identical gravity-regime projec-
tile) is smaller than in two dimensions. The three-dimen-
sional results show the gravity-regime impactor fragmenting
barely enough rock to allow the flow field to open up un-
encumbered by strength. The discrepancy arises because
axisymmetric models cannot relieve stress along radial
cracks, resulting in a larger crater bowl. With strength-re-
gime impactors too big and gravity-regime impactors too
small, Stickney on Phobos may be intermediate between the
Fig. 4. (a) Fracture damage (black) on the surface of an ellip- classic scaling regimes.
soidal Phobos viewed during half a rotation, one minute after the A strongly heterogeneous Phobos was found to be in-
Stickney-forming event (Asphaug and Benz, 1994a). The initial compatible with groove formation. By removing 30% of the
SPH hydrocode target has a flaw distribution and other material SPH particles at random from a basalt (ρ = 2.7 g/cm3) tar-
properties (other than density) derived from basalt (used in the get, Asphaug and Benz (1994a) constructed a macroscopi-
absence of better alternatives), substituting a reference density of cally porous, highly scattering target of the appropriate bulk
1.95 g/cm3. The impactor is a 230-m-diameter sphere of the same
density. The top frame of Fig. 4c shows seven “potato chip”
material impacting at 6 km/s. The interior, homogeneous except
for the explicit flaw distribution (see text), allows for the trans-
slices, 2 km thick, through the final target interior of Fig. 4a.
mission of coherent stresses to the backside of the target, leading The bottom frame shows the same slices through the 30%
to focusing and antipodal rupture broadly consistent with obser- porous body (the flecks of black are the interstitial voids).
vations. (b) Cross section through the final Phobos target 12 s after As porous targets are poor transmitters of impact stress,
impact. Fast ejecta is escaping, but the crater bowl has only be- fragmentation is confined to the impacted hemisphere. Pho-
gun to open. An astronaut witnessing the event could read this bos cannot have had this kind of highly scattering interior
entire chapter in the meantime. (c) Parallel slices 2 km thick if fracture stresses propagated coherently to the antipode.
through the postimpact targets for two SPH models of Phobos. With sufficient numerical resolution and time, one might
The top slices show the competent “monolith” with Weibull flaws tune the interior model of Phobos to yield the best possible
[(a) and (b) above], with cracks throughout the cratered hemi- agreement between crack morphologies, crater diameter,
sphere and at the antipode. The bottom slices show an object of
ejecta placement, and interior structure. That is the prom-
the same bulk density (1.95 g/cm3) suffering the same impactor,
but whose porosity is 30% with material specific density 2.7 g/
ise of crater profiling of asteroid interiors. At present we
cm3. The flecks of black in the bottom slices are interstitial voids arrive at some preliminary conclusions: For either model,
(random particles that were removed), not damaged rock. The the velocities subsequent to impact are too low throughout
porous target is a poor transmitter of impact stress; collisional Phobos to greatly reduce bulk density. If Phobos was not
effects are confined to the impacted hemisphere — a crater and highly porous before Stickney (so that distal cracks could
little more. form), and if Stickney did not introduce significant poros-
 Asphaug et al.: Asteroid Interiors 475

ity, then the low density of Phobos is compositional or diameter projectile strikes at 3.55 km/s [ vimpact at Ida (Bottke
microstructural in nature. et al., 1994)]. Gravity scaling assumes constant gravity (in
this case, the local effective gravity at the impact site) when
5.2. Ida in fact gravity varies by a factor of ~4 across the asteroid
(Thomas et al., 1996), and by a factor of ~2 over the region
By the time Galileo encountered asteroid Ida (Belton et of this particular collision. Wave interference is complex in
al., 1996), model resolution had improved to the point that this irregular target, and potentially important focusing might
image-derived shapes could be used in impact simulations. occur if the asteroid is a homogeneous transmitter of com-
Figure 5 shows an SPH model of Ida based upon the shape pressive stress. The simulation (again using fracture and
derived by Thomas et al. (1996): a highly irregular body elastic constants for laboratory basalt, pending better alter-
with mean radius 15.7 km. As with Gaspra (Carr et al., 1994) natives) shows the opening of fractures in the same narrow
and Eros (Prockter et al., 2000), this S-type asteroid exhibits opposite end of Ida (Pola Regio) where grooves are found. A
expressions of internal shattering in the form of linear fur- heterogeneous or porous interior would have dissipated or
rows almost certainly related to large collisions. Using this scattered these stresses (Asphaug and Benz, 1994a), so this
Ida model, Asphaug et al. (1996) attempted to recreate a model outcome lends support to the hypothesis that the deep
few major craters including the ~12-km-diameter Vienna interior of Ida is competent and homogeneous, in agreement
Regio (Fig. 5a). Figure 5b plots particle velocity through a with its presumably low porosity [from its satellite-derived
slice of the target 9, 10, and 12 s after a gravity-scaled 330-m- density of 2.6 ± 0.5 g/cm3 (Belton et al., 1996)]. As with
fractured Phobos, mechanical competence is needed only
under compression. A well-connected interior is required,
but tensile strength is not.
(a)
5.3. Eros

The NEAR Shoemaker mission to asteroid Eros, com-

pleted in 2001, represented a quantum leap for asteroid
geology but left deep puzzles about the asteroid’s interior.
The mission was instrumented to determine asteroid com-
position, the only interior probe being the radio science
experiment, which tracked gravitational influence on orbit

(b)

Fig. 5. (a) Smooth particle hydrodynamics (SPH) model of asteroid Ida, using the shape derived by Thomas et al. (1996) from Galileo
imaging. This model was used by Asphaug et al. (1996) to recreate three major craters on Ida and a suite of smaller craters. Prior to
the impact, Vienna Regio (~12-km crater on the upper left) was filled in and then impacted by a gravity-scaled impactor in an attempt
to simulate the key aspects of its formation. Particles close to 10° grid lines are color coded in this view. (b) Particle velocity is shaded
within a slice of the Ida target at t = 8, 9 and 12 s after the 330-m-diameter impactor strikes at 3.55 km/s to create Vienna Regio.
Reflections from the complex shape lead to complex waveforms and stress wave interferences as can be seen in the dark zero-velocity
nodes. This model resulted in distal, isolated fracture on the far narrow end where grooves are observed, and lent support to the hy-
pothesis that the deep interior of Ida is a good transmitter of compressive stress.
476 Asteroids III

