A Inao 01-06

Homi Bhabha Centre for Science Education
Tata Institute of Fundamental Research
7th Indian National Astronomy Olympiad

May 1 to 20, 2005
List of Constants
Mass of Sun: M~ = 2.0 x 1030 kg
Mass of Earth: M = 6.0 x 1024 kg
Mass of Jupiter: mJ = 2.0 x 1027 kg
Radius of earth = 6400 km
1 A.U. = 1.5 x 1011 m
1pc = 3.26 ly
Tropical year = 365.25d
Sidereal month = 27.33d
Gravitational acceleration at Earth's surface = 10 m/s2
Obliquity of the ecliptic = 23.5
Eccentricity of Earth's orbit = 0.016
Stephan Boltzman Constant = 5.67 x 10
G = 6.67 x 10-11 N m2 / kg2

c = 3 x 108 m/s
k = 1.38 x 10 23 J/K
h = 6.63 x 1034 Js
mass of electron: me = 9.1 x 10 31 kg
mass of proton: mp = 1.67 x 10
27
kg
Avogadro constant NA = 6.02 x 1026 /kmole

World population = 6.2 billion
W/ m2 K4
3rd INDIAN ASTRONOMY OLYMPIAD CAMP

Nehru Science Centre, Worli, Mumbai, May 16 to 29, 2001
Theory Test I
May 22, 2001

ATTEMPT ALL QUESTIONS
Total marks: 100

(Each question carries 10 marks)
Duration 90 Minutes
1.
Neptune has a period of 165 years. Without neglecting revolution of earth, what would be the
maximum angle that Neptune would appear to cover in the sky in 6 months?
2.
The SOHO satellite is located at the Inner Lagrengian Point of the Earth-Sun system. Suppose
it is trying to photograph the sun in H (6563 A) then at what frequency should it be looking
at the Sun? (Orbital velocity of earth = 30 km/s. assume velocity of Sun goes around Milky
Way centre = 200 Km/s)
3.
During this camp, we have already seen a few satellites moving across the sky. Given that the
reflecting area of the satellite is effectively 1 square meter that it reflects sunlight equally in
all directions, find the amount of light received by the eyes of the observer. (Solar constant =
1352 W/m2 period of sat. = 110 min)
4.
Suppose an asteroid of mass 2 x 1020 Kg. is going around the sun at a distance of 2.6 AU,
estimate: (a) its momentum (b) energy required for a head on collision with another asteroid
to reverse its path.
5.
Astronauts on the International Space Station (ISS) would soon have PSA or personal
satellite assistants which would practically be a robots floating about, and going about the
station carrying messages etc. How difficult would it be for the 1 Kg. PSA to move towards
the outside of the 420 ton ISA, when it is 100 m from the center of ISS?
6.
A star has coordinates RA 6hr Dec 0o. Write, to the nearest hour, (local time), when it would
be seen highest in the sky. Also give the three months when you have the least chance of
seeing it.
7.
A student doubting his professors decided to estimate the mass of the earth by himself,
astronomically. He has following data: (a) Radius of earth = 6400 km/s. (b) speed of light, c =
3 X 105 km/s. (c) true orbital period of Moon = 27.3 days (d) signals sent by Apollo astronauts
reached earth in 1.3 sec. Help him estimate the mass of the Earth.
8.
A spacecraft lands on the asteroid Ceres. After completion of its mission on the surface of the
asteroid it has to take off to return to earth. If the mass of Ceres is 1.7 x 1021 kg. and its radius
is 3.8 X 105 m. what is the minimum velocity with which the rocket should be fired for it to
start its journey back to earth. (The Universal constant of Gravitation = 6.67 x 10-11 mks units)
9.
The distance from the surface of the earth to the satellite at its perigee is 700 km and at its
apogee 56000 km. Calculate the period of satellite and the eccentricity of its orbit.
10.
A typical neutron star may have a mass equal to that of the Sun but a radius of only 10 Km.
(a) what is the gravitational acceleration at the surface of the such a star? (b) How fast would
an object be moving if it fell from rest through a distance of 1.00 m on such a star? (Assume
the star does not rotate).
Test 2
24 May 2001
Attempt all questions
(Each question in worth 10 marks)
Total Marks 100

NAME:
Duration: 90 Mimutes
CITY:
J/S
1. A comparison of the main sequence star in a cluster in a colour magnitude diagram with
that in a standard HR Diagram shows that the apparent magnitude of the stars on the
cluster main sequence are 7 magnitudes larger than the absolute magnitudes of stars in
the corresponding positions in the standard HR Diagram. How far away is the cluster?
2. Vega is a main sequence star with an apparent magnitude of 0.03. By trigonometric
parallax, Vega is 26 light years away. Merak from Ursa Major is also a main sequence
star and is of the same spectral class of Vega. It has an apparent magnitude of +2.4.
Estimate the distance to Merak.
3. A possible cause for your worries is whether or not Orion will be seen during your
observational test. As a confirmatory test, calculate the local setting time of Betelguese
for Mumbai. (RA = 5 hrs 50 min, Dec = +7o. Mumbai Latitude = +19o) Assume that your
test was on 23rd May, 2001.
4. An enthusiastic student proposes, for some reason, that a space craft be launched in a
circular orbit around the Sun at 0.6 AU from the Sun, with its direction of revolution
opposite to that of the Earth. Find the Sidereal period of the satellite and its Synodic
period with respect to Earth.
5. A 2000 Hz siren and an observer are both at rest with respect to ground. What frequency
does the observer hear if a) Wind is blowing at 12 m/s from source to observer, b) Wind
is blowing at 3.4 m/s from observer to source and c) wind stops but the observer moves at
3.4 m/s towards the source. (Velocity of sound in air is 340 m/s)
6. Assume that Venus and Mercury have circular orbits with semi major axes 0.723 AU and
0.387 AU respectively. Find the angle of maximum elongation and the corresponding
phase angles for both.
7. An astronaut is in a circular orbit around a neutron star of unknown mass and the period
of orbit is 1s. Find the maximum and minimum tidal forces that act on his body
depending on his orientation. (Mass of the astronaut is 100 kg and assume a reasonable
value for height and all other parameters).
8.
For the Earth, find a) Schwarzschild radius b) Roche Limit with respect to a satellite of
density = 1000 kg/m3. (ME = 6x1024 kg, and E = 5500 kg/m3). Evaluate the same
quantities for Jupiter with MJ = 2x1027 kg and RJ = 7.1x107 m).
9. Compare the resolutions of a) Keck (D = 10 m) in Optical, b) Hubble (D = 2.4 m) in

Optical, c) A single dish of GMRT (D = 45 m) in Meter-wave, d) Subaru (D = 8.3 m) at 1
m and arrange them in ascending order.
10. Two stars are very close to each other and their brightness ratio is 2:3. The stars together
have an apparent magnitude mc = +5. Find the individual app. magnitudes of the stars.
THIRD TEST (SENIORS)
28 May 2001
Total Marks 100

NAME:
CITY:

J/S
1. Suppose you are sitting on a full moon night with the moon behind your back, shining
with an apparent magnitude of 12.7. In front of you is the ball that reflects 100% of the
light incident on it. You see the image of the full moon in it. Find the apparent magnitude
of the image. (Distance to the ball = 2 m, and radius of the ball = 5 cm).
2. A recent e-hoax claimed that a certain planetary alignment on 5 May would stop the
rotation of earth. If the earth stopped rotating what effects would such a catastrophe
have? (Give a list of 5 most important affects).
3. The X-ray telescope on the orbital station Salut 7 was not being used to observe the
objects within an angle of 60o of the Sun to ensure safety of the detectors. What is the
minimum time of the expedition on Salut 7 during which the whole X-ray sky would be
covered.
4. You know that observing from space has its own benefits. What are they? If we want to
put a solar telescope on the moon, where will we put it?
5. A globular cluster contains a million main sequence stars of absolute magnitude M = +6
and 10,000 red giants of absolute magnitude +1. Would it be visible to the naked eye if
seen from 10 kpc away?
6. You know that for all practical purposes, the stars are point sources. Explain
qualitatively, why the stellar images have definite diameters on a photographic plate and
further, a brighter star has a larger image.
7. The Lunar occultation is an eclipse of a star by the moon. The exact time when a star was
occulted (eclipsed) by the moon is quite significant in astronomy. Assume that there are
6000 stars brighter than sixth magnitude distributed evenly over the entire sky. If the
orbit of the moon is inclined at 5o to the ecliptic, how often would stars brighter than 6m
be occulted by the moon on an average? How many (what fraction) of these would you
be able to see by the naked eye?
8. The semi-major axis of the earths orbit is 1.4959787 x 1011m and the orbital eccentricity
is e=0.0167. Find the maximum and minimum distance of the earth from the sun. Given
that the perihelion occurs in winter for the northern hemisphere, why then are summers
hotter than winters?
9. What are more common for the entire earth - Solar eclipses or lunar eclipses? Why are
solar eclipses more common in summer than in winter, especially at more northern
(higher) latitudes? State qualitatively where on earth you would see the longest solar
eclipses.
10. Find the density of a white dwarf with mass 2 x 1030 kg, luminosity 3.86 x 1023 W and a
peak emission at 258.6 nm.
3rd Indian Astronomy Olympiad

Nehru Science Centre, Worli Mumbai
May 16 to 29, 2001

THIRD TEST (JUNIORS)
28 May 2001
Total Marks 100

NAME:
CITY:

