homi bhabha centre for science education tata institute of … · homi bhabha centre for science...

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 σ = 5.67 x 10 – 8 W/ m2 K4

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 10–34 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

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 Duration 90 Minutes(Each question carries 10 marks)

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 Hα (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 it’s 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 Duration: 90 Mimutes NAME: 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 ρE = 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 μm 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 Attempt all questions

(Each question in worth 10 marks) Total Marks 100 Duration: 180 Mimutes 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 earth’s 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

Attempt all questions (Each question in worth 10 marks)

Total Marks 100 Duration: 180 Mimutes 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 earth’s 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

Attempt all questions (Each question is worth 50 marks)

Total Marks 100 Duration 120 minutes Name: City: J/S 1) 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 Saturn’s radius to be 6 x 107 m at its equator.

a) find polar radius of Saturn b) find inner and outer radius of Saturn’s rings c) Assume the orbit of Saturn to be circular with period of 29.46 years.

Find earth – Saturn distance when the photo was taken. d) using the values calculated up to now, find the angular scale of the

image (1 mm = ? arc seconds) e) Find the angle made by the plane of Saturn’s rings to the line of

sight. 2) 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 λ = 150o, β = 0o. Find α and δ. 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, Mass of earth = 6 1024 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 α 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 it’s 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



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 α 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 it’s 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



1. Astronomers need to study Hα lines from Aldebaran (α = 4h 36m, δ = 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 α = 12h 42m, δ = -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 Hα 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



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 λ - β for the Sun today. 6. The emission from Sun peaks at 550 nm. Estimate the width of the Hα line.

5th Indian Astronomy Olympiad Camp 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

All Questions are compulsory and all questions carry equal marks 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 0.5746029920 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 0.5099258140 0.526144765 240 0.383383434 440 0.42300791 640 0.588476774 840 0.4713702250 0.505171111 250 0.353129417 450 0.40555363 650 0.559104669 850 0.4322309860 0.491324186 260 0.330509447 460 0.39389352 660 0.532437115 860 0.3953460270 0.485543723 270 0.317042046 470 0.38986395 670 0.510802949 870 0.3633870180 0.487961688 280 0.313474568 480 0.39462633 680 0.495992507 880 0.3386228390 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 0.31659281110 0.533958637 310 0.357274561 510 0.46127149 710 0.499401905 910 0.32033311120 0.555578116 320 0.38470903 520 0.49686141 720 0.514783318 920 0.33319885130 0.576110676 330 0.41456414 530 0.53548907 730 0.534612779 930 0.35368959140 0.592959403 340 0.44409238 540 0.57438272 740 0.556487442 940 0.37968576150 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 0.43783214170 0.601233944 370 0.506309049 570 0.66554172 770 0.608261914 970 0.46457622180 0.586392966 380 0.51265216 580 0.68023666 780 0.613205113 980 0.48650717190 0.562969347 390 0.51078845 590 0.68508801 790 0.609408988 990 0.50177458200 0.532294261 400 0.501323224 600 0.68009461 800 0.596417033 1000 0.50921415

Observation of an Unknown Stellar Object

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 200 400 600 800 1000 1200

Time (hours)

Flux

(jan

sky)

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 1.54943100 0.01978 1050 0.23076 2000 0.583552 2950 1.606608150 0.030106 1100 0.243328 2050 0.614004 3000 1.69803200 0.041469 1150 0.25776 2100 0.653152 3050 1.809616250 0.050344 1200 0.266882 2150 0.68318 3100 1.909934300 0.061924 1250 0.274549 2200 0.702221 3150 2.069829350 0.070092 1300 0.309398 2250 0.75707 3200 2.320536400 0.083645 1350 0.311998 2300 0.809168 3250 2.422528450 0.092047 1400 0.321717 2350 0.823285 3300 2.747519500 0.103167 1450 0.336316 2400 0.867878 3350 3.071024550 0.12284 1500 0.3491 2450 0.936967 3400 3.037833600 0.121769 1550 0.393837 2500 1.002637 3450 3.782714650 0.142164 1600 0.405446 2550 1.039302 3500 4.060282700 0.147057 1650 0.413626 2600 1.066479 3550 4.645803750 0.170371 1700 0.40778 2650 1.129138 3600 6.416421800 0.181261 1750 0.427979 2700 1.237516 3650 11.47536850 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

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500 3000 3500 4000

Distance (MPc)

Red

shift

(Z)