(Yeomans et al., 2000). This enabled determination of den- TABLE 2. Approximate angles of
sity and broad-frequency (approximately kilometer-scale) repose for common materials.
variations in density; of the latter it found none. Details of
this mission are recounted in Farquhar et al. (2002); here Angle
Material of Repose
we consider the implications of these results for asteroid
interior structures. In composition and shape, and roughly Glass beads ~20°
in size, Eros is akin to Ida, also an S-type with bulk den- Common unconsolidated materials (e.g., sand) ~33°
sity ~2.7 g/cm3. This is somewhat lower than the mean Steepest value for highly angular, poorly
density of ordinary chondrites [the closest compositional sorted rocks ~40°–50°
Water-rich soils up to 90°
analog according to Trombka et al. (2000)], so Eros is prob-
ably as nominally porous as any heavily fractured rock
mass. Given its battered appearance (Prockter et al., 2002),
Eros’ density is not a mystery.
Despite this evidence for disruption, a number of obser- Is this evidence for or against structural control? One can
vations exhibit structural competence: the twisted planform argue both ways from the dataset. In order to have some
of Eros, its clustered regions of high slopes (Zuber et al., slopes steeper than the presumed angle of repose, Eros must
2000), its long, continuous grooves (Prockter et al., 2002), possess some cohesion at ~100-m scales. Conversely, the
its polygonal craters (indicative of fault structure, just as at total area steeper than repose is less than a few percent, and
Meteor Crater in Arizona), and its subdued or missing crater highly localized. Plate 1, derived from the NEAR Shoemaker
rims (particularly at the low-gravity ends of the asteroid). laser rangefinder (NLR) experiment (Zuber et al., 2000),
The latter suggest crater formation in the strength-regime, shows these local slopes plotted on a shape model of the
where ejecta velocities are higher than vesc. But geological asteroid. Almost all slopes exceeding ~30° lie inside the
competence is different from dynamical competence, and rims of craters, which on Eros (as on the Moon and Earth
this has led to a healthy debate about structural nomencla- and other bodies) have slopes consistent with the angle of
ture [perhaps now resolved; see Richardson et al. (2002)] repose of unconsolidated rock.
and asteroid mechanics.
Nearly all agree the saddle-shaped depression Himeros
is an impact crater. Crater fracture models (Asphaug et al.,
Measured gravity, r = 20 km, Imax = 6
1996) and seismic profiles at Meteor Crater (Ackerman et
al., 1975) show that impact craters have major fractures 180

extending about one crater radius beyond the crater in all 160
directions. For Himeros, fractures would extend through the

mgal
asteroid’s narrow waist. If so, the asteroid is disconnected, 140

possibly evidenced by the complex fault structure Rahe

120
Dorsum, which strikes through Himeros. Dynamicists might
then call Eros a “rubble pile” since it comes apart into 100
pieces under modest tension (rotations or tides). To impact
modelers, it might fall into that category as well, because Gravity from shape, r = 20 km, Imax = 6, Topo Imax = 12

a binary object can, like an assemblage of smaller rubble, 180

absorb considerable collisions by trapping impact energy 160

inside the impacted lobe (Asphaug et al., 1998). To recon-
mgal

cile dynamical ideas, that the body might simply float apart 140

if gravity were turned off, with geological ideas, that Eros

120
exhibits considerable strength-controlled structure, we call
this S asteroid a shattered monolith, and apply the same term 100
to Ida based upon the modeling just presented.
Despite its irregular shape (see Plate 1) actual slopes on
Eros, as on Ida, are moderate. Variations in the gravity vec- Fig. 6. The NEAR Shoemaker gravity experiment (Yeomans et
tor (including centrifugal force) are extreme, largely can- al., 2000) detected no sign of heterogeneity within Eros, as evi-
celing extreme variations in topography. One can quantify denced by these almost indistinguishable gravity maps. The upper
figure shows gravity as determined by the radio science experi-
slopes by plotting a histogram of cumulative area steeper
ment, and the lower shows gravity computed from the NLR shape
than a given angle (see Zuber et al., 2000), although such model (Zuber et al., 2000) assuming uniform density. Gravity is
histograms depend upon the measurement baseline: Geo- only resolved to low degree and order by spacecraft Doppler track-
logic (fractal) surfaces become jagged at small scale. At ing, corresponding to a resolution at scales of 1 km or larger.
100 m baseline, ~2% of Eros is steeper than can be main- Gravity is also more sensitive to exterior than interior components.
tained by a pile of talus (see Table 2), and ~3–4% of the If Eros is of heterogeneous density, it must be well-mixed at ki-
slopes are steeper than can be maintained by sand. lometer scales.
 Asphaug et al.: Asteroid Interiors 477

The only interior probe of Eros was the radio science

(a)
experiment that Doppler-tracked the spacecraft position and
velocity (Yeomans et al., 2000) and yielded a gravity map
of the asteroid’s interior. Because orbital speeds were only
a few meters per second, intrinsic limits to Doppler accu-
racy resulted in coarse (approximately kilometer-scale) de-
termination of interior density distribution. Moreover, most
of the power in gravity variation is found in the asteroid’s
exterior, so that interior structure is not well characterized
other than bulk density. Figure 6 shows the gravity field of
Eros as measured by the spacecraft, plotted at 20 km ra-
dius from the center of mass, vs. the gravity field that is
deduced from the NLR shape model, assuming a uniform
bulk density. The variations are extremely slight, and can
be accounted for by tens of meters of regolith thickness
variations overlying a uniform substrate, or by a density gra-
dient across the asteroid of 0.006 g cm–3 km–1.
Another aspect of Eros is its highly fractured state
(Prockter et al., 2002; see also Sullivan et al., 2002), which
has been used to support the notion of geologic competence. (b)
This dataset also argues both ways. On the one hand it Nonporous Mathilde Impact:
shows that the asteroid can support global fault structures. 1.2-km-diameter, 1.3-g/cm3 impactor,
Conversely, in a dynamical sense, those global fault struc- at 5 km/s
tures are probably what disconnect the asteroid. The dis-
tinction is critical, for as we shall see, an asteroid that is
broken behaves very differently during impact than one that
is not.

5.4. Mathilde

En route to Eros, NEAR Shoemaker encountered the

primitive C-type asteroid 253 Mathilde and retrieved high-
quality images despite limited solar power and challenging
illumination (Veverka et al., 1997) (see Fig. 7a). Mathilde is
the first visited of those dark, primitive asteroids that domi-
nate the main belt; it may be typical of unequilibrated or
carbonaceous asteroids and perhaps representative of early
planetesimals. Orbiting the Sun at a = 2.6 AU, Mathilde Three-dimensional Impact
Surface Fractures
measures 66 × 48 × 46 km (best-fit ellipsoid). Its mass,
determined by deflection of the spacecraft, is ~1.0 × 1020 g,
yielding a bulk density of ρ ~ 1.3 g/cm3, a low density that Fig. 7. (a) The second image mosaic of asteroid Mathilde (~66 ×
would be consistent with an icy composition except that 48 × 46 km), the only C-type asteroid imaged to date, taken just
groundbased astronomy detects no water on the surface prior to closest approach (Veverka et al., 1997). Two vast craters
(Rivkin et al., 1997). Mathilde is a typically red C-type as- span the foreground; there are ~5–7 craters of comparable size
teroid whose spectrum is best matched by primitive carbon- (Thomas et al., 1999). Equally baffling are the observations that
aceous meteorites with densities over twice as great, and Mathilde’s craters lack raised rims or any other evidence of ejecta
this has led to the idea of >50% porosity. Mathilde’s rota- deposition, and that Mathilde at ~5 km/pixel shows no sign of
tion period is among the longest measured, P = 17.4 d, fracture grooves, impact disruption, or even rim-disturbance of
which is difficult to reconcile with its incredible cratering preexisting craters. Each giant crater left no apparent trace of its
history: five to seven giant craters, at least four larger in formation other than an enormous cavity; we cannot tell which
was the last to form. (b) A failed attempt using SPH to produce
diameter than the asteroid’s mean radius, none exhibiting
~33-km-diameter Karoo Crater on Mathilde by introducing a 1.2-
clear signs of structural degradation or overprinting by sub- km-diameter impactor at 5 km/s (Asphaug and Thomas, 1999).
sequent collisions, and no evidence for the impact fragmen- The result is a sufficiently large fractured region, but also (as re-
tation that is widespread on Phobos and Eros (Thomas et vealed in this side view) widespread impact fragmentation, and
al., 1999). Regarding the spin period, it is hard to believe bulk ejecta flow velocities slow enough to be gravity-controlled.
(e.g., Davis, 1999) that the momentum contribution from all The result is a seriously fragmented asteroid covered in gravity-
these impacts just happened to cancel out. regime ejecta deposits — the opposite of what is observed.
478 Asteroids III