J/S
1. Suppose that the moon was a perfect sphere that reflected all incident light. How would it
have appeared when seen from the Earth?
2. A recent e-hoax claimed that a certain planetary alignment on 5 May would stop the
rotation of earth. If the earth stopped rotating what effects would such a catastrophe
have? (Give a list of 5 most important affects).
3. The X-ray telescope on the orbital station Salut 7 was not being used to observe the
objects within an angle of 60o of the Sun to ensure safety of the detectors. What is the
minimum time of the expedition on Salut 7 during which the whole X-ray sky would be
covered.
4. You know that observing from space has its own benefits. What are they? If we want to
put a solar telescope on the moon, where will we put it?
5. A globular cluster contains a million main sequence stars of absolute magnitude M = +6.
What apparent magnitude would it have if seen from 10 kpc away? Would it be visible to
the naked eye?
6. The parallax of a star is 0.01 and the diameter of the star in red giant stage is 1011m. If
you photograph it with a 6 f/8 telescope, what would be the size of the star image? Is
your answer right?
7. The Lunar occultation is an eclipse of a star by the moon. The exact time when a star was
occulted (eclipsed) by the moon is quite significant in astronomy. Assume that there are
6000 stars brighter than sixth magnitude distributed evenly over the entire sky. If the
orbit of the moon is inclined at 5o to the ecliptic, how often would stars brighter than 6m
be occulted by the moon on an average?
8. The semi-major axis of the earths orbit is 1.4959787 x 1011m and the orbital eccentricity
is e=0.0167. Find the maximum and minimum distance of the earth from the sun. Given
that the perihelion occurs in winter for the northern hemisphere, why then are summers
hotter than winters?
9. What are more common for the entire earth - Solar eclipses or lunar eclipses? Why are
solar eclipses more common in summer than in winter, especially at more northern
(higher) latitudes?
10. Find the density of a white dwarf with mass 2 x 1030 kg, luminosity 3.86 x 1023 W and a
peak emission at 258.6 nm.
3rd Indian Astronomy Olympiad

Nehru Science Centre, Worli, Mumbai
May 16 to 29, 2001
PRACTICAL TEST
28 May 2001
(Each question is worth 50 marks)
Total Marks 100

Name:
1)
City:
J/S
Fig. 1 is a photograph of Saturn taken from an earth based telescope.

You can assume that the photo was taken at quadrature (Sun Earth
Saturn angle is 900). Take Saturns radius to be 6 x 107 m at its equator.
a)
b)
c)
d)
e)
2)
Duration 120 minutes
find polar radius of Saturn

find inner and outer radius of Saturns rings
Assume the orbit of Saturn to be circular with period of 29.46 years.
Find earth Saturn distance when the photo was taken.
using the values calculated up to now, find the angular scale of the
image (1 mm = ? arc seconds)
Find the angle made by the plane of Saturns rings to the line of
sight.
Fig. 2 shows a sketch of the path of a binary system 70 Ophiuchi with

position of one star (B) is marked with respect to the other (A) assumed to
be at the point of intersection of axes. The parallax of the central is 0.199
arcsec. Observational data indicates mass of 1 star is 1.3 times the mass
of the other. Find the masses of the A and B components of the system.
-----xoxox-----
5th Indian Astronomy Olympiad Camp

Nehru Science Centre , Worli, Mumbai 400 018
May 18 to 27, 2003
Test 1: Question paper: May 22, 2003, 17.30 to 19.30
All Questions are compulsory and all questions carry equal marks
1. A 5 Msun star causes gravitational redshift such that a 500 nm photon is detected
with a wavelength of 600 nm. What is the radius of the Star?
2. Andromeda Galaxy has a magnitude of 3.4 and there are 1010 stars in it. What is
the average absolute magnitude of each star? (The distance to the galaxy is 2.4
million light years.)
3. In observations taken on Summer Solstice and Winter Solstice the position of
Polaris is seen to be shifted by 0.007 arc sec. What is the distance to the Pole
Star?
4. Regulus has = 150o, = 0o. Find and .
5. The velocity of the Sun with respect to the centre of our Galaxy is 200 km/s and it
is 8.5 kpc from the centre of our Galaxy. Take the Galaxy mass as 1011 Msun and
find the semimajor axis of the Sun's "orbit". Will the Sun have a closed orbit?
Why?
6. Come Hale Bopp had a perihelion distance of 0.9141 AU and eccentricity 0.9951.
Find the aphelion distance, velocity at aphelion and perihelion, semimajor axis
and period. (1 AU = 1.496 x 1011 m)
7. India soon plans to have a moon mission. If we plan a Lunar Stationary Satellite,
what would be its distance from the Moon? (Moon's mass = 7 1022 kg and period
= 27.3 days).
8. Consider a satellite in a Low Earth Orbit (LEO) with a period of 97 minutes. Is it
within the Roche Limit of Earth? If yes, why does it not break? Mass of the Earth
is 6 1024 kg.
9. A six-inch telescope has an exit pupil 10 mm in diameter and there is no light loss
in the object. If the diameter of the pupil of our eye is 6 mm, what is the faintest
star we can see with the telescope? (Exit pupil is the area in which the light of the
telescope comes out of the eyepiece.)
10. A nova is seen to have a diameter of 60" on a certain day and 61" when observed
6 days later. The redshift of the ejected material is z = 0.01. How far away is the
Nova?
Test 2: JUNIORS
Question paper: May 24, 2003, 11.30 to 13.30
Important Data are:
Radius of the Earth = 6400 km,
Radius of moon 1700 km,
Radius of Sun is 700,000 km.
Earth Sun distance = 1.5 x 108 km,
Earth Moon distance = 384400 km,
Period of Moon = 27.3 days,
Length of 1 year = 365.25 days
Mass of moon = 7 1022 kg,
24
Mass of earth = 6 10 kg,
Mass of the Sun = 1.9892 1030 kg
Stephen Boltzmann Radiation Constant = 5.67 10-8 W/m2/K4
11. Estimate the speed of the lunar shadow during a solar eclipse.
12. Light of wavelength 589 nm is incident on a grating of 5000 lines per cm. The
interference pattern is observed on a screen placed 50 cm away. Find the distance
between the 0th and 1st order maxima, and also the 0th and second order maxima.
13. Find the velocity of the center of earth with respect to the center of mass of the
earth moon system.
14. Write the balance of force equations for the lagrangian points 1, 2, and 3 for a
two-body system. Using your formulae, calculate the location of L1 for the Sun
Earth System neglecting centrifugal force.
15. The radial velocity of Centauri is 18.1 km/s Its parallax is 0.73. How much
would the parallax change in 100 years.
16. The star delta Orionis lies on the celestial equator. Its RA changes by 0.0001
sec/year and declination changes by 0.0006/year. Its radial velocity is + 16. 1
km/s and its parallax is 0.0036. Find the actual velocity of the star.
17. Calculate the length of the day on the Summer Solstice at 20o N latitude.
18. Sun has its peak emission at a wavelength of 550 nm. Find its absolute
luminosity.
19. Cepheids vary in luminosity by up to a factor of 100. If this variation is only due
to change in radii, find the ratio of radii during maxima and minima. Conversely,
if it is only due to change in temperature, calculate the ratio of maximum and
minimum temperatures.
20. The components of a binary star system are approaching at 40 km/s and receding
at 20 km/s respectively. The distance between the stars is 1 AU. Find the masses
of the components.
Test 2: SENIORS
Question paper: May 24, 2003, 11.30 to 13.30
Important Data are:
24
1. Estimate the speed of the lunar shadow during a solar eclipse.
2. Light of wavelength 589 nm is incident on a grating of 5000 lines per cm at an angle of
45o. The interference pattern is observed on a screen placed 50 cm away. Find the
distance between the 0th and 1st order maxima.
3. An observer sees the moon overhead. Find the velocity of the observer with respect to the
center of mass of the earth moon system.
4. Calculate the positions of the Lagrangian points 2 and 3 for the Sun Earth System.
5. The radial velocity of Centauri is 18.1 km/s Its parallax is 0.73. How much would
the parallax and magnitude change in 100 years?
6. The star Sirius has RA = 6h 45m and Dec = -16o 43m. Its RA changes by 0.038 sec/year
and declination changes by 1.223/year. Its radial velocity of 7.6 km/s and its parallax
is 0.3792. Find the actual velocity of the star.
7. Calculate the length of the day on the Summer Solstice at 20o N latitude.
8. Sun has its peak emission at a wavelength of 550 nm. Find its absolute luminosity and
apparent magnitude.
9. The apparent magnitude of Cepheid varies by 5. If this variation is only due to change in
radii, find the ratio of radii during maxima and minima. Conversely, if it is only due to
change in temperature, calculate the ratio of maximum and minimum temperatures. Plot a
graph of all intermediate combinations of temperature and radius changes which will give
the same change in magnitude.
10. The components of a binary star system are approaching at 40 km/s and receding at 20
km/s respectively. The parallax of the binary is 0.5 and Their separation is also 0.5.
Find the masses of the components.
SENIORS Theory Test 3: May 26, 2003, 11.30 am to 13.30 pm

Important Data are:
1. Astronomers need to study H lines from Aldebaran ( = 4h 36m, = 16o 31',
radial velocity 54.1 km/s away from us) on 1 March 2003 from Mumbai (19o N
72o E). Give the proposed observation log specifying the time when they should
point their telescope and the wavelength filter that should be used.
2. Sadal Melik (Aquarius) has a magnitude of 2.93, RA of 22h- 6m, and Dec of 0o 18'
and a parallax 0.0043". How bright will it appear when seen from Porrima (Virgo)
with = 12h 42m, = -1o 28', magnitude 2.71 and parallax 0.084.
3. At opposition, Mars has a magnitude of 2.75 and an angular size of 25". It is
observed through a telescope with an aperture of 70 mm in diameter and 100X
magnification. How bright would it appear? Note that angular resolution of
unaided eye = 1'.
4. A satellite orbits earth with a period of 100 minutes. It has a light source on board
with an apparent magnitude of +2 when overhead. Calculate the power of the
source and sketch the magnitude as a function of time when it is above the
horizon.
5. A radio antenna beams out a signal with power 1 MW. Half an hour later, it
receives the signal back after it has been reflected off an asteroid, assumed to be
spherical in shape. Find the relation between the power received back and the
radius of the asteroid.
6. The emission from Sun peaks at 550 nm. Estimate the width of the H line. How
do you think it will compare with real observations?
JUNIORS Theory Test 3: May 26, 2003, 11.30 am to 13.30 pm