5th Indian Astronomy Olympiad Camp

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 0.5746029920 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 0.5099258140 0.526144765 240 0.383383434 440 0.42300791 640 0.588476774 840 0.4713702250 0.505171111 250 0.353129417 450 0.40555363 650 0.559104669 850 0.4322309860 0.491324186 260 0.330509447 460 0.39389352 660 0.532437115 860 0.3953460270 0.485543723 270 0.317042046 470 0.38986395 670 0.510802949 870 0.3633870180 0.487961688 280 0.313474568 480 0.39462633 680 0.495992507 880 0.3386228390 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 0.31659281110 0.533958637 310 0.357274561 510 0.46127149 710 0.499401905 910 0.32033311120 0.555578116 320 0.38470903 520 0.49686141 720 0.514783318 920 0.33319885130 0.576110676 330 0.41456414 530 0.53548907 730 0.534612779 930 0.35368959140 0.592959403 340 0.44409238 540 0.57438272 740 0.556487442 940 0.37968576150 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 0.43783214170 0.601233944 370 0.506309049 570 0.66554172 770 0.608261914 970 0.46457622180 0.586392966 380 0.51265216 580 0.68023666 780 0.613205113 980 0.48650717190 0.562969347 390 0.51078845 590 0.68508801 790 0.609408988 990 0.50177458200 0.532294261 400 0.501323224 600 0.68009461 800 0.596417033 1000 0.50921415

Observation of an Unknown Stellar Object

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 200 400 600 800 1000 1200

Time (hours)

Flux

(jan

sky)

Question 2: The Energy Density Curve for a particular object measured by Hanley Observatory is given below. Interpret the curve.

Inte

nsity

(W/m

2 at e

arth

)

1000 nm 100 nm Wavelength (nm)



Theory Test 1 May 10, 2005: 10:00 IST Duration 2h

Note: All questions carry equal marks.

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 Way–like galaxy and found an Hα line at 7219Å. Meanwhile, Vishal studied various other galaxies and found the value of Hubble's constant to be 75 km/s/Mpc. The wavelength of Hα line found at the NSC labs is 6563Å. 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 Sun’s disk to cross it.

6. Xiao Minong is observing Jupiter at opposition from Beijing(φ=39° 54.996' N, λ =116° 22.998' E) on 30th July. She reports seeing it at an altitude of 48° at midnight. Is she correct? Justify.




All questions carry equal marks

Seniors 1. You know that the sun crosses the celestial equator on 23rd September. Find the

time required for the Sun’s 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 (14°C). 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.




Note: All questions carry equal marks.

Juniors 1. Estimate the duration for which Jupiter is in retrograde motion.

2. The Galactic North Pole is at α = 12h40m, δ = +28°. When does the sun cross the plane

of the Milky Way? 3. At Murbad, Parag is enjoying the colourful double star Albireo (19h31m, 27°58') 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.




Note: All questions carry equal marks

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?

δ α

Castor 32° 7h 35m

Pollux 28° 7h 45m

Procyon 6° 7h 40m

Gomeisa 8° 7h 25m

2. The adjacent figure shows the intensity profile of a cluster (something) for Hα line (6563Å 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.



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 sun’s 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 φ=30°N, λ=113°E and their watches (which were still showing UT) read 1:25. Calculate the geocentric right ascension and declination of the moon.



Theory Test 3 2453508.58333 JD Duration 4 hrs

Seniors1. 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 sun’s 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. 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, β = vi. 1°, λ = 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 φ=30°N, λ=113°E and their watches (which were still showing UT) read 1:25. Calculate the geocentric right ascension and declination of the moon.



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 (Hα = 6563 Å and Hβ = 4860 Å) 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.



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 (Hα and Hβ) 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.

Fig. 1.

Fig. 2.

Tycho

'Jewel Handle'

Grimaldi

N

WE

S

0d 5d 10d 15d 20d 25d 30d

Lab Test I 7th Indian National Astronomy Olympiad

Fig. 3

Lab Test I 7th Indian National Astronomy Olympiad



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. α Centauri is a known binary with a period of 79.92 years. You are given the

position angles of the secondary (α2 Centauri) with respect to the primary (α1 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 α 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.