Following NEAR Shoemaker’s determination of Ma- the Hollywood blockbuster Deep Impact, in which brave
thilde’s low density, a half dozen primitive asteroids have astronauts use nuclear devices to blow up a rogue comet,
been found to have similar densities, computed from orbital so the comparison was unfortunate.) This modeling showed
periods of their newly discovered companion satellites (see what laboratory studies had hinted at: that monolithic as-
Merline et al., 2002). Once density is known, structure and teroids are actually easier to disperse than rubble piles or
composition are inseparable, since molecular weight then gravitational aggregates. The contact binary (not shown)
depends on the distribution of voids. Along with previous trapped impact energy in the impacted lobe, reflecting it at
determinations of low density for the martian moons and the discontinuity and preventing any severe perturbation of
Comets Halley and Shoemaker-Levy 9 (Sagdeev et al., 1987; the distal lobe.
Asphaug and Benz, 1994b), these low C-type asteroid den- The same modeling technique was used to assemble
sities support a consensus that primitive small bodies are Mathilde out of basalt spheres (Plate 2b) ranging in diam-
highly porous — rubble piles, primordial aggregates, or vola- eter from 0.5 to 3 km, just touching, with bulk porosity ~0.5
tile-depleted residues. Whatever the origin of a body’s po- and bulk density ~1.3 g/cm3, this time using the material
rosity, it is significant to impact mechanics (Trucano and density of basalt (2.7 g/cm3). Resolving shock waves in
Grady, 1995) and the topic must be revisited. each sphere requires a resolution of ~1000 particles per
The absence of ejecta deposits around a crater can sig- component, requiring supercomputer modification of the
nify formation in the strength regime. Despite earlier mod- code. This places approximately six particles across each
eling to the contrary for a much smaller low-density body, component’s radius. Because numerical shock waves can-
Phobos (Asphaug and Melosh, 1993), a strength-regime not be treated with fewer than three zones (von Neumann
crater model was attempted for Mathilde by Asphaug and and Richtmyer, 1950), that is probably a safe minimum for
Thomas (1998) and the result is shown in Fig. 7b. As in such simulations. The contact portion of touching spheres
Fig. 4c for Phobos, a size-dependent strength was computed is replaced with damaged rock of slightly lower material
for Mathilde’s volume, the largest crater Karoo was filled in, density (1.7 g/cm3) and can be seen as red flecks in the
and a strength-scaled impactor (1.2 km diameter) was in- bottom of the center figure. Damaged rock cannot support
troduced at 5 km/s into the 1.3-g/cm3 continuum. The result tensile or shear stress, so the modeled Mathilde is just like
can be seen as a fractured region larger than Karoo, and a contact binary, only with thousands of components. The
also as widespread impact fragmentation all around the as- size of the component spheres is established by the resolu-
teroid. Nevertheless, flow velocities within the resultant cra- tion requirement of modeling each individual sphere by
ter are slow enough to be gravity controlled, as they were for ~1000 particles, not by any guiding philosophy of rubble
Stickney. The result is a globally fragmented asteroid cov- pile structure.
ered in gravity-regime ejecta deposits — entirely the oppo- A shock wave can propagate freely through a rubble pile
site of observation. A bold modeler might remedy this by so long as it melts, vaporizes, or collapses pores in the rock
making Mathilde stronger than basalt, but primitive mete- it encounters. But shocks attenuate rapidly even in compe-
orites are weak, often falling apart in one’s hands. tent rock (Rodionov et al., 1972), and even the most pow-
5.4.1. Survival of the weakest. An alternative has erful elastic wave has difficulty propagating in an aggregate.
emerged from these failed attempts: Perhaps Mathilde is too Stress energy is trapped, and as a result the impact energy
weak to be disrupted by collisions. This scenario (Asphaug, is confined to a local region (the shattered region colored
1999) is borrowed from armament lore, and has roots in red in the central figure of Plate 2b), so this receives all the
the experimental literature (Love et al., 1993). Davis (1999), energy that would have otherwise been transmitted to dis-
commenting upon Mathilde, recounts the use of porous cac- tant regions.
tus ribs to dissipate the energy of cannon balls colliding into Ejection velocities (left) in the damaged region (middle)
the walls of Sonoran forts. Perhaps a similar heterogeneity are therefore greater due to this energy confinement. Indeed,
or porosity has enabled Mathilde to survive each giant cra- the nonescaping fraction (right) equals all the damaged
tering event without any noticeable disturbance to its pre- rock. The conclusion is that structural porosity can lead to
existing morphology. stalled shocks, and hence crater ejecta in a weak asteroid,
The effects of structure and prefragmentation on colli- just as in a strength-controlled asteroid, might never return
sional evolution was examined by Asphaug et al. (1998), to the asteroid. Furthermore, because almost no stress en-
following the work on asteroid porosity by Asphaug and ergy propagates beyond the crater bowl, preexisting craters
Benz (1994a) and motivated by the experimental work of on Mathilde would not feel the occurrence of subsequent
Ryan et al. (1991) and Love et al. (1993). For these simu- large impacts, and would preserve their original forms, as
lations, shown in Plate 2a, the approximately kilometer- observed in the NEAR Shoemaker images.
sized near-Earth asteroid Castalia (Ostro et al., 1990) was 5.4.2. Compaction cratering. An alternative model for
rendered in a variety of ways: a monolith, a contact binary, cratering on Mathilde has very different implications for
and a rubble-pile. Each target was impacted by the same asteroid structure and evolution. Housen et al. (1999) pro-
projectile (16 m diameter, 2.7 g/cm3, 5 km/s) whose kinetic pose that Mathilde is so underdense that craters form by
energy happened to equal the yield of one Hiroshima bomb. crushing rather than ejection. In their model no ejecta leaves
(This work was published the same week as the release of the crater — just opposite the previous scenario in which
 Asphaug et al.: Asteroid Interiors 479