Important Data are:
Photon from a 0 magnitude star is 1010 photons/m2 in visible wavelength
1. The spiral galaxy Andromeda is spread over an area of 3o x 1o in the sky.
Calculate its radius if it is 2.2 million light years away from us. Also find out the
angle of tilt of the galaxy to our line of sight. Andromeda galaxy is moving
towards the Milkyway at 250 km/s. Calculate the blue shift. Is this in violation of
Hubble's law? Explain.
2. After the lectures are over you plan to relax on the terrace. You see a hundred
watt bulb at Haji Ali and the Sirius just above it. Which one of them would be
brighter and by how much. Calculate their distance moduli. Take Haji Ali to be 1
km away.
3. Calculate the resolving power of Keck telescope and GMRT observing at 1 m
wavelength and compare it with the resolving power of your eye. If the Keck
telescope plans to observe the headlights of a car approaching the telescope, up to
what distance can it be placed for it to be resolved? If the car's headlights work in
1 meter wave length and approaching GMRT, how far can it be before GMRT can
resolve it?
4. Calculate the maximum possible red shift of Mars as observed from Earth. Its
average distance from Sun 1.5 AU. Assume that Mars has a circular orbit.
5. Estimate the RA - Dec, and - for the Sun today.
6. The emission from Sun peaks at 550 nm. Estimate the width of the H line.

Nehru Science Centre, Worli, Mumbai 400 005, INDIA
May 18 to 28, 2003
SENIORS PRACTICAL TEST: May 27, 2003, 9.30 am to 11.30 pm
Question 1 In table 1 the observational data of an unknown galactic object is given and
the same data is plotted in figure 1. Interpret the data.
Table 1. Observational Data of an unknown galactic object
Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)
10
0.612497401
210
0.496374804
410
0.48562062
610
0.666082225
810
0.57460299
20
0.582235837
220
0.457718971
420
0.46567428
620
0.644624649
820
0.5451449
30
0.552580062
230
0.419114757
430
0.44392007
630
0.617897297
830
0.50992581
40
0.526144765
240
0.383383434
440
0.42300791
640
0.588476774
840
0.47137022
50
0.505171111
250
0.353129417
450
0.40555363
650
0.559104669
850
0.43223098
60
0.491324186
260
0.330509447
460
0.39389352
660
0.532437115
860
0.39534602
70
0.485543723
270
0.317042046
470
0.38986395
670
0.510802949
870
0.36338701
80
0.487961688
280
0.313474568
480
0.39462633
680
0.495992507
880
0.33862283
90
0.497894194
290
0.319719884
490
0.40855331
690
0.489096284
890
0.3227192
100
0.513908459
300
0.334868443
500
0.43118678
700
0.490408147
900
0.31659281
110
0.533958637
310
0.357274561
510
0.46127149
710
0.499401905
910
0.32033311
120
0.555578116
320
0.38470903
520
0.49686141
720
0.514783318
920
0.33319885
130
0.576110676
330
0.41456414
530
0.53548907
730
0.534612779
930
0.35368959
140
0.592959403
340
0.44409238
540
0.57438272
740
0.556487442
940
0.37968576
150
0.603830584
350
0.470657082
550
0.61071135
750
0.577766139
950
0.4086443
160
0.606950309
360
0.491972153
560
0.64183565
760
0.595816531
960
0.43783214
170
0.601233944
370
0.506309049
570
0.66554172
770
0.608261914
970
0.46457622
180
0.586392966
380
0.51265216
580
0.68023666
780
0.613205113
980
0.48650717
190
0.562969347
390
0.51078845
590
0.68508801
790
0.609408988
990
0.50177458
200
0.532294261
400
0.501323224
600
0.68009461
800
0.596417033 1000
0.50921415
Observation of an Unknown Stellar Object

0.8
Flux (jansky)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
200
400
600
Time (hours)
800
1000
1200
Question 2: In table 2 the data is given for some extragalactic objects and it is plotted in
figure 2. If gravity was the only effective force at large distances, what is the expected
distance of the highest redshift galaxy. Conversely, if gravity was switched off after the
objects formed, what would have been the size of the Universe at the time of the Big
bang. If the current age of the visible Universe is 1010 years, what would have been its
size without gravity?
Table 2. Distance of Some Extragalactic objects and their Redshift
Distance (MPc)
Z
Distance (MPc)
Z
Distance (MPc)
Z
Distance (MPc)
Z
50
0.010141
1000
0.227623
1950
0.556806
2900
1.54943
100
0.01978
1050
0.23076
2000
0.583552
2950
1.606608
150
0.030106
1100
0.243328
2050
0.614004
3000
1.69803
200
0.041469
1150
0.25776
2100
0.653152
3050
1.809616
250
0.050344
1200
0.266882
2150
0.68318
3100
1.909934
300
0.061924
1250
0.274549
2200
0.702221
3150
2.069829
350
0.070092
1300
0.309398
2250
0.75707
3200
2.320536
400
0.083645
1350
0.311998
2300
0.809168
3250
2.422528
450
0.092047
1400
0.321717
2350
0.823285
3300
2.747519
500
0.103167
1450
0.336316
2400
0.867878
3350
3.071024
550
0.12284
1500
0.3491
2450
0.936967
3400
3.037833
600
0.121769
1550
0.393837
2500
1.002637
3450
3.782714
650
0.142164
1600
0.405446
2550
1.039302
3500
4.060282
700
0.147057
1650
0.413626
2600
1.066479
3550
4.645803
750
0.170371
1700
0.40778
2650
1.129138
3600
6.416421
800
0.181261
1750
0.427979
2700
1.237516
3650
11.47536
850
0.195385
1800
0.465334
2750
1.306714
900
0.192553
1850
0.496163
2800
1.338373
950
0.215683
1900
0.524038
2850
1.464878
Redshift of extragalactic objects

12
Redshift (Z)
10
0
0
500
1000
1500
2000
2500
Distance (MPc)
3000
3500
4000

Nehru Science Centre, Worli, Mumbai 400 005, INDIA
May 18 to 28, 2003
JUNIORS PRACTICAL TEST: May 27, 2003, 9.30 am to 11.30 pm
Question 1 In table 1 the observational data of an unknown galactic object is given and
the same data is plotted in figure 1. Interpret the data.
Table 1. Observational Data of an unknown galactic object
Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)Time(hrs)Intensity(Jy)
10
0.612497401
210
0.496374804
410
0.48562062
610
0.666082225
810
0.57460299
20
0.582235837
220
0.457718971
420
0.46567428
620
0.644624649
820
0.5451449
30
0.552580062
230
0.419114757
430
0.44392007
630
0.617897297
830
0.50992581
40
0.526144765
240
0.383383434
440
0.42300791
640
0.588476774
840
0.47137022
50
0.505171111
250
0.353129417
450
0.40555363
650
0.559104669
850
0.43223098
60
0.491324186
260
0.330509447
460
0.39389352
660
0.532437115
860
0.39534602
70
0.485543723
270
0.317042046
470
0.38986395
670
0.510802949
870
0.36338701
80
0.487961688
280
0.313474568
480
0.39462633
680
0.495992507
880
0.33862283
90
0.497894194
290
0.319719884
490
0.40855331
690
0.489096284
890
0.3227192
100
0.513908459
300
0.334868443
500
0.43118678
700
0.490408147
900
0.31659281
110
0.533958637
310
0.357274561
510
0.46127149
710
0.499401905
910
0.32033311
120
0.555578116
320
0.38470903
520
0.49686141
720
0.514783318
920
0.33319885
130
0.576110676
330
0.41456414
530
0.53548907
730
0.534612779
930
0.35368959
140
0.592959403
340
0.44409238
540
0.57438272
740
0.556487442
940
0.37968576
150
0.603830584
350
0.470657082
550
0.61071135
750
0.577766139
950
0.4086443
160
0.606950309
360
0.491972153
560
0.64183565
760
0.595816531
960
0.43783214
170
0.601233944
370
0.506309049
570
0.66554172
770
0.608261914
970
0.46457622
180
0.586392966
380
0.51265216
580
0.68023666
780
0.613205113
980
0.48650717
190
0.562969347
390
0.51078845
590
0.68508801
790
0.609408988
990
0.50177458
200
0.532294261
400
0.501323224
600
0.68009461
800
0.596417033 1000
0.50921415
Observation of an Unknown Stellar Object

0.8
Flux (jansky)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
200
400
600
Time (hours)
800
1000
1200
Intensity(W/m2 at earth)
Question 2: The Energy Density Curve for a particular object measured by Hanley
Observatory is given below. Interpret the curve.
100 nm
Wavelength (nm)
1000 nm


May 1 to 20, 2005
Theory Test 1
May 10, 2005: 10:00 IST

Note: All questions carry equal marks.
Duration 2h
Juniors
1. Is it possible to observe an eclipse of the Sun from the Earth at midnight?
2. The distance between Sun and Jupiter is 5.2 AU. The biggest moon of Jupiter,
Ganymede is 5262 km in diameter. Calculate the distance at which it must
revolve around Jupiter to give a perfect total solar eclipse for the 'Jovians'? How
the answer will change if the 'Ganys' want to see the solar eclipse?
Now that you are at it, find the magnitude of Ganymede from Jupiter at
opposition in the first case. Albedo of Ganymede is 0.1(Radius of Jupiter =
142,800 km)
3. Two small bodies Pingu and Tingu orbit the
a white dwarf Xaerox(1 M~ ) along the
same orbit. The distance between them is
small enough for the part of the orbit
between them to be considered a straight
line. Their maximum separation in the
orbit is d = 10 m, and their minimum
separation while joining hands is 2m.
Assuming the time period of the orbit be
30, find the eccentricity of the orbit.
4. Anti studied a Milky Waylike galaxy and found an H line at 7219. Meanwhile,
Vishal studied various other galaxies and found the value of Hubble's constant
to be 75 km/s/Mpc. The wavelength of H line found at the NSC labs is 6563.
What telescope should AnandG use to observe this galaxy visually? Make any
reasonable and justifiable assumptions.
5. You know that the sun crosses the celestial equator on 23rd September. Find
the time required for the Suns disk to cross it.
6. Xiao Minong is observing Jupiter at opposition from Beijing(=39 54.996' N,
=116 22.998' E) on 30th July. She reports seeing it at an altitude of 48 at
midnight. Is she correct? Justify.