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

Fig. 4

JD 2452450 2452454 2452458 2453462 2453466 JD 2452556 2452560 2452564 2453568 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) Show any one constellation (given direction) 2) Any two stars (given direction). Any details 3) Any DSO in the given direction. 4) Given a star, give alt-az/declination 5) Give any GC/OC/Nebula/Binary/Variable/Galaxy & some details 6) Magnitude estimation 7) Galactic lat long 8) Miscellaneous


7th Indian National Astronomy Olympiad

May 1 to 20, 2005 Observational Test 2

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



Theory Test I, Juniors / Seniors

8th May 2006 9:00 am to 11:00 am

Note: All questions carry equal marks. 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 (ρ) of the planet. The ship is still very far away from the planet.

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 λ = 5000Å. 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.

0hr 20hr 40hr 60hr 80hr

Fig. 1

0 50 100 150 200

A B

r (light years)

v (km/s)

200

250

Fig.3.

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 λ = 8300Å. 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


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 sin sin cos cos cosa a A

δ β ε β ε λ β δ ε δ ε αλ ε β ε α ε δ εα λ

λ α

δ φ φ

= + = − − + = =

= + sin tan

sin cos cos tan

AH

A aφ φ=

−

10

Q2) General Theory of Relativity adds up a correction to Newtonian gravitation formula. As

per the theory Force of gravitation can be taken as GR

GMm vF

cr

= +

2

21 6 where M &

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

using the binomial theorem, by which ( ) , if na na a+ = +1 1 1! . Find the additional angle

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 Mercury’s perihelion point.

15

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?

5

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

Homi Bhabha Center for Science Education

Tata Institute for Fundamental Research 8th Indian National Astronomy Olympiad

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 earth’s 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( )

δ β ε β ε λ β δ ε δ ε αλ ε β ε α ε δ εα λ

λ α

= + = − − + = =

10

Q2) General Theory of Relativity adds up a correction to Newtonian gravitation formula. As

per the theory Force of gravitation can be taken as GR

GMm vF

cr

= +

2

21 6 where M &

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

using the binomial theorem, by which ( ) , if na na a+ = +1 1 1! .

10

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?

5

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?

5

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



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-of-

change of these periods. Pulsar spin slows down with age; hence ages of pulsars PP

τ =2 ! are

plotted across one diagonal, while magnetic field B PP= ⋅19

3 10 ! is along the other diagonal. It 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

10

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 50º 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 wasn’t 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, balloon’s 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



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 observer’s 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 comet’s orbit. c. The angle of inclination (i) of the comet’s 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.

10o

20o

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) :

Lens Array

CCD Imager

Incoming wavefront

Fig.4

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.

Wavefront Sensor Flexible Mirror

h

Fig.5

Lens Deviation (in 10-3 mm)1 19.68 2 -31.61 3 -47.41 4 43.92 5 -10.18 6 -37.33

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 Saturn’s rings. What does this tell you about the Saturnian system?

2.965yrs 5.93yrs 8.895yrs 11.86yrs

Fig. 3

n

T



Lab Test I 13th May 2006, 2:30 pm to 5:00 pm

Juniors

0

2

4

6

8

-2

-4

-6

-8

90 180 270 360 λ

β

1. The ecliptic latitude (β) and longitude (λ) 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 β is not the same as the value of the maximum negative β. Why?

2. Discovery of the Period-Luminosity Law: H.V. Max. Min. Period 1505 14m.8 16m.1 1d.25336 1436 14.8 16.4 1.6637 1446 14.8 16.4 1.7620 1506 15.1 16.3 1.87520 1413 14.7 15.6 2.17352 1460 14.4 15.7 2.913 1422 14.7 15.9 3.501 842 14.6 16.1 4.2897 1425 14.3 15.3 4.547 1742 14.3 15.5 4.9866 1646 14.4 15.4 5.311 1649 14.3 15.2 5.323 1492 13.8 14.8 6.2926 1400 14.1 14.8 6.650 1355 14.0 14.8 7.483 1374 13.9 15.2 8.397 818 13.6 14.7 10.336 1610 13.4 14.6 11.645 1365 13.8 14.8 12.417 1351 13.4 14.6 13.08 827 13.4 14.3 13.47 822 13.0 14.6 16.75 823 12.2 14.1 31.94 824 11.4 12.8 65.8

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 Period-Luminosity 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.

There are many Cepheid variables in our own galaxy, δ Cephei & Polaris for example, that were known much before Leavitt’s 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:

2.965yrs 5.93yrs 8.895yrs 11.86yrs

Fig. 3

n

T

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 Saturn’s rings. What does this tell you about the Saturnian system?