Pressure (dyn/cm2)
t = 190 s 6e + 07
5.75e + 07
5.5e + 07
5.25e + 07
5e + 07
4.75e + 07
4.5e + 07
4.25e + 07
4e + 07
3.75e + 07
3.5e + 07
3.25e + 07
3e + 07
2.75e + 07
2.5e + 07
2.25e + 07
2e + 07
1.75e + 07
1.5e + 07
1.25e + 07
1e + 07
7.5e + 06
5e + 06
2.5e + 06
0
–2.5e + 06
–5e + 06
–7.5e + 06
–1e + 07
–1.25e + 07
–1.5e + 07
–1.75e + 07
–200 0 200 400

x (km)

Fig. 8. An impact into the differentiated ~530-km-diameter asteroid Vesta using the two-dimensional hydrocode of Melosh et al.
(1992). In this calculation a 34-km-diameter impactor strikes at 8 km/s in an attempt to reproduce the hemispheric crater on Vesta and
the V-type asteroids (Asphaug, 1997; Keil, 2002). It turns out to be relatively easy to launch crustal meteorites from parent bodies at
high speed, whereas excavation of interior Fe requires truly gargantuan events. Interestingly, much of the stress energy (shown here
three minutes after impact as the primary wave reflects from the core/mantle boundary) is trapped in the asteroid’s core, reverberating
for the remainder of the calculation.

all ejecta leaves the crater. Under compaction cratering, an While large asteroid interiors are treated in other chap-
asteroid crushes up to higher density over time, leaving mass ters in this book (McSween et al., 2002; Keil, 2002), one
concentrations at each crater floor. Compaction cratering, aspect is worth mentioning in passing — that cores can trap
if it occurs, would have facilitated planetary growth, as it impact stress energy in a manner reminiscent of how con-
allows primitive asteroids to accrete material with ease. That tact binaries trap energy in their impacted lobe. Figure 8
is also its problem, however, given Mathilde’s near-absence shows an impact simulation where asteroid Vesta (Asphaug,
of spin. In a regime of perfectly inelastic collisions (see 1997) is modeled using the two-dimensional hydrocode of
Agnor et al., 1999) accreting bodies almost always begin to Melosh et al. (1992) to resolve a basaltic crust, a denser
spin with periods of hours, not tens of days. mantle, and an iron core. The impact (an attempt to recre-
ate the hemispheric crater on Vesta and the V-type aster-
6. LARGER ASTEROIDS oids) transmits a shock deep into the asteroid, where it
reverberates throughout the course of the calculation.
Little has been said in this chapter about larger aster-
oids, those that have differentiated into cores, mantles, and 7. SEISMIC AND RADAR IMAGING OF
crusts. For these, meteoriticists would like impact model- ASTEROID INTERIORS
ers to help them remove their mantles so as to expose their
iron cores and deliver iron meteorites to Earth, while at the Geophysical exploration tools that are commonly de-
same time getting rid of mantle material not evident in the ployed on Earth can be flown on spacecraft to image as-
meteorite collection (see Burbine et al., 2002). This has teroid interiors directly. Many are designed for field deploy-
proven to be a difficult prospect. ment in remote areas and are compact and lightweight.
480 Asteroids III

Radio reflection tomography (ground-penetrating radar or asteroid population at large, and may include dormant comet
GPR) is commonly used to image sinkholes, pipes, burial nuclei (see Morbidelli et al., 2002; Weissman et al., 2002).
grounds, etc.; similar imaging is in principle obtainable on Anchored seismology landers would be too costly, given
asteroids, although the instruments would probably have to the surface material uncertainties. Spring-fired grenades (a
be deployed from orbit, reducing resolution and posing precursor to seismic studies) would blast several small (~5-m)
challenges with regard to data inversion and echo noise. The craters at selected sites on each asteroid or comet nucleus.
European Space Agency’s Rosetta spacecraft will use trans- Ejecta ballistics and crater formation filmed from orbit at
mission radio tomography (Kofman et al., 1998) to inves- high time and spatial resolution would facilitate the devel-
tigate the interior of Comet Wirtanen during its 2011–2016 opment of comet- and asteroid-analog simulation chambers
rendezvous as the comet approaches perihelion; in this at impact research laboratories. Together with long-term
mode of exploration radio energy is transmitted from a imaging of ejecta orbital evolution, this would greatly re-
lander and received by the orbiter. Another popular field- duce uncertainties and design parameters for future landed
deployable tool, magnetotelluric imaging, probes subsur- spacecraft.
face geology using the fact that the magnetic to electric-field Until we proceed with direct geophysical exploration of
ratio (impedance) is constant at given frequency for con- asteroids and comets, our understanding of their interiors
stant resistivity. On Earth this technique takes advantage of shall remain a matter of educated speculation. Science
natural fluctuations in the background magnetic field, aside, there are practical reasons to learn more in the short
whereas on an asteroid field generation would require the term. To divert or disrupt a potentially hazardous near-Earth
deployment of antennae across the surface. asteroid, one must understand its internal structure, as po-
Certain asteroid materials (clays, rocks flecked with rous or discontinuous asteroids can absorb or divert disrup-
metal) may be opaque to electromagnetic energy and might tive energy. Composite targets appear to be able to sacrifice
be better explored by other means. Deep Impact, a NASA small regions near an impact or explosion without perturb-
Discovery mission, will pioneer the technique of kinetically ing disconnected regions. Monoliths, rubble piles, and po-
blasting holes in small bodies [Belton and A’Hearn (1999); rous ice-dust mixtures might each require a different mode
see Farquhar et al. (2002) for an overview of recent and of diversion, disruption, or resource exploitation (Huebner
planned small-body missions]. In July 2005, Deep Impact will and Greenberg, 2000). Except for the mean densities of a
slam ~350 kg of copper into Comet Tempel 1 at ~10 km/s dozen asteroids and the broadly resolved homogeneous
for the purpose of investigating outer crust and mantle phys- mass distribution of Eros, we know none of the basic bulk
ical and compositional properties. constitutive properties of any asteroid. Obviously the mod-
A more refined technique, more complex to deploy, is eling presented here is fraught with guesswork. Lacking
seismic imaging. This has taught us the detailed structure such knowledge, a standoff blast (Ahrens and Harris, 1992)
of Earth, and more recently has been refined for small-scale might fail to impart the expected momentum or might dis-
imaging (e.g., Wu and Yang, 1997). Seismic imaging may rupt a body without diverting it, sending a cluster of frag-
prove to be an ideal complement to electromagnetic imag- ments toward Earth. Nonnuclear scenarios (Melosh et al.,
ing of asteroid interiors, since its spatial resolution can be 1994) are greatly preferred, but these also require detailed
comparable but its means of data acquisition and inversion awareness of asteroid geology and composition for the
are entirely distinct. In some cases where seismic imaging is purposes of anchoring, momentum loading, and resource
challenging (highly attenuative porous bodies such as com- extraction.
ets) radio imaging may be optimal, and perhaps vice versa.
Seismic imaging requires surface probes. In one scenario 8. CONCLUSIONS
instrumented penetrators detect signals broadcast from
cratering grenades. Blasts produce white noise and are not Asteroids include about a million objects between ~100 m
optimal for tomographic data inversion (compared with and ~100 km across. Many have satellites (see Merline et
drills or thumpers), but they are convenient, reliable, and al., 2002), and they have long served as test particles for
cheap. They also produce small-scale cratering experiments understanding the detailed evolution of planetary dynamics
as a bonus, enabling the imaging and spectroscopy of shal- (see Gladman et al., 1997). Their geophysics is a complex
low layers. Alternatively, and at much lower cost, an armada interplay between long- and short-range forces (self-grav-
of ballistic penetrators could be deployed to strike an as- ity and mechanical cohesion), making Earth-based intuition
teroid in the manner that the pieces of Comet Shoemaker- a fickle guide, yet until we peer inside an asteroid directly
Levy 9 struck Jupiter, hitting it one after another, with each we can only strive to interpret their exterior geology.
embedded penetrator acquiring seismic reverberations from We presently believe that most asteroids larger than
successive impacts at diverse locations. ~1 km are gravitational aggregates. Highly tentative is our
One can deploy, at the NASA Discovery level, a dual- conclusion that Gaspra, Ida, Eros (all S-types), and perhaps
wavelength radar tomography mission pursuing multiple Phobos are shattered monoliths sufficiently competent to
rendezvous with a variety of near-Earth objects (Asphaug transmit compressive stress. As for Mathilde and other low-
et al., 2001b). This population is fairly representative of the density primitive bodies, detailed explanations diverge, but
 Asphaug et al.: Asteroid Interiors 481