May 1 to 20, 2005
Theory Test 1
May 10, 2005: 10:00 IST

All questions carry equal marks
Duration 2h
Seniors
1. You know that the sun crosses the celestial equator on 23rd September. Find the
time required for the Suns disk to cross it.
2. The distance between Sun and Jupiter is 5.2 AU. The biggest moon of Jupiter,
Ganymede is 5262 km in diameter. Calculate the distance at which it must revolve
around Jupiter to give a perfect total solar eclipse for the 'Jovians'? How the answer
will change if the 'Ganys' want to see the solar eclipse? Now that you are at it, find
the magnitude of Ganymede from Jupiter at opposition in the first case. Albedo of
Ganymede is 0.1. (Radius of Jupiter = 142,800 km)
3. Some arbit sailor happens to see a solar eclipse. He notices that the moon is
covering the sun from the bottom. Where could he be? More specifically, at what
latitude do you expect this sailor to be. What time of the day is it? Where does he
see the sun?
4. Two small bodies Pingu and Tingu orbit a white dwarf Xaerox (1M~) along the same
closed orbit. The distance between them is small enough for the part of the orbit
between them to be considered a straight line. Now, Pingu & Tingu (both long
separated brothers) want to shake hands. Their maximum separation in the orbit is
d = 10 m, and each of them can reach out 1 m. Assuming the time period of the
orbit be 30 years, find the limit on the eccentricity of the orbit if Pingu is able to
shake hands with Tingu.
Max
5. The Earth gets energy from the sun at the rate

of 1400 W/m2 at the top of the atmosphere.
Some of it (37%) gets reflected from the cloud
tops, polar snow caps etc. Assuming that the
solid part of the Earth is a perfect blackbody
and that the temperature of interplanetary
space is about 100 K, what is the equilibrium
temperature of Earth. Compare it with the real
mean temperature of Earth (14C). What
effects invalidate the assumption?
6. In the figure you see a photograph of a star

field taken by 2.3 m Vainu Bappu Telescope at
Kavalur last December. The stars were tracked; hence two asteroids Mux and Max
left a trail. Assuming almost circular and coplanar orbits, which one of them is
closer to:
i) the Earth,
ii) the Sun.


May 1 to 20, 2005
Theory Test 2
May 12, 2005: 9:30 IST

Duration 3h
Juniors
1. Estimate the duration for which Jupiter is in retrograde motion.
2. The Galactic North Pole is at = 12h40m, = +28. When does the sun cross the plane
of the Milky Way?
3. At Murbad, Parag is enjoying the colourful double star Albireo (19h31m, 2758') in
Cygnus. He needs to adjust his telescope (Celestron LX-45S, 1m objective focal length,
5 aperture, motorized tracking with GPS enabled GOTO, $870 local taxes apply) every
2 minutes to keep the star in view. What must be the focal length of the eyepiece?
4. Algol is an eclipsing binary with apparent magnitude V = 2.10 and colour (B-V)=0.05.
If the ratios of the luminosities of the two components of the binary are 2.1 in V and
2.8 in B, find the apparent V and B magnitudes and B-V colours of each component.
5. Find out the mass of the double star Alpha Centauri for which parallax is 0.75'',
period is 79 years and observed semi-major axis subtends 17.6''. Moreover, these
stars are observed to follow a wavy trajectory with respect to the background stars. If
the maximum deviation from the straight path for these two stars in 4.2'' and 2.1'',
find the limit on the individual masses of the two stars.
6. Tiger Thyangarajan from Vishakhapattanam showed me a beautiful photograph of a
crescent Moon he had taken, looking towards the waters of the Bay of Bengal. I was
fascinated looking at it, because I also had taken a photo of the Moon around the
same season of the year from Mumbai, which showed the Arabian Sea. The crescents
in both the pictures not only have similar phases but were also at the same altitude
from the horizon line of the waters. Estimate the shortest periods possible when these
photographs might have been taken. Give what all differences these two photographs
might have.


May 1 to 20, 2005
Theory Test 2
May 12, 2005: 9:30 IST

Note: All questions carry equal marks
Duration 3h
Seniors
1. Estimate the duration for which Jupiter is in retrograde motion. At the start of this
period, Jupiter was seen in the 'Gateway of Heavens'. Where will it be at the end of
this period?
Castor
32
7h 35m
Pollux
28
7h 45m
Procyon
7h 40m
Gomeisa
7h 25m
2. The adjacent figure shows
the intensity profile of a cluster
(something) for H line (6563 as
observed in the laboratory). The
spectral analyses of individual
stars in the cluster suggest that
all stars belong to the main
sequence and are 10 times
brighter than the sun. Discuss the
nature of this cluster if it is at the
distance of 1kpc. Is the cluster
closed?
3. Pingu and Tingu now have moved from the White Dwarf Xaerox to a pulsar
ModiXaerox. Pulsars are thought to be rapidly rotating neutron stars. ModiXaerox has
a radius of about 10km, a mass of about one solar mass, and revolves at a rate of 30
times per second. While moving around the pulsar in the circular orbit with the period
of 40d they push each other so that Pingu goes into the eccentric orbit and goes to the
nearest distance of ModiXaerox without being pulled apart. Assume that his body
mass is uniformly distributed along his height (2m tall), his feet point toward the
pulsar, and dismemberment begins when the force that each half of his body exerts on
the other exceeds ten times his body weight on the Earth. What is the period of
revolution in a circular orbit about the pulsar at this minimum distance? With what
orbit Tingu must be moving around the pulsar.
4. Algol is an eclipsing binary in Perseus with apparent magnitude V=2.10 and colour
(B-V) = -0.05. If the ratios of the luminosities of the two components of the binary
are 2.1 in V and 2.8 in B, find the apparent V and B magnitudes and B-V colours of
each component.
5. Find out the mass of the double star Alpha Centauri for which parallax is 0.75'',
period is 79 years and observed semi-major axis subtends 17.6''. If the minimum
separation between them is 4.2'', find the limit on the individual masses.
6. Tiger Thyangarajan from Vishakhapattanam showed me a beautiful photograph of a
crescent Moon he had from the seashore, looking towards the waters of the Bay of
Bengal. I was fascinated looking at it, because I also had taken a photo of the Moon
around the same season of the year from Mumbai, which showed the Arabian Sea.
The crescents in both the pictures not only have similar phases but were identical in
size. Estimate the shortest periods possible when these photographs might have been
taken. Give what all differences these two photos might have.


May 1 to 20, 2005
Theory Test 3
2453508.58333 JD
Duration 4 hrs
Juniors
1. Tiger Thyangarajan with his camera (20 marks)

After his photograph of Moon at Vishakhapattanam was appreciated at INAO, Tiger
Thyangarajan decides to continue his hobby and comes to Mumbai.
i. He photographed the sun and got it as 0.6 mm disc on the negative. Calculate the
focal length of his camera.
ii. Now he takes the photograph of the famous 'Queen's Necklace'-the street lamps on
the arc of Marine Drive from a helicopter. Recall that during your visit from TIFR, you
have seen sodium vapour lamps on Marine Drive that are fitted at every 20m,
iii. 180W (with 40% light efficiency). He got 38 images of the lamps in the 35 mm
negative. Calculate the height from which the photograph must have been taken.
iv. Calculate what is the apparent magnitude of each lamp from this height.
v. What should be the minimum size of the telescope if the entire 'Necklace' (of 5 km
circular arc) is to be seen as just one bright spot from Moon?
2. Mining on Miranda: (50 marks)
Scientists at ISRO find evidences for the presence of platinum, ruthenium and
gadolinium on Miranda one of the satellites of Uranus. You are sent to Miranda as a
part of a team to set up a mining station. In the leisure time you continue your hobby of
astronomy. You observe that Uranus the mother planet rises every 2.0 x 106 s and
from the same point on the horizon. The orbit of the Uranus is observed to be making
90 with its equator. The suns apparent magnitude is 21m.4 while you recall that it was
27m.8 from earth.
i. You also observe that the solar eclipse can take place only in certain seasons.
Calculate after how much time the season of eclipses repeats.
ii. What will the Jupiter's maximum elongation from Sun?
iii. Explain qualitatively when the Jupiter will be brightest?
iv. Draw the celestial sphere. Show the diurnal motion of Sun on the celestial sphere
during summer and spring from the northern hemisphere of Uranus.
v. Calculate the distance (in Uranus light years) of 1 parsec for Uranus.
3. The return of Pingu and Tingu: (30 marks)
Pingu and Tingu, bored of their cosmic adventures, decide to return to the earth. But
their journey back is not free of misadventures. Being away from earth for so long, they
know nothing about it and its neighbourhood.
i. They land on earth, but they have no idea where they are. They observe the moon
rising at the same sidereal time on two consecutive days. Where could they be?
ii. They decide to travel and explore the earth. They reach a place where the moon is
visible continuously for 48 hours. What is the minimum latitude of that place?
iii. They travel some more and observe a total solar eclipse. From the local
astronomersthey find out that it is 22nd July 2009 and that =30N, =113E and
their watches (which were still showing UT) read 1:25. Calculate the geocentric
right ascension and declination of the moon.


