1. a) The distance of planet Jupiter from the Sun is 5 AU. Express this distance in light year and parsec.
b) Calculate the ratio of the surface temperatures of the stars A and B from the following data:
| Star |
Absolute magnitude |
Radius (RΘ) |
| A |
2 |
62 |
| B |
6 |
4(5) |
c) Show the horizon coordinates of a star X on a celestial sphere for a location at latitude 30° N.
d) Which telescope, optical or X-ray, would have higher resolving power for the same aperture? Calculate the magnitude of the faintest object that a 15 m optical telescope can detect.
e) The local time at Chennai is 9 p.m. Calculate the local time at Mumbai at that time.
2. a) Explain how we estimate the effective surface temperature of the Sun. A main sequence star has mass 2 × 1031 kg and radius 3 × 109 m. Obtain an estimate of the average temperature throughout the star.
b) Explain how sunspots survive for so long even though they are surrounded by hotter matter.
c) Derive an expression for the tidal force for the earth-moon system and show that its magnitude depends on the latitude. Explain tidal bulge on the basis of this expression.
3. a) Derive Jeans criteria for the stability of a gas cloud. A collapsing cloud is made only of neutral hydrogen (H1). If the temperature of the cloud is 50 K and its number density is 105 m-3, calculate its Jeans mass.
b) Derive the expression for the mean temperature in a star:
∝ M2/3 <Ρ>1/3
c) The mean free path of photons in stars is of the order of 0.2 cm. Show that the time taken for a photon to reach the surface of a star of radius 4 RΘ is of the order of one million year.
d) Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds.
4. a) Describe Hubble's Classification scheme for galaxies.
b) With the help of a diagram, explain the unified scheme for understanding active galactic nuclei.
c) What is cosmic background radiation? Explain why it is so important to the debate between evolving and a steady-state universe.
d) If the temperature of the background radiation today is 3 K, at what time after the birth of the universe was the temperature 1015 K. Take the age of the universe as 15 × 109 years.