they appear to require a mechanically uncoupled interior, I. Method and tests. Icarus, 107, 98–116.
either structural or microstructural. Their porosity may be Benz W. and Asphaug E. (1995) Simulations of brittle solids using
primordial or the aftermath of collisional evolution; it helps smooth particle hydrodynamics. Comput. Phys. Commun., 87,
them withstand the gargantuan collisions that have been the 253–265.
Benz W. and Asphaug E. (1999) Catastrophic disruptions revis-
norm in the evolving solar system.
ited. Icarus, 142, 5–20.
There is much to learn. Our present state of knowledge
Binzel R. P. and Xu S. (1993) Chips off of asteroid 4 Vesta —
comes as no surprise, for complex characteristics are ex- Evidence for the parent body of basaltic achondrite meteorites.
pected of objects at the boundary between primary forces Science, 260, 186–191.
of nature. Bottke W. F., Nolan M. C., Greenberg R., and Kolvoord R. A.
(1994) Collisional lifetimes and impact statistics of near-Earth
REFERENCES asteroids. In Hazards Due to Comets and Asteroids (T. Gehrels
et al., eds.), pp. 337–357. Univ. of Arizona, Tucson.
Agnor C. B., Canup R. M., and Levison H. F. (1999) On the char- Bottke W. F. Jr., Vokrouhlický D., Rubincam D. P., and Broz M.
acter and consequences of large impacts in the late stage of (2002) The effect of Yarkovsky thermal forces on the dynami-
terrestrial planet formation. Icarus, 142, 219–237. cal evolution of asteroids and meteoroids. In Asteroids III
Ahrens T. J. and Harris A. W. (1992) Deflection and fragmenta- (W. F. Bottke Jr. et al., eds.), this volume. Univ. of Arizona,
tion of near-earth asteroids. Nature, 360, 429–433. Tucson.
Asphaug E. (1993) Dynamic fragmentation in the solar system. Bridges F. G., Supulver K. D., Lin D. N. C., Knight R., and Zafra
Ph.D. thesis, Univ. of Arizona, Tucson. M. (1996) Energy loss and sticking mechanisms in particle
Asphaug E. (1997) Impact origin of the Vesta family. Meteoritics aggregation in planetesimal formation. Icarus, 123, 422–435.
& Planet. Sci., 32, 965–980. Britt D. T. and Consolmagno G. J. (2001) Modeling the structure
Asphaug E. (1999) Survival of the weakest. Nature, 402, 127–128. of high porosity asteroids. Icarus, 152, 134–139.
Asphaug E. and Benz W. (1994a) The surface and interior of Bunch T. E. and Rajan R. S. (1988) Meteorite regolith breccias.
Phobos (abstract). In Lunar and Planetary Science XXV, In Meteorites and the Early Solar System (J. F. Kerridge and
pp. 43–44. Lunar and Planetary Institute, Houston. M. S. Matthews, eds.), pp. 144–164. Univ. of Arizona, Tucson.
Asphaug E. and Benz W. (1994b) Density of Comet Shoemaker- Burbine T. H., Meibom A., and Binzel R. P. (1996) Mantle mate-
Levy-9 deduced by modelling breakup of the parent rubble rial in the main belt: Battered to bits? Meteoritics & Planet.
pile. Nature, 370, 120–124. Sci., 31, 607–620.
Asphaug E. and Benz W. (1996) Size, density, and structure of Burbine T. H., McCoy T. J., Meibom A., Gladman B., and Keil
Comet Shoemaker-Levy 9 inferred from the physics of tidal K. (2002) Meteoritic parent bodies: Their number and identi-
breakup. Icarus, 121, 225–248. fication. In Asteroids III (W. F. Bottke Jr. et al., eds.), this
Asphaug E. and Melosh H. J. (1993) The Stickney impact of volume. Univ. of Arizona, Tucson.
Phobos: A dynamical model. Icarus, 101, 144–164. Carr M. H., Kirk R. L., McEwen A., Veverka J., Thomas P., Head
Asphaug E. and Thomas P. C. (1999) Modeling mysterious J. W., and Murchie S. (1994) The geology of Gaspra. Icarus,
Mathilde (abstract). In Lunar and Planetary Science XXX, 107, 61.
Abstract #2028. Lunar and Planetary Institute, Houston (CD- Cellino A., Michel P., Tanga P., Zappalà V., Paolicchi P., and
ROM). Dell’Oro A. (1999) The velocity-size relationship for members
Asphaug E., Moore J. M., Morrison D., Benz W., Nolan M. C., of asteroid families and implications for the physics of cata-
and Sullivan R. J. (1996) Mechanical and geological effects of strophic collisions. Icarus, 141, 79–95.
impact cratering on Ida. Icarus, 120, 158–184. Chapman C. R. (1976) Asteroids as meteorite parent bodies: The
Asphaug E., Ostro S. J., Hudson R. S., Scheeres D. J., and Benz astronomical perspective. Geochim. Cosmochim. Acta, 40,
W. (1998) Disruption of kilometre-sized asteroids by energetic 701–719.
collisions. Nature, 393, 437–440. Chapman C. R. (2001) Eros at very high resolution: Meteoritical
Asphaug E., King P. J., Swift M. R., and Merrifield M. R. (2001a) implications (abstract). Meteoritics & Planet. Sci., 36, A39.
Brazil nuts on Eros: Size-sorting of asteroid regolith (abstract). Chapman C. R. and Davis D. R. (1975) Asteroid collisional evo-
In Lunar and Planetary Science XXXII, Abstract #1708. Lu- lution — Evidence for a much larger early population. Science,
nar and Planetary Institute, Houston (CD-ROM). 190, 553.
Asphaug E., Belton M. J. S., and Kakuda R. Y. (2001b) Geophysi- Chapman C. R., Paolicchi P., Zappala V., Binzel R. P., and Bell
cal exploration of asteroids: The Deep Interior Mission con- J. F. (1989) Asteroid families: physical properties and evolu-
cept (abstract). In Lunar and Planetary Science XXXII, Abstract tion. In Asteroids II (R. P. Binzel et al., eds.), pp. 386–415.
#1867. Lunar and Planetary Institute, Houston (CD-ROM). Univ. of Arizona, Tucson.
Avanesov G.A. and 39 colleagues (1989) Television observations Davis D. R. (1999) The collisional history of asteroid 253
of Phobos. Nature, 341, 585–587. Mathilde. Icarus, 140, 49–52.
Belton M. J. S. and A’Hearn M. F. (1999) Deep sub-surface ex- Davis D. R., Chapman C. R., Greenberg R., Weidenschilling S. J.,
ploration of cometary nuclei. Adv. Space Res., 24, 1175–1183. and Harris A. W. (1979) Collisional Evolution of asteroids:
Belton M. J. S. and 20 colleagues (1996) The discovery and orbit Populations, rotations and velocities. In Asteroids (T. Gehrels,
of 1993 (243)1 Dactyl. Icarus, 120, 185–199. ed.), pp. 528–557. Univ. of Arizona, Tucson.
Benz W. (2000) Low velocity collisions and the growth of plan- Davis D. R., Chapman C. R., Weidenschilling S. J., and Greenberg
etesimals. Space Sci. Rev., 92, 279–294. R. (1985) Collisional history of asteroids: Evidence from Vesta
Benz W. and Asphaug E. (1994) Impact simulations with fracture: and Hirayama families. Icarus, 62, 30–53.
482 Asteroids III