May 1 to 20, 2005
Theory Test 3
2453508.58333 JD
Duration 4 hrs
Seniors
1. Binary Stars: (20 marks)

HP2110psc is a binary in Scutum. The two members are moving in elliptical orbit around
each other with the orbit making nearly (but not exactly) 90 with the plane of sky.
i. If the ratios of their redshifts as observed along the minor axis is 0.6, calculate the
eccentricity of the orbit. The difference in the magnitudes is 0m.5 and they are observed
to be of the same spectral class. The mass luminosity relation is L m3.5.
ii. The maximum angular separation of the two members is observed as 0".34. If the orbit
were in the plane of sky estimate the aperture and focal length of the telescope (to be
mounted on Astrosat) which will resolve it at all times. CCD mounted at the prime focus
of this telescope has a 3000 dpi (dots per inch) resolution.
2. Mining on Miranda: (50 marks)
Scientists at ISRO find evidences for the presence of platinum, ruthenium and gadolinium
on Miranda one of the satellites of Uranus. You are sent to Miranda as a part of a team to
set up a mining station. In the leisure time you continue your hobby of astronomy. You
observe that Uranus the mother planet rises every 2.0 x 106 s and from the same point on
horizon. The orbit of the Uranus is observed to be making 90 with its equator. The suns
27m.8 from earth.
apparent magnitude is 21m.4 while you recall that it was
i. You also observe that the solar eclipse can take place only in certain seasons. Calculate
after how much time the season of eclipses repeats.
ii. Calculate the maximum duration for which Jupiter will occult the sun. Jupiter is seen to
have 14" diameter. Plot its path on the sun's disk.
iii. What will the Jupiter's maximum elongation from Sun?
iv. Draw the celestial sphere. Show the diurnal motion of Sun on the celestial sphere
during summer and spring from the northern hemisphere of Uranus.
v. Vernal equinox for Uranus points in the direction of Denebola (to be more specific, =
vi. 1, = 168 as defined from the earth's coordinates). Calculate the distance (in Uranus
light years) of 1 parsec for Uranus. Hence show the parallactic ellipse for Denebola on
the celestial sphere in spring and summer. Recall that Denebola is 2m.1 star 36 earth
light years away from the sun.
3. The return of Pingu and Tingu: (30 marks)
Pingu and Tingu, bored of their cosmic adventures, decide to return to the earth. But their
journey back is not free of misadventures. Being away from earth for so long, they know
nothing about it and its neighbourhood.
i. They land on earth, but they have no idea where they are. They observe the moon rising
at the same sidereal time on two consecutive days. Where could they be?
ii. They decide to travel and explore the earth. They reach a place where the moon is
visible continuously for 48 hours. What is the minimum latitude of such a place?
iii. They travel some more and observe a total solar eclipse. From the local astronomers
they find out that it is 22nd July 2009 and that =30N, =113E and their watches
(which were still showing UT) read 1:25. Calculate the geocentric right ascension and
declination of the moon.


May 1 to 20, 2005
Laboratory Test 1
2453505.72916 JD
Duration 2h
Juniors
1. A picture of moon was taken on 30th April 2005 . Fig. 1. shows a

negative of that picture.
i. Estimate the size of the 'Tycho' crater.
ii. Find the north-south and the east-west dimensions of the 'Grimaldi'
crater.
iii. The top right of the same figure shows something well known as the
'Jewel Handle effect'. Explain what you see.
iv. Estimate the time of the next new Moon day.
The radius of moon is known to be 1738 km.
2. Fig. 2 shows a graph of the distances of five satellites of a planet 'Caenon'
plotted against time (in days).
i. Find the mass of Caenon.
ii. Further investigation of this planet showed that it has a very thin ring.
Estimate the maximum radius of such a ring. Comment on this value
with respect to the observed satellites of Caenon.
Independent measurements have shown that the diameter of 'Caenon' is
6780 km (Claude et al ApJ 123/23).
3. You are given spectra of six stars (Fig. 3). Estimate their temperatures.
Find the two Balmer lines (H = 6563 and H = 4860 ) in the spectra.
What pattern do you see when you go from the hotter to cooler star. If V =
2.0 for the star BD9547, then calculate V for the other stars. Comment
about the velocities of the stars.


May 1 to 20, 2005
Laboratory Test 1
2453505.72916 JD
Duration 2h
Seniors
1. A picture of moon was taken on 30th April 2005 . Fig. 1. shows a negative
of that picture.
i. Find the north-south and the east-west dimensions of the 'Grimaldi'
crater.
ii. The top right of the same figure shows something known as the 'Jewel
Handle effect'. Explain what you see and estimate the height of the
crater edge. State any assumptions you make.
iii. The angle of elongation for any body is defined as the sun-earth-body
angle. Find the angle of elongation of moon from the given picture.
Also find the time of the nearest full moon within an accuracy of a few
hours.
The radius of moon is known to be 1738 km.
2. Fig. 2 shows a graph of the distances of five satellites of a planet 'Caenon'
plotted against time (in days).
i. Find the mass of Caenon.
ii. Further investigation of this planet showed that it has a very thin ring.
Estimate the maximum radius of such a ring. Comment on this value
with respect to the observed satellites of Caenon.
Independent measurements have shown that the diameter of 'Caenon' is
6780 km (Claude et al ApJ 123/23).
3. Fig. 3 gives you the spectra of six stars. Comment about their
temperatures. Find the two Balmer lines (H and H) in the spectra. What
pattern do you see when you go from the hotter to cooler star. If V = 2.0 for
the star BD9547, then calculate V for the other stars.
Lab Test I
'Jewel Handle'
Grimaldi
N
E
W
S
Tycho
Fig. 1.
0d
5d
10d
15d
Fig. 2.
20d
25d
30d
Lab Test I
Fig. 3


May 1 to 20, 2005
Laboratory Test 2
2453509.58333 JD
Duration 3hrs
Juniors
1. The multiple exposure of the sun (Fig. 1) is taken at 8:00 a.m. LT at regular
intervals are shown in the above photograph. From what location on the Earth
photograph must have been taken and at what intervals?
2. Centauri is a known binary with a period of 79.92 years. You are given the
position angles of the secondary (2 Centauri) with respect to the primary (1
Centauri) over the time (Fig. 2). Estimate the eccentricity of the system.
Parallax measurements show that the system is at the distance of 4.395 ly.
Estimate the limits on the mass of the system. Assuming the proxima centauri
is orbiting at the distance of 0.208 ly find the period of its orbit. The distance of
proxima centauri as seen from the earth is 4.228 ly. What must be its angular
separation from the centauri?
3. The magnitude plot (Fig. 4) of a variable star XMP 2359 is given to you. It is
observed that the star is not only a variable but also a part of a binary system
with one member as 5 solar mass black hole. The points plotted on the same
graph are during two different intervals. The magnitude curve can be seen as a
thick periodic line. The lower continuum (i.e. lower part of the entire curve) is
the magnitude variation seen regularly. Estimate the distance of the source
from us. The higher continuum (i.e. upper part of the entire curve) is observed
during a phase of high mass transfer between the stars. Assuming that the
40% of the gravitational energy of falling mass is converted to light, calculate
the amount of mass transfer.


May 1 to 20, 2005
Laboratory Test 2
2453509.58333 JD
Duration 3hrs
Seniors
1. You must have seen 'Comet Macholz' when it came closer to the sun during
February this year. Various orbital parameters (date, R.A., declination, Delta Distance from Earth, r distance from the Sun, Elongation, phase and
magnitude) of Comet Macholz is given to you. Estimate the space velocity on
19th May 2005. Estimate the eccentricity of the orbit.
2. The magnitude plot (Fig. 4) of a variable star XMP 2359 is given to you. It is
observed that the star is not only a variable but also a part of a binary system
with one member as 5 solar mass black hole. The points plotted on the same
graph are during two different intervals. The magnitude curve can be seen as a
thick periodic line. The lower continuum (i.e. lower part of the entire curve) is
the magnitude variation seen regularly. Estimate the distance of the source
from us. The higher continuum (i.e. upper part of the entire curve) is observed
during a phase of high mass transfer between the stars. Assuming that the
40% of the gravitational energy of falling mass is converted to light, calculate
the amount of mass transfer.
3. The sundial is one of the oldest instruments astronomers had built to estimate
the time. It's based on measuring the shadow of a vertical stick at different
times as the sun travels from east to west in the sky. You are given (Fig. 5) the
locus of the shadows of the tip of the vertical stick 1m long plotted in a day.
Where on the Earth this experiment must have been performed? When?
Fig. 1 (For Juniors Only)
Fig. 2. (For Juniors Only)
Fig. 3
JD 2452450
JD 2452556
2452454
2452560
2452458
2452564
Fig. 4
2453462
2453568
2453466
2453572
Fig. 5 (For Seniors Only)

7th Indian National Astronomy

Olympiad
May 1 to 20, 2005
Observational Test 1
May 8, 2005: 20:00 IST
Any five of the following:
1)
2)
3)
4)
5)
6)
7)
8)
Show any one constellation (given direction)

Any two stars (given direction). Any details
Any DSO in the given direction.
Given a star, give alt-az/declination
Give any GC/OC/Nebula/Binary/Variable/Galaxy & some details
Magnitude estimation
Galactic lat long
Miscellaneous

7th Indian National Astronomy

Olympiad
May 1 to 20, 2005
May 12, 2005: 20:00 IST
Any five of the following:
1) Any three stars in the given direction.
2) Questions on moon. In which constellation is it at present? In which
constellation is it expected to be in two days?
3) What is the sidereal time now?
4) Given a star, estimate its RA.
5) Given the magnitude of a particular star, estimate the magnitude of
another star.
6) Miscellaneous