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 these stars are given. It is known that the relation,

No. V B-V U-B T 1 6.29 1.1 1.02 4346 2 4.61 1.04 0.87 4486 3 4.28 0.96 0.71 4679 4 4.38 0.87 0.47 4922 5 6.33 0.74 0 5320 6 6.39 0.66 0 5600 7 4.23 0.58 0.02 5910 8 5.7 0.52 0 6166 9 5.93 0.44 -0.02 6544 10 5.69 0.35 0 7028 11 6.37 0.23 1 7799 12 6.19 0.14 0 8497 13 4.76 0.03 0.1 9541

B-V = A + B/T holds for T < 10,000K.

a. Use the data in this table to estimate the values of A and B.

The above equation can be derived theoretically from Planck’s blackbody equation assuming that the B and the V filters are of equal bandwidth (assumed narrow) The B and V filters have central wavelengths at 450 nm and 550 nm respectively. The Planck’s equation is given by,

1

125

2

−=

kThc

e

hcFλ

λ λπ

where is the flux at the wavelength λ per unit bandwidth. λFb. 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?

x(Mpc) y(Mpc) r(Mpc) θ vr(km/s) 1 4.42 1.54 4.68 19.18 334 2 4.09 4.44 6.03 47.36 411 3 0.44 1.12 1.20 68.31 114 4 2.07 0.72 2.19 19.26 160 5 1.68 3.24 3.65 62.62 265 6 2.46 2.46 3.48 44.96 263 7 2.86 0.94 3.01 18.22 258 8 2.38 4.68 5.25 63.11 349 9 1.31 0.63 1.46 25.68 162

10 0.05 0.72 0.73 85.83 100 11 1.68 3.24 3.65 62.62 265 12 2.46 2.46 3.48 44.96 263

The position vectors and the radial velocities of various galaxies are given in the above table. It is well known that Hubble’s Law is of the form v=Hr.

a. Use the data given to verify the law and find the value of the Hubble’s constant. Does the Hubble’s 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

Hubble’s Law.



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 (dλ). Calculate the brightness for each wavelength and sketch a graph of Bλ Vs λ. Hence or otherwise obtain the star’s effective temperature and comment upon the spectral class of the star. λ (m) 0.2 10-3 10-5 3 x 10-5 10-6 4 x 10-7 7 x 10-7

mλ 14.2 7.6 5.1 11.2 14.0 17.3 18.3 dλ (m) 300 3 3 x 10-3 10-4 10-8 10-10 10-10

4. Would Hubble on Andromeda discover the same law?

x(Mpc) y(Mpc) r(Mpc) θ vr(km/s) 1 4.42 1.54 4.68 19.18 334 2 4.09 4.44 6.03 47.36 411 3 0.44 1.12 1.20 68.31 114 4 2.07 0.72 2.19 19.26 160 5 1.68 3.24 3.65 62.62 265 6 2.46 2.46 3.48 44.96 263 7 2.86 0.94 3.01 18.22 258 8 2.38 4.68 5.25 63.11 349 9 1.31 0.63 1.46 25.68 162

10 0.05 0.72 0.73 85.83 100 11 1.68 3.24 3.65 62.62 265 12 2.46 2.46 3.48 44.96 263

The position vectors and the radial velocities of various galaxies are given in the above table. It is well known that Hubble’s Law is of the form v=Hr.

a. Use the data given to verify the law and find the value of the Hubble’s constant. Does the Hubble’s 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 Hubble’s Law.



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.

Q1) Observe the instrument and fill the following table without detailed calculations: Physical Quantity Value / Description Mk Telescope & Mount Type

f-ratio

Magnification

Approx. Limiting Magnitude

Instrumental Errors, if any

5

Q2) Make sure that the lock nuts are loose, the tube is held tightly and the mirror screws are at hand-tight. Ensure that the tube is correctly balanced for movements up to 450 from the ground.

5

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.

5



Exam Observational Test 2 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 LST at 7 pm tonight ~ φφφφ : : : : 18° 58' N l: 72° 50' E Moon-rise (LT): 11:17 pm

Estimate from map Calculate local data at rising Object αααα δδδδ m

Comment: Will you see the object, tonight? What min. instrument should be used? LT A h Seq

Canopus, Alpha Carinae

-520 42’ -0.63

Orion Nebula, M42 5h 35m 5.0

Horseshoe Nebula, NGC 6618

18h 21m 6.0

Gamma Hydrae -230 10’ 2.96

18

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. 4

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.

8

Q4) Report to an examiner, who will quiz you based on observational guess-work. 5

homi bhabha centre for science education tata institute of … · homi bhabha centre for science...

Documents