Dobrovolskis A. R. and Burns J. A. (1984) Angular momentum Hirayama K. (1923) Families of asteroids. Ann. Tokyo Astron.
drain — A mechanism for despinning asteroids. Icarus, 57, Obs., 11, 55.
464–476. Holsapple K. A. (1994) Catastrophic disruptions and cratering of
Drake M. J. (1979) Geochemical evolution of the eucrite parent solar system bodies: A review and new results. Planet. Space
body: Possible nature and evolution of asteroid 4 Vesta? In Sci., 42, 1067–1078.
Asteroids (T. Gehrels, ed.), pp. 765–782. Univ. of Arizona, Tuc- Holsapple K. A. (2002) Equilibrium configurations of solid cohe-
son. sionless bodies. Icarus, in press.
Durda D. D., Greenberg R., and Jedicke R. (1998) Collisional Holsapple K. A. and Housen K. R. (1986) Scaling laws for the
models and scaling laws: A New interpretation of the shape catastrophic collisions of asteroids. Mem. Soc. Astron. Ital., 57,
of the main-belt asteroid size distribution. Icarus, 135, 431– 65–85.
440. Holsapple K., Giblin I., Housen K., Nakamura A., and Ryan E.
Fanale F. P. and Salvail J. R. (1990) Evolution of the water re- (2002) Asteroid impacts: Laboratory experiments and scal-
gime of Phobos. Icarus, 88, 380–395. ing laws. In Asteroids III (W. F. Bottke Jr. et al., eds.), this
Farinella P., Paolicchi P, and Zappalà V. (1982) The asteroids as volume. Univ. of Arizona, Tucson.
outcomes of catastrophic collisions. Icarus, 52, 409–433. Housen K. R. and Holsapple K. A. (1990) On the fragmentation
Farquhar R., Kawaguchi J., Russell C., Schwehm G., Veverka J., of asteroids and planetary satellites. Icarus, 84, 226–253.
and Yeomans D. (2002) Spacecraft exploration of asteroids: Housen K. R. and Holsapple K. A. (1999) Scale effects in stength-
The 2001 perspective. In Asteroids III (W. F. Bottke Jr. et al., dominated collisions of rocky asteroids. Icarus, in press.
eds.), this volume. Univ. of Arizona, Tucson. Housen K. R., Wilkening L. L., Chapman C. R., and Greenberg R.
Flynn G. J., Moore L. B., and Klöck W. (1999) Density and po- (1979) Asteroidal regoliths. Icarus, 39, 317–351.
rosity of stone meteorites: Implications for the density, poros- Housen K. R., Schmidt R. M., and Holsapple K. A. (1983) Cra-
ity, cratering, and collisional disruption of asteroids. Icarus, ter ejecta scaling laws: Fundamental forms based on dimen-
142, 97–105. sional analysis. J. Geophys. Res., 88, 2485–2499.
Fujiwara A. (1980) On the mechanism of catastrophic destruction Housen K. R., Holsapple K. A., and Voss M. E. (1999) Compac-
of minor planets by high-velocity impact. Icarus, 41, 356–364. tion as the origin of the unusual craters on the asteroid Ma-
Fujiwara A. (1991) Stickney-forming impact on Phobos: Crater thilde. Nature, 402, 155–157.
shape and induced stress distribution. Icarus, 89, 384–391. Horstman K. C. and Melosh H. J. (1989) Drainage pits in cohe-
Fujiwara A. and Tsukamoto A. (1980) Experimental study on the sionless materials: Implications for the surface of Phobos. J.
velocity of fragments in collisional breakup. Icarus, 44, 142– Geophys. Res., 94, 12433–12441.
153. Huebner W. F. and Greenberg J. M. (2000) Needs for determining
Fujiwara A., Cerroni P., Davis D. R., Ryan E. V., Di Martino M., material strengths and bulk properties of NEOs. Planet. Space
Holsapple K., and Housen K. (1989) Experiments and scal- Sci., 48, 797–799.
ing laws for catastrophic collisions. In Asteroids II (R. P. Binzel Jaeger J. C. and Cook N. G. W. (1969) Fundamentals of Rock
et al., eds.), pp. 240–265. Univ. of Arizona, Tucson. Mechanics. Chapman and Hall, London. 515 pp.
Gault D. E. and Heitowit E. D. (1963) The partition of energy for Jaeger H. M., Nagel S. R., and Behringer R. P. (1996) The physics
hypervelocity impact craters formed in rock. Proc. 6th Hyper- of granular materials. Phys. Today, 49, 32–39.
velocity Impact Symposium, Vol. 2, pp. 419–456. Jiongming S., Binglu S., and Bin W. (1998) Dynamics of size
Gault D. E., Horz F., and Hartung J. B. (1972) Effects of micro- segregation of granular materials by shaking. Nuovo Cimento,
cratering on the lunar surface. Proc. Lunar Sci. Conf. 3rd, 20, 1443.
pp. 2713–2734. Keil K. (2002) Geological history of asteroid 4 Vesta: The “small-
Gladman B. J., Migliorini F., Morbidelli A., Zappalà V., Michel est terrestrial planet.” In Asteroids III (W. F. Bottke Jr. et al.,
P., Cellino A., Froeschlé C., Levison H. F., Bailey M., and eds.), this volume. Univ. of Arizona, Tucson.
Duncan M. (1997) Dynamical lifetimes of objects injected into Keil K., Haack H., and Scott E. R. D. (1994) Catastrophic frag-
asteroid belt resonances. Science, 277, 197–201. mentation of asteroids: Evidence from meteorites. Planet.
Grady D. E. and Kipp M. E. (1980) Continuum modeling of ex- Space Sci., 42, 1109–1122.
plosive fracture in oil shale. Intl. J. Rock Mech. Min. Sci. Geo- Kofman W. and 20 colleagues (1998) Comet nucleus sounding
mech. Abstr., 17, 147–157. experiment by radiowave transmission. Adv. Space Res., 21,
Grady D. E. and Lipkin J. (1980) Criteria for impulsive rock frac- 1589–1598.
ture. Geophys. Res. Lett., 7, 255–258. Lange M. A. and Ahrens T. J (1983) The dynamic tensile strength
Greenberg R. and Nolan M. C. (1989) Delivery of asteroids and of ice and ice-silicate mixtures. J. Geophys. Res., 88, 1197–
meteorites to the inner solar system. In Asteroids II (R. P. 1208.
Binzel et al., eds.), pp. 778–804. Univ. of Arizona, Tucson. Lawn B. R. and Wilshaw T. R. (1975) Fracture of Brittle Solids.
Griffith A. A. (1920) The phenomena of rupture and flow in solids. Cambridge Univ., Cambridge. 160 pp.
Philos. Trans. R. Soc. London, A221, 163–198. Lee P. C. (1996) Dust levitation on asteroids. Icarus, 124, 181–
Harris A. W. (1996) The rotation rates of very small asteroids: 194.
Evidence for “rubble pile” structure (abstract). In Lunar and Leinhardt Z. M., Richardson D. C., and Quinn T. (2000) Direct
Planetary Science XXVII, p. 493. Lunar and Planetary Institute, N-body simulations of rubble pile collisions. Icarus, 146, 133–
Houston. 151.
Head J. N. and Melosh H. J. (2000) Launch velocity distribution Lindholm U. S., Yeakley L. M., and Nagy A. (1974) The dynamic
of the martian clan meteorites (abstract). In Lunar and Plan- strength and fracture properties of Dressler basalt. Intl. J. Rock
etary Science XXXI, Abstract #1937. Lunar and Planetary In- Mech. Min. Sci. Geomech. Abstr., 11, 181–191.
stitute, Houston (CD-ROM). Love S. G. and Ahrens T. J. (1996) Catastrophic impacts on grav-
 Asphaug et al.: Asteroid Interiors 483