May 1 to 20, 2006
Theory Test I,
Juniors / Seniors
8th May 2006

9:00 am to 11:00 am

1. Starship SS. Geromino is exploring the galactic neighborhood for habitable places. An onboard radar
detects a planet likely to be habitable. The Ship automatically launches a satellite that goes into an
orbit around the planet, whose plane is along the line of sight of the Ship. Once in orbit, the satellite
continuously sends radio signals towards the Ship. Fig.1 shows an Intensity vs. Time plot for the
received signal. Your task, as an Explorer-In-Charge is to interpret this signal and obtain:
a. The ratio of the radii of the planet and the orbit of the satellite (r/R). State clearly any
assumptions you make.
b. The density () of the planet.
The ship is still very far away from the planet.
0hr
20hr
40hr
60hr
80hr
Fig. 1
2. The change in wavelength caused due to the loss in gravitational potential energy of a photon is
called Gravitational redshift. A 5M~ star of radius of 2 x 109 m emits a radiation at = 5000. Find the
wavelength of this radiation as seen from infinity.
3. A velocity profile, v(r) (Fig.2) was
obtained for a globular cluster SM171P in
Eridanus. The curve in the Region B can
be approximated by a straight line.
Assuming
that
this
system
is
gravitationally bounded, draw the mass
profile M(r) in both the regions, where
M(r) is the mass contained within a radius
r.
v (km/s)
250
200
50
100
Fig.3.
150
200
r (light years)
4. Betelgeuse was the first star whose angular diameter was actually measured using interferometeric
techniques. The value was found to be 0.019. The radiation from Betelgeuse is seen to peak at =
8300. Given the distance to Betelgeuse as 430 light years, predict its apparent magnitude. The real
apparent magnitude of Betelgeuse, corrected for atmospheric effects, is 0.43m. Discuss the sources of
error if any.
5. A satellite is revolving around a planet at an orbital radius of r, while the planet is separated from the
central star (spectral type G2V) by distance R. The terminator of the satellite is the line separating
bright side from the dark side. The view of the satellite and its terminator as seen from the planet is
given in Fig.3. Find r if the apparent magnitude of the star as seen from the planet is -30.1m and the
angle of elongation (the Star-Planet-Satellite angle) is 830.
Fig.3
Homi Bhabha Center for Science Education

Tata Institute for Fundamental Research

May 1 to 20, 2006
Exam
Theory Test 2-Sr
Date May 15, 2006
Time 09:00 Marks
50
Duration 2h
Q1) A star HIP41727 in Cancer lies very close to the ecliptic. Its equatorial coordinates for the
present day are (8h 30.881m, 180 55.403). It is presently moving along the RA & Dec axes
at speeds -0.0136 /yr & -0.0108 /yr, respectively. What would be its equatorial
coordinates on 14th Dec 2016 at 12:00 noon? You may use any of the given
transformation equations.
sin( ) = sin( ) cos( ) + cos( ) sin( ) sin( ) sin( ) = sin( ) cos( ) cos( ) sin( ) sin( )
sin( ) cos( ) tan( ) sin( )

sin( ) cos( ) + tan( ) sin( )
tan( ) =
tan( ) =
cos( )
cos( )
sin A
sin = sin sin a + cos cos a cos A
tan H =
sin cos A cos tan a
10
Q2) General Theory of Relativity adds up a correction to Newtonian gravitation formula. As

2
GMm
v
1 + 6 where M &
per the theory Force of gravitation can be taken as F =
GR
2
c
r
m are the masses of Sun & Mercury, r is the radius of orbit & v is its velocity. Find the
new expression for the time period in terms of the Newtonian time period. Approximate
15
using the binomial theorem, by which (1 + a ) = 1 + na, if a ! 1 . Find the additional angle
n
through which the planet has to travel to reach the new perihelion point (give a valid
reason for the same). Using the data, find the precession of Mercurys perihelion point.
Q3) Stacking is a method used by many amateur astronomers to get a better signal to noise
ratio by capturing many short exposure frames and averaging them pixel by pixel to
cancel out the random noise and improve the signal. Professional astronomers, however,
prefer giving very long exposures by which the signal to noise ratio increases too. What is
the difference between the two methods? Which would give better results (in terms of
signal to noise ratio / contrast)? What would be the difficulties associated with each of
these?
Q4) On 16th May, 2006, at 10:02 am, as seen from Mumbai (72.50E, 18.60N), the moon
shares its RA with the winter solstice and is 50 16m to its north. At what time will its next
meridian crossing occur? In what constellation will the moon be at this time? Assuming a
circular orbit what is the RA of the sun at this time?
10
Q5) A planet is in circular orbit of radius R about a central star of mass M. At some instant,
the star bursts and sheds x percent of its mass. Find the eccentricity of the resulting orbit
of planet after outburst. Discuss the cases for elliptical, parabolic & hyperbolic orbits.
Assume that the mass going out of star does not affect or tear apart the planet. If the star
were now to become a black hole then how will your answer change?
10


May 1 to 20, 2006
Exam
Theory Test 2-Jr
Date May 15, 2006
Time 09:00 Marks
50
Duration 2h
Q1) A star HIP41727 in Cancer lies very close to the ecliptic. Its equatorial coordinates for the
present day are (8h 30.881m, 180 55.403). It is presently moving along the RA & Dec axes
at speeds -0.0136 /yr & -0.0108 /yr, respectively. What would be its equatorial
coordinates on 14th Dec 2016 at 12:00 noon? (Compute the coordinates using precession
of earths axes) You may use any of the given transformation equations.
sin( ) = sin( ) cos( ) + cos( ) sin( ) sin( ) sin( ) = sin( ) cos( ) cos( ) sin( ) sin( )
sin( ) cos( ) tan( ) sin( )

sin( ) cos( ) + tan( ) sin( )
tan( ) =
tan( ) =
cos( )
cos( )
10
Q2) General Theory of Relativity adds up a correction to Newtonian gravitation formula. As

2
GMm
v
1 + 6 where M &
per the theory Force of gravitation can be taken as F =
GR
2
c
r
m are the masses of Sun & Mercury, r is the radius of orbit & v is its velocity. Find the
new expression for the time period in terms of the Newtonian time period. Approximate
10
using the binomial theorem, by which (1 + a ) = 1 + na, if a ! 1 .

n
Q3) Stacking is a method used by many amateur astronomers to get a better signal to noise
ratio by capturing many short exposure frames and averaging them pixel by pixel to
cancel out the random noise and improve the signal. Professional astronomers, however,
prefer giving very long exposures by which the signal to noise ratio increases too. What is
the difference between the two methods? Which would give better results (in terms of
signal to noise ratio/contrast)? What would be the difficulties associated with each of
these?
Q4) A rover is operating on Mars and its motion is being controlled directly by the ground
station here on earth. What should be the largest speed the rover is allowed, given that
the rover is able to see dangerous large rocks only from a distance of 10 m? How can
you make the rover go faster?
Q5) On 16th May, 2006, at 10:02 am, as seen from Mumbai (72.50E, 18.60N), the moon
shares its RA with the winter solstice and is 50 16m to its north. At what time will its next
meridian crossing occur? In what constellation will the moon be at this time?
10
Q6) A planet is in circular orbit of radius R about a central star of mass M. At some instant,
the star bursts and sheds x percent of its mass. Find the eccentricity of the resulting orbit
of planet after outburst. Discuss the cases for elliptical, parabolic & hyperbolic orbits.
Assume that the mass going out of star does not affect or tear apart the planet. If the star
were now to become a black hole then how will your answer change?
10


May 1 to 20, 2006
Exam
Theory Test 3
Date May 19, 2006
Time 09:00 Marks
60
Duration 3h
Q1) Given is a P Vs P-dot plot for pulsars, where period of rotation is plotted against the rate-ofchange of these periods. Pulsar spin slows down with age; hence ages of pulsars = P ! are
2P
10
19
PP! is along the other diagonal. It
plotted across one diagonal, while magnetic field B = 3 10
shows regular pulsars, binaries, Supernovae remnant associations, Soft gamma-ray repeaters and
radio-quiet pulsars.
1. Calculate the age of the Crab pulsar
2. Calculate the approximate angular velocity of the Vela pulsar
3. Discuss the plot along the following lines:
a. Life cycle of pulsars characteristics of young & old pulsars; their stages
b. Energy (in form of magnetic dipole radiation) & stability of pulsars
Q2) Some students saw a speck of light near the zenith, move from south to north, at around 8 pm in
summer from Mumbai. The full moon had risen. It moved about 50 in ~1 min after which it
disappeared and was constantly about 3m. One student pointed out that its path did not pass
through the pole. One person claimed he could make out some structure in the speck. At this point,
the group started wondering about what the speck of light was. Analyse the feasibility of the
following theories and determine the one that best-fits the observation: Write down values of all
20
numbers you used from memory, for the examiners reference.

