Chapter 2: Astronomy for

Surveying
Star Observation Solution by Triangle

Conducted on June 20, 2019 by

Dr. Terrance M. Rengarasu

Overlook

1 Mean Solar and Sidereal Time

2 Exercises on Time

June 20, 2019 2

Mean Solar and Sidereal Time
Greenwich Mean Time, GMT, or Universal Time, UT (the terms
are used synonymously throughout the text) and Greenwich Side-
real Time are in phase when the First Point of Aries (à) and the
Mean Sun are diametrically opposite one another on the celestial
sphere.

This situation occurs at the time of the Autumnal Equinox on or

about the 21st of September.

When these two points are together the time systems are 180◦
or 12 h out of phase and this occurs at the time of the Vernal
Equinox on or about the 21st of March.

Mean Solar and Sidereal Time June 20, 2019 3

Autumnal Equinox
1 Greenwich Mean Time, GMT, or
Universal Time, UT (the terms are MS
used synonymously throughout the
text) and Greenwich Sidereal Time
are in phase when the First Point
of Aries (à) and the Mean Sun are Earth
diametrically opposite one another
on the celestial sphere.
2 This situation occurs at the time of
the Autumnal Equinox on or about
the 21st of September. à
3 Here Mean solar time and Sidreal
time are equal

Mean Solar and Sidereal Time June 20, 2019 4

VernalEquinox

à MS

When these two points are together

Earth
the time systems are 180◦ or 12 h
out of phase and this occurs at the
time of the Vernal Equinox on or
about the 21st of March.

Mean Solar and Sidereal Time June 20, 2019 5

Mean Solar and Sidereal Time
In addition to knowing the phase relationship at a particular time,
it will be necessary to know the ratio between the lengths of the
subdivisions of the year in each time system.

During the course of one year there were 365.2422 · · · mean or

apparent solar days.

With respect to a star or the First Point of Aries(à), there are

366.2422 · · · sidereal days in the year because of the retrograde
motion of the sun through the background of stars.

This motion accumulates to one complete revolution.

Mean Solar and Sidereal Time June 20, 2019 6

Mean Solar and Sidereal Time

The ratio between the sidereal and mean time units is therefore,
366.2422
= 1.0027379 = F
365.2422

Thus, if a time interval is measured as M mean time units, the

corresponding measure of this interval in sidereal time units is M × F
and conversely if a time interval is expressed as S sidereal time units
the corresponding measure of this interval in mean time units is S/F .

Mean Solar and Sidereal Time June 20, 2019 7

Star Observation Exampe

An Star was observed from Hapugala at 8:30 pm SST(Altitude16◦ 90 22.500

Azimuth =313◦ 190 36.000 ).

(a) Determine the sidreal time at Hapugala which is located at 80.1959◦ E

and 6.0766◦ N , when SST is 8:30 pm. (Note:Sri Lanka standard time
SST = U T + 5h 30m .)

(b) Determine the hour angle of star (c) Determine the RA and
declination of star (d) Identify the star using the star map provided.

Exercises on Time June 20, 2019 8

Star Observation Exampe (a)

When SST=8:30 pm GM T /U T = SST − 5h 30m = 15h 00m am

For June 20, 2019, 15:00 when refereing Star alamanac gives

0
GHAAries = 133◦ 31.9 Location λE = 80.1959◦

Draw this on the sphere as seen from the north pole of Earth.

Exercises on Time June 20, 2019 9

Star Observation Exampe (a)

Exercises on Time June 20, 2019 10

Star Observation Exampe (a)

P
Hapuga
la

λE
G

Exercises on Time June 20, 2019 10

Star Observation Exampe (a)
à

A
/GH
GST

P
Hapuga
la

λE
G
a
al
uh
ap
T H
LS
Exercises on Time June 20, 2019 10
Star Observation Exampe (a)
à

133 ◦31 0
.9

P
Hapuga
la
◦
9
95
80.1
G =
λE al
a
uh
ap
TH
LS
Exercises on Time June 20, 2019 10
Star Observation Exampe (a)

LSTHapugala = λEHapugala + GHA

0
LSTHapugala = 80.1959◦ + 133◦ 31.9
= 213.7275667◦
= 14h 14m 54.616s

Exercises on Time June 20, 2019 11

Star Observation
P Exampe (b)
N
Z

n
N

o
riz
Ho
on
riz

Equator
Ho

S E

S
As seen from
Exercises east
on Time June 20, 2019 12
Star Observation
P Exampe (b)
N
Ho
riz
o N Z

Ho
n

riz
on
Equator
W S

As see from
Exercises west
on Time June 20, 2019 12
Star Observation Exampe (b)

Exercises on Time June 20, 2019 13

Star Observation ZExampe (b)
SA = Alt
SB = δ

W
S B
S N
A
E

Star is in the south-eastern sky. 90 < Azimuth < 180 δ < 0

Exercises on Time June 20, 2019 13
Star Observation ZExampe (b)
SA = Alt
SB = δ

S
P

E
B
N
S

W A

Star is in the south-western sky. 180 < Azimuth < 270 δ > 0
Exercises on Time June 20, 2019 13
Star Observation ZExampe (b)
SA = Alt
SB = δ

P S

N
S
B
A
W

Star is in the north-western sky. 270 < Azimuth < 360 δ > 0
Exercises on Time June 20, 2019 13
Star Observation Exampe (b)
Since Azimuth =313◦ 190 36.000 star is in north western sky we have
to use the fourth figure.
For countries in northern hemisphere stars having δ > 90 − φ will be
Z
visible. SA = Alt
SB = δ
φ NP = φ
−
90 360 − Azimuth
t
Al
−

90 − δ
90

P S

N
S
B
Exercises on Time June 20, 2019 14
Problem 2

Find the GHA of the Sun at GMT 11 h 00 m 00 s on 17 October 2016,

if the appropriate value for E was 12 h 14 m 36.6 s. What is the LHA
at 45◦ E?

If E = 12hrs 14min 36.6sec, then the “equation of time” ET =

00hrs ¯14min 36.6sec. The minus sign indicates that M is behind A.
Thus the time diagram can be constructed as follows:

Exercises on Time June 20, 2019 15

Solution 2
G
A
M

ET
λ
A
P
LH
GMT

GHA

G0

Exercises on Time June 20, 2019 16

Solution 2

GHA = 12 + GM T + ET
= 12hrs + 11hrs + 00hrs 14min 36.6sec
= 23hrs 14min 36.6sec

Since the point id 45◦ East

LM T = GM T − λE
= 11hrs + (45/15) = 14hrs
LHA = LM T − 12 + ET
= 2hrs 14min 36.6sec

N.B. In this last equation LMT is measured from Z 0 .

Exercises on Time June 20, 2019 17
 QUESTION TIME

Exercises on Time June 20, 2019 18