ity dominated asteroids. Icarus, 124, 141–155. Rinehart J. S. (1965) Dynamic fracture strength of rocks. Proc.
Love S. G., Hörz F., and Brownlee D. E. (1993) Target porosity 7th Symposium on Rock Mechanics, Vol. 1, pp. 205–208.
effects in impact cratering and collisional disruption. Icarus, Rivkin A. S., Clark B. E., Britt D. T., and Lebofsky L. A. (1997)
105, 216–224. Infrared spectrophotometry of the NEAR flyby target 253 Ma-
Martelli G., Ryan E. V., Nakamura A. M., and Giblin I. (1994) thilde. Icarus, 127, 255–257.
Catastrophic disruption experiments: Recent results. Planet. Rivkin A. S., Howell E. S., Vilas F., and Lebofsky L. A. (2002)
Space Sci., 42, 1013–1026. Hydrated minerals on asteroids: The astronomical record. In
McSween H. Y. (1999) Meteorites and Their Parent Planets, 2nd Asteroids III (W. F. Bottke Jr. et al., eds.), this volume. Univ.
edition. Cambridge Univ., New York. 322 pp. of Arizona, Tucson.
McSween H. Y. Jr., Ghosh A., Grimm R. E., Wilson L., and Young Rodionov V. N., Adushkin V. V., Kostyuchenko V. N., Nikolaevskii
E. D. (2002) Thermal evolution models of asteroids. In Aster- V. N., Romashov A. N., Sadovskii M. A., and Tsvetkov V. M.
oids III (W. F. Bottke Jr. et al., eds.), this volume. Univ. of (1972) Mechanical Effect of an Underground Explosion. U.S.
Arizona, Tucson. Atomic Energy Commission, Los Alamos.
Melosh H. J. and Ryan E. V. (1997) Asteroids: Shattered but not Rubincam D. P. (2000) Radiative spin-up and spin-down of small
dispersed. Icarus, 129, 562–564. asteroids. Icarus, 148, 2–11.
Melosh H. J., Ryan E. V., and Asphaug E. (1992) Dynamic frag- Ryan E. V. (1992) Catastrophic collisions: Laboratory impact
mentation in impacts: Hydrocode simulation of laboratory im- experiments, hydrocode simulations, and the scaling problem.
pacts. J. Geophys. Res., 97, 14735–14759. Ph.D. thesis, Univ. of Arizona, Tucson.
Melosh H. J., Nemchinov I. V., and Zetzer Yu. I. (1994) Non- Ryan E. V. and Melosh H. J. (1998) Impact fragmentation: From
nuclear strategies for deflecting comets and asteroids. In Haz- the laboratory to asteroids. Icarus, 133, 1–24.
ards Due to Comets and Asteroids (T. Gehrels, ed.), pp. 1111– Ryan E.V., Hartmann W. K., and Davis D. R. (1991) Impact ex-
1132. Univ. of Arizona, Tucson. periments III — Catastrophic fragmentation of aggregate tar-
Merline W. J., Weidenschilling S. J., Durda D. D., Margot J.-L., gets and relation to asteroids. Icarus, 94, 283–298.
Pravec P., and Storrs A. D. (2002) Asteroids do have satellites. Sagdeev R. Z., Elaysberg P. E., and Moroz V. I. (1987) An esti-
In Asteroids III (W. F. Bottke Jr. et al., eds.), this volume. Univ. mate of the mass and density of the Comet Halley nucleus.
of Arizona, Tucson. Pisma Astron. Zh., 13, 621–629.
Morbidelli A., Bottke W. F. Jr., Froeschlé Ch., and Michel P. Scott E. R. D., Taylor G. J., Newsom H. E., Herbert F., and
(2002) Origin and evolution of near-Earth objects. In Aster- Zolensky M. (1989) Chemical, thermal and impact processing
oids III (W. F. Bottke Jr. et al., eds.), this volume. Univ. of of asteroids. In Asteroids II (R. P. Binzel et al., eds.), pp. 701–
Arizona, Tucson. 739. Univ. of Arizona, Tucson.
Nolan M. C., Asphaug E., Melosh H. J., and Greenberg R. (1996) Sears D. W. G. and Akridge D. G. (1998) Nebular or parent body
Impact craters on asteroids: Does gravity or strength control alteration of chondritic material: Neither or both? Meteoritics
their size? Icarus, 124, 359–371. & Planet. Sci., 33, 1157–1167.
Ostro S. J., Chandler J. F., Hine A. A., Rosema K. D., Shapiro I. I., Sekanina Z., Chodas P. W., and Yeomans D. K. (1994) Tidal dis-
and Yeomans D. K. (1990) Radar images of asteroid 1989 PB. ruption and the appearance of periodic comet Shoemaker-
Science, 248, 1523–1528. Levy 9. Astron. Astrophys., 289, 607–636.
Ostro S. J., Pravec P., Benner L. A. M., Hudson R. S., Sarounova Stewart S. T., Ahrens T. J., and Lange M. A. (1999) Correction
L., Hicks M. D., Rabinowitz D. L., Scotti J. V., Tholen D. J., to the dynamic tensile strength of ice and ice-silicate mixtures
Wolf M., Jurgens R. F., Thomas M. L., Giorgini J. D., Chodas (Lange and Ahrens 1983) (abstract). In Lunar and Planetary
P. W., Yeomans D. K., Rose R., Frye R., Rosema K. D., Wink- Science XXX, Abstract #2037. Lunar and Planetary Institute,
ler R., and Slade M. A. (1999) Radar and optical observations Houston (CD-ROM).
of asteroid 1998 KY26. Science, 285, 557–559. Sullivan R. J., Thomas P. C., Murchie S. L., and Robinson M. S.
Ostro S. J., Hudson R. S., Benner L. A. M., Giorgini J. D., Magri (2002) Asteroid geology from Galileo and NEAR Shoemaker
C., Margot J.-L., and Nolan M. C. (2002) Asteroid radar as- data. In Asteroids III (W. F. Bottke Jr. et al., eds.), this volume.
tronomy. In Asteroids III (W. F. Bottke Jr. et al., eds.), this vol- Univ. of Arizona, Tucson.
ume. Univ. of Arizona, Tucson. Thomas P. C. (1998) Ejecta emplacement on the martian satellites.
Perret W. R., Rutter R. L., Millsap F. K., Thornbrough A. D., and Icarus, 131, 78–106.
Hansen G. H. (1967) Free-Field Particle Motion from a Nu- Thomas P., Veverka J., Bloom A., and Duxbury T. (1979) Grooves
clear Explosion in Salt, Part I, Project Dribble, Salmon Event. on Phobos: Their distribution, morphology, and possible ori-
Sandia Rept. VUF-3012, Sandia Laboratory. gin. J. Geophys. Res., 84, 8457–8477.
Pravec P. and Harris A. W. (2000) Fast and slow rotation of aster- Thomas P. C., Belton M. J. S., Carcich B., Chapman C. R., Davies
oids. Icarus, 148, 12–20. M. E., Sullivan R., and Veverka J. (1996) The shape of Ida.
Pravec P., Harris A. W., and Michalowski T. (2002) Asteroid rota- Icarus, 120, 20–32.
tions. In Asteroids III (W. F. Bottke Jr. et al., eds.), this volume. Thomas P. C. and 11 colleagues (1999) Mathilde: Size, shape,
Univ. of Arizona, Tucson. and geology. Icarus, 140, 17–27.
Prockter L., Thomas P., Robinson M., Joseph J., Milne A., Bussey Thomas P. C., Veverka J., Sullivan R., Simonelli D. P., Malin
B., Veverka J., and Cheng A. (2002) Surface expressions of M. C., Caplinger M., Hartmann W. K., and James P. B. (2000)
structural features on Eros. Icarus, 155, 75–93. Phobos: Regolith and ejecta blocks investigated with Mars
Richardson D. C., Leinhardt Z. M., Melosh H. J., Bottke W. F. Jr., Orbiter Camera images. J. Geophys. Res., 105, 15091–15106.
and Asphaug E. (2002) Gravitational aggregates: Evidence and Thomas P. C., Veverka J., Robinson M. S., and Murchie S. (2001)
evolution. In Asteroids III (W. F. Bottke Jr. et al., eds.), this Shoemaker crater as the source of most ejecta blocks on the
volume. Univ. of Arizona, Tucson. asteroid 433 Eros. Nature, 413, 394–396.
484 Asteroids III