1. A high-flying commercial aircraft whose flashing lights were too dim to be seen and too far to
be resolved. Think about the Intensity of the headlamps & flashing lights, speed of the
aircraft & its disappearance after travelling 500.
2. A stray meteor which grazed into the mesosphere at a very low angle enters denser layers of
the atmosphere, compressing the air in front created a glowing shockwave. Soon it passes out
into the rarer layers and the glowing stops. Think along the lines of the speed of the meteor,
energy given out as light to shine for a minute, magnitude variation of the meteor & direction
of travel
3. A stratosphereic meteorological balloon reflected sunlight, still available at those altitudes. It
wasnt large enough to be resolved into a significant disk. Analyse this proposal along the
following lines Speed of the balloon at that altitude, availability of sunlight at the location of
the balloon, size of the balloon, its brightness and its resolvability, balloons disappearance
after a minute.
4. A satellite in low earth polar orbit (peiod ~ 90 min), reflecting sunlight from its body,
isotropically. Verify their claim with the following guidelines - Speed of the satellite,
Polar satellite not passing through the pole, Brightness of the reflection
Q3) Calculate the duration of Venus transit (assuming central eclipse of
the sun) assuming average values of required parameters. Also
assume that both the Earth & Venus orbits are coplanar with the
Solar equator.
A real transit is plotted in the diagram. How will your calculation
of duration change in this case? Discuss the factors you think, are
relevant.
10
Q4) The spectra of a globular cluster shows three types of spectral classes prominently A (M ~ 0m), F
(M ~ 2.7m) & G (M ~ 4.5m). Assume that there are 4780, 9930 & 14050 stars, respectively.
Compute the combined apparent magnitude of the cluster if it is 3 Kpc away from us. Using the
Luminosity-Mass relation for main sequence stars, work out the mass of the cluster.
10
Q5) On a certain day the sun sets on the north pole. How much time will the setting of the sun take
(edge to edge)? At what time will it rise at the south pole? What day is it?
10


May 1 to 20, 2006
Lab Test I
13th May 2006, 2:30 pm to 5:00 pm
Seniors
1) A photograph of a comet C2006-L1 was taken on 21st March, 2006 when it was at perihelion.
The photograph is shown in Fig.2 (Not drawn to scale). The angular distance between the
sun and the comet in this photograph is 160.
The same comet was photographed again on 22nd June, 2082 at midnight (Fig. 1.). By this
time the comet had reached the aphelion of its orbit. The ecliptic and the observers meridian
are given. The comet had its maximum ecliptic latitude at aphelion.
Find:
a. Distance to the comet from earth at aphelion.
b. The eccentricity (e) of the comets orbit.
c. The angle of inclination (i) of the comets orbit with the ecliptic.
d. The period (T) of the comet.
e. Length of the semi-major axis (a) of the orbit of the comet.
20o
10o
0o
Fig.1
Fig.2
2) Adaptive Optics
Many professional telescopes now use systems called adaptive optics to correct the distortion
caused due to the atmosphere. Let us learn a bit about these systems and how they work.
The incoming wavefront from the star is plane (as it is from a point source from infinity). The
distortion medium (the atmosphere) causes the wavefront to change shape and local direction of
propagation.
Incoming
Plane
Wavefront
Distortion
Medium
(Atmosphere)
Distorted
Wavefront
The wavefront sensor is a sensor used to measure the shape of the wavefront. This is what it
looks like (Fig.4) :
Incoming
wavefront
Lens Array
Fig.4
CCD Imager
Each lens focuses the local wavefront as a spot on the CCD imager. Software is used to measure
the deviation of each of the spot from the nominal center position and thus the shape of the
wavefront is reconstructed.
The correction is applied in two steps.
1. Overall tilt correction: A fast tilting mirror is used to reduce the overall tilt of the
wavefront to zero.
2. Local correction: A flexible mirror with mechanical actuators on the back surface is used
to correct to local wavefront to make it a plane wavefront. In other words, the shape of
the mirror is changed so that the distorted wavefront becomes plane after reflecting off
from the mirror (Fig.5).
Consider a simplified 1-dimensional adaptive optics setup. In the wavefront sensor, each lens
has a diameter of 10cm and a focal length of 100cm. In this simplified setup, the tilt mirror is not
used. Instead, all the corrections are done by the flexible mirror alone. The flexible mirror has 7
independent mechanical actuators (positioners) which can move the surface up or down.
These are aligned linearly with a spacing of 10cm. The setup is as shown in Fig.5. The table
shows the measured deviations of the focal spots of each lens from the nominal center.
Lens
1
2
3
4
5
6
Deviation (in 10-3 mm)

19.68
-31.61
-47.41
43.92
-10.18
-37.33
Flexible Mirror
Wavefront Sensor
Fig.5
Your task is to calculate the positions of the actuators (value of h) for the given deviations.
3) Kirkwood Gaps:
American astronomer Daniel Kirkwood plotted the number density (n) of asteroids in the
asteroid belt as a function of distance (d) from sun. He discovered certain gaps or regions within
the belt where there are a very few asteroids. A plot similar to his is shown in Fig.3 where n is
the number density of asteroids with a period P around the sun. Only a few of all the gaps the
observed are shown in the plot.
a. Find the distances of these gaps from the sun.
b. Comment on why such gaps might exist.
c. Similar gaps also exist in Saturns rings. What does this tell you about the Saturnian system?
T
2.965yrs
5.93yrs
Fig. 3
8.895yrs
11.86yrs


May 1 to 20, 2006
Lab Test I
13th May 2006, 2:30 pm to 5:00 pm
Juniors
1. The ecliptic latitude () and longitude () of Mars at various oppositions in plotted in Fig.
Use this figure to find an upper bound on the value of the angle of inclination (i) of the
Martian orbit with respect to the ecliptic.
Observe that the value of the maximum positive is not the same as the value of the
maximum negative . Why?
8
6
4
2
0
-2
90
180
270
360
-4
-6
-8
2. Discovery of the Period-Luminosity Law:

The adjacent table gives data for the Cepheid
variables in the Small Magellenic Cloud (SMC).
Columns
#1: Name of the Cepheid (H.V. = Havard Variable
Catalogue)
#2: Apparent Visual Magnitude at maximum
#3: Apparent Visual Magnitude at minimum
#4: P = Period of pulsation
(Data taken from the original work of Henrietta
Leavitt that led to the discovery of the PeriodLuminosity law for Cepheid variables.)
Given that a Cepheid with a period P = 10d

period has an average absolute magnitude of
M = -3.5, and the absolute magnitude (M) of a
Cepheid is related to its period by a relation of
the form M = a log (P) + b, find the distance to
the SMC in kiloparsecs.
H.V.
1505
1436
1446
1506
1413
1460
1422
842
1425
1742
1646
1649
1492
1400
1355
1374
818
1610
1365
1351
827
822
823
824
Max.
14m.8
14.8
14.8
15.1
14.7
14.4
14.7
14.6
14.3
14.3
14.4
14.3
13.8
14.1
14.0
13.9
13.6
13.4
13.8
13.4
13.4
13.0
12.2
11.4
Min.
16m.1
16.4
16.4
16.3
15.6
15.7
15.9
16.1
15.3
15.5
15.4
15.2
14.8
14.8
14.8
15.2
14.7
14.6
14.8
14.6
14.3
14.6
14.1
12.8
Period
1d.25336
1.6637
1.7620
1.87520
2.17352
2.913
3.501
4.2897
4.547
4.9866
5.311
5.323
6.2926
6.650
7.483
8.397
10.336
11.645
12.417
13.08
13.47
16.75
31.94
65.8
There are many Cepheid variables in our own galaxy, Cephei & Polaris for example, that were
known much before Leavitts work. Why do you think the Period-Luminosity Law was first
discovered for the Cepheids in SMC and not for those in our own galaxy?
3. Kirkwood Gaps:
T
2.965yrs
5.93yrs
8.895yrs
11.86yrs
Fig. 3
American astronomer Daniel Kirkwood plotted the number density (n) of asteroids in the
asteroid belt as a function of distance (d) from sun. He discovered certain gaps or regions within
the belt where there are a very few asteroids. A plot similar to his is shown in Fig.3 where n is
the number density of asteroids with a period P around the sun. Only a few of all the gaps he
observed are shown in the plot.
a. Find the distances of these gaps from the sun.
b. Comment on why such gaps might exist.
c. Similar gaps also exist in Saturns rings. What does this tell you about the Saturnian system?


May 1 to 20, 2006
Lab Test II
18th May 2006, 9.00 pm to 12.00 pm

Seniors
1. Martian Retrograde Motion

Turkish astronomer Tunc Tezel takes series images of Mars from late July 2005 to February 2006,
while Mars is in retrograde motion. On November 7th, the Red planet was at opposition, a date
that occurred close to the center of this series when Mars was near its closest (0.482 AU) and
brightest. The familiar Pleiades star cluster lies at the upper left.
4o
Fig.1
Around 2 years before Tunc took this picture, he had taken another series of pictures of a
Martian Opposition. A digitally stacked composite of those pictures is shown in Fig. 2. This
August 28, 2003 opposition was the great perihelic opposition of Mars, when Earth was farthest
away from Sun and Mars was closest, making the distance between the two planets least.
Incidentally, the picture also shows Uranus performing retrograde motion (a dotted line to the
right of the image center).
a. Calculate how often you would see Mars in opposition.
Notice a striking difference in the two photographs - the shape of the retrograde loop. There is a
rich variety in the form that the path of a planet has while it undergoes retrograde motion. Quite
obviously, the difference has got to do with the shapes of the orbit of the two planets, their
orientation and the timing of the opposition.
5o
Fig. 2
b. Comment on the exact causes of these shapes. More specifically, describe the geometrical
circumstances that cause the loop and the Z-shape.
In his paper titled "Using retrograde motion to understand and determine orbital parameters",
Bruce G. Thompson of Ithaca College, New York describes the significance of retrograde motion
in understanding the geometry of planetary orbits and its importance in determination of
various orbital parameters. Two of his various observations are listed below:
If the ecliptic latitude & longitude of Mars during two oppositions is similar, the shape of
the retrograde loops around the two oppositions is also similar.
The width (in ecliptic latitude) of the retrograde loop is not the same at all oppositions:
some retrograde loops are narrower than others.
c. Explain these observations with regard to the orbital geometry of the two planets.
d. Demonstrate how you can use the above figures to determine the angle of inclination of the
Martian orbit assuming that Mars was almost on the ecliptic at opposition.
Any elliptical orbit is defined by five parameters. Analysis of retrograde motions spread over
years can yield quite accurate values of all five of those parameters, one of which (i) will be
calculated as in d). The data for this kind of analysis can come from continuous naked-eye
observation & plotting of planetary positions with respect to stars the kind of observation
typical of ancient astronomers like Tycho Brahe. This is the kind of analysis that astronomers of
the pre-telescope times did to determine orbital parameters of planets and to convey the
appreciation of this was the point of this lab exercise.
2. Magnitudes
The data presented in this table is the result of multicolor photometric observation of stars listed
in the Bright Star Catalog. Observations were made on the 21, 28 and 60 telescopes of the
Lunar and Planetary Laboratory of the Observatorio Astronomico Nacional, Mexico.
The V, B-V, U-B magnitudes and the temperatures of
No.
V
B-V
U-B
T
these stars are given. It is known that the relation,
1
6.29
1.1
1.02
4346
2
4.61
1.04
0.87
4486
B-V = A + B/T
3
4.28
0.96
0.71
4679
holds for T < 10,000K.
4
4.38
0.87
0.47
4922
a. Use the data in this table to estimate the values of
5
6.33
0.74
0
5320
A and B.
6
6.39
0.66
0
5600
The above equation can be derived theoretically from
7
4.23
0.58
0.02
5910
Plancks blackbody equation assuming that the B and
8
5.7
0.52
0
6166
the V filters are of equal bandwidth (assumed narrow)
9
5.93
0.44
-0.02
6544
The B and V filters have central wavelengths at 450 nm 10
5.69
0.35
0
7028
11
6.37
0.23
1
7799
and 550 nm respectively.
12
6.19
0.14
0
8497
The Plancks equation is given by,
13
4.76
0.03
0.1
9541
2hc 2
1
F =
hc
5
e kT 1
where F is the flux at the wavelength per unit bandwidth.
b. Find the values of Ath and Bth. Comment of why there is a difference in theoretical and
observed values of these constants.
c. The temperatures of these stars were also calculated spectroscopically using elemental
abundances. These values were found to be slightly greater than the values listed in the
table. Give reasons as to why this might be the case.
3. Would Hubble on Andromeda discover the same law?
1
2
3
4
5
6
7
8
9
10
11
12
x(Mpc)
4.42
4.09
0.44
2.07
1.68
2.46
2.86
2.38
1.31
0.05
1.68
2.46
y(Mpc)
1.54
4.44
1.12
0.72
3.24
2.46
0.94
4.68
0.63
0.72
3.24
2.46
r(Mpc)
4.68
6.03
1.20
2.19
3.65
3.48
3.01
5.25
1.46
0.73
3.65
3.48
19.18
47.36
68.31
19.26
62.62
44.96
18.22
63.11
25.68
85.83
62.62
44.96
vr(km/s)
334
411
114
160
265
263
258
349
162
100
265
263
The position vectors and the radial velocities of various galaxies are given in the above table. It is
well known that Hubbles Law is of the form v=Hr.
a. Use the data given to verify the law and find the value of the Hubbles constant.
Does the Hubbles Law give a preferential position to observer at the origin (earth in our case)?
Or does apply in the same form from all points in the universe?
b. Shift you origin to Galaxy (5) and repeat part (a) for that galaxy?
c. Also, show that your finding of part (b) mathematically follows from the expression for
Hubbles Law.


May 1 to 20, 2006
Lab Test II
18th May 2006, 9.00 pm to 12.00 pm

Juniors
1. Retrograde Motion
Turkish astronomer Tunc Tezel takes series images of Mars from late July 2005 to February 2006,
while Mars is in retrograde motion. On November 7th, the Red planet was at opposition, a date
that occurred close to the center of this series when Mars was near its closest (0.482 AU) and
brightest. The familiar Pleiades star cluster lies at the upper left.
4o
Fig.1
Around 2 years before Tunc took this picture, he had taken another series of pictures of a
Martian Opposition. A digitally stacked composite of those pictures is shown in Fig. 2. This
August 28, 2003 opposition was the great perihelic opposition of Mars, when Earth was farthest
away from Sun and Mars was closest, making the distance between the two planets least.
Incidentally, the picture also shows Uranus performing retrograde motion (a dotted line to the
right of the image center).
d. Calculate how often you would see Mars in opposition.
Notice a striking difference in the two photographs - the shape of the retrograde loop. There is a
rich variety in the form that the path of a planet has while it undergoes retrograde motion. Quite
obviously, the difference has got to do with the shapes of the orbit of the two planets, their
orientation and the timing of the opposition.
5o
Fig. 2
In his paper titled "Using retrograde motion to understand and determine orbital parameters",
Bruce G. Thompson of Ithaca College, New York describes the significance of retrograde motion
in understanding the geometry of planetary orbits and its importance in determination of
various orbital parameters. Two of his various observations are listed below:
If the ecliptic latitude & longitude of Mars during two oppositions is similar, the shape of
the retrograde loops around the two oppositions is also similar.
The width (in ecliptic latitude) of the retrograde loop is not the same at all oppositions:
some retrograde loops are narrower than others.
The Z-shape is observed when Mars is on or very close to the ecliptic at opposition. On the
other hand, a loop is observed when Mars is close to its highest ecliptic latitude at
opposition
e. Explain these observations with regard to the orbital geometry of the two orbits.
f. Demonstrate how you can use Fig. 1 to determine the angle of inclination of the Martian
orbit assuming that Mars was almost on the ecliptic at opposition.
Any elliptical orbit is defined by five parameters. Analysis of retrograde motions spread over
years can yield quite accurate values of all five of those parameters, one of which (i) will be
calculated as in d). The data for this kind of analysis can come from continuous naked-eye
observation & plotting of planetary positions with respect to stars the kind of observation
typical of ancient astronomers like Tycho Brahe. This is the kind of analysis that astronomers of
the pre-telescope times did to determine orbital parameters of planets and to convey the
appreciation of this was the point of this lab exercise.
2. Magnitudes
The following are the observed magnitudes for a certain star in different wavelengths when
observed at specified bandwidths (d). Calculate the brightness for each wavelength and sketch
a graph of B Vs . Hence or otherwise obtain the stars effective temperature and comment
upon the spectral class of the star.
(m)
m
d (m)
0.2
14.2
300
10-3
7.6
3
10-5
5.1
3 x 10-3
3 x 10-5
11.2
10-4
10-6
14.0
10-8
4 x 10-7
17.3
10-10
7 x 10-7
18.3
10-10
4. Would Hubble on Andromeda discover the same law?

1
2
3
4
5
6
7
8
9
10
11
12
x(Mpc)
4.42
4.09
0.44
2.07
1.68
2.46
2.86
2.38
1.31
0.05
1.68
2.46
y(Mpc)
1.54
4.44
1.12
0.72
3.24
2.46
0.94
4.68
0.63
0.72
3.24
2.46
r(Mpc)
4.68
6.03
1.20
2.19
3.65
3.48
3.01
5.25
1.46
0.73
3.65
3.48
19.18
47.36
68.31
19.26
62.62
44.96
18.22
63.11
25.68
85.83
62.62
44.96
vr(km/s)
334
411
114
160
265
263
258
349
162
100
265
263
The position vectors and the radial velocities of various galaxies are given in the above table. It is
well known that Hubbles Law is of the form v=Hr.
a. Use the data given to verify the law and find the value of the Hubbles constant.
Does the Hubbles Law give a preferential position to observer at the origin (earth in our case)?
Or does apply in the same form from all points in the universe?
b. Shift you origin to Galaxy (5) and repeat part (a) for that galaxy?
c. Also, show that your finding of part (b) mathematically follows from the expression
for Hubbles Law.


May 1 to 20, 2006
Exam
Observational
Test 1
Date May 16, 2006
Time 18:00 Marks
15
Duration 20m
Note: You are given a telescope to observe with. Proceed with the following: (The examiner may ask oral
questions along the way to ascertain your understanding). Use of calculators is not allowed.
5
Q1) Observe the instrument and fill the following table without detailed calculations:
Physical Quantity
Telescope &
Mount Type
Value / Description
Mk
f-ratio
Magnification
Approx. Limiting
Magnitude
Instrumental
Errors, if any
Q2) Make sure that the lock nuts are loose, the tube is held tightly and the mirror screws are at handtight. Ensure that the tube is correctly balanced for movements up to 450 from the ground.
Q3) Pick an appropriate object to check the alignment. Is the object aligned correctly in both the
telescope and the viewfinder? If not align the object to within a few mm precision as seen from the
center of the viewfinder, and show the examiner.


May 1 to 20, 2006
Exam
Date May 17, 2006
Time 18:00
Marks
35
Duration
2h
Name
Note: You should keep only your calculator, pen, pencil, rubber, scale & one set of star-maps with you. You are free to make reasonable approximations.
You should first begin with Q1 and then as called out to the field, you will do Q2 to Q4. In the field you may proceed in any sequence. You can come back from the
field and continue with Q1.
Q1) Given is a list of objects. Assume that you have the entire night to observe (7 pm to 5 am) and the sky is clear. Assume that everything above the tree-line
(roughly 100 above the true horizon) is visible. Do not ignore light pollution. Use your map to determine if, when & where each object will rise tonight.
Also comment upon the minimum instrument (including eye) in terms of aperture, required to see the object. Finally assign a sequence to the observation
of each object. Hence, fill up the following table:
Position data
: 18 58' N
LST at 7 pm tonight ~
Object
Estimate from map

m
Canopus, Alpha
Carinae
-520 42
5h 35m
5.0
Horseshoe Nebula,
NGC 6618
18h 21m
6.0
-230 10
Comment: Will you see the object, tonight?

What min. instrument should be used?
Moon-rise (LT): 11:17 pm

Calculate local data at rising
LT
A
h
Seq
-0.63
Orion Nebula, M42
Gamma Hydrae
l: 72 50' E
18
2.96
Q2) When you report to the examiner he/she will point out a certain object in the sky. You get 5 min to identify and describe the object, using your maps.
Q3) Point the telescope you are assigned to an object (Binary / Messier) as named by the examiner, within 15 min. You will need to use the maps to trace the
object.
Q4) Report to an examiner, who will quiz you based on observational guess-work.

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Homi Bhabha Centre for Science Education

Tata Institute of Fundamental Research

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