Tonks W. B. and Melosh H. J. (1992) Core formation by giant Weidenschilling S. J. and Cuzzi J. N. (1993) Formation of plan-
impacts. Icarus, 100, 326–346. etesimals in the solar nebula. In Protostars and Planets III
Trombka, J. I. and 23 colleagues (2000) The elemental composi- (E. H. Levy and J. I. Lunine, eds.), pp. 1031–1060. Univ. of
tion of asteroid 433 Eros: Results of the NEAR Shoemaker Arizona, Tucson.
X-ray spectrometer. Science, 289, 2101–2105. Weissman P. R. (1986) Are cometary nuclei primordial rubble
Trucano G. T. and Grady D. E. (1995) Impact shock and pene- piles? Nature, 320, 242–244.
tration fragmentation in porous media. J. Impact Eng., 17, 861– Weissman P. R., Bottke W. F. Jr., and Levison H. F. (2002) Evolu-
872. tion of comets into asteroids. In Asteroids III (W. F. Bottke Jr.
Veverka J. and Thomas P. (1979) Phobos and Deimos — A pre- et al., eds.), this volume. Univ. of Arizona, Tucson.
view of what asteroids are like? In Asteroids (T. Gehrels, ed.), Wetherill G. W. (1985) Occurrence of giant impacts during the
pp. 628–651. Univ. of Arizona, Tucson. growth of the terrestrial planets. Science, 228, 877–879.
Veverka J., Thomas P., Johnson T. V., Matson D., and Housen K. Whipple F. L. (1949) Comets, meteors and the interplanetary
(1986) The physical characteristics of satellite surfaces. In complex. Astron. J., 54, 179–180.
Satellites (J. A. Burns and M. S. Matthews, eds.), pp. 342–402. Wu R. and Yang F. (1997) Seismic imaging in wavelet domain:
Univ. of Arizona, Tucson. Decomposition and compression of imaging operator. In Wave-
Veverka J. and 16 colleagues (1997) NEAR’s flyby of 253 Ma- let Applications in Signal and Image Processing (V. A. Al-
thilde: Images of a C asteroid. Science, 278, 2109–2112. droubi et al., eds.), pp. 148–162. Proc. SPIE Vol. 3169.
von Neumann J. and Richtmyer R. D. (1950) A method for the Yeomans D. K. and 15 colleagues (2000) Radio science results
numerical calculation of hydrodynamic shocks. J. Appl. Phys., during the NEAR Shoemaker spacecraft rendezvous with Eros.
21, 232–237. Science, 289, 2085–2088.
Warren P. H. (1994) Lunar and martian meteorite delivery services. Zappalà V., Cellino A., Dell’Oro A., and Paolicchi P. (2002) Physi-
Icarus, 111, 338–363. cal and dynamical properties of asteroid families. In Aster-
Weibull W. A. (1939) A statistical theory of the strength of mate- oids III (W. F. Bottke Jr. et al., eds.), this volume. Univ. of
rials (translation). Ingvetensk. Akad. Handl. (Stockholm), 151, Arizona, Tucson.
5–45. Zuber M. T. and 11 colleagues (2000) The shape of 433 Eros from
Weibull W. A. (1951) A statistical distribution function of wide the NEAR Shoemaker Laser Rangefinder. Science, 289, 2097–
applicability. J. Appl. Mech., 18, 293–297. 2101.