IGNOU PHE-15 - Astronomy and Astrophysics

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: 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 × 10 31 kg and radius 3 × 10 9 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 itsmagnitude 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: 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 10 15 K. Take the age of the universe as 15 × 10 9 years.

1. a) The distance modulus of a star is -0.1. At what distance is it from the earth? b) After about 1 billion year, the radius of a star is expected to increase by 100 times its present radius. If its temperature becomes half of what it is today, determine the change in its absolute magnitude. c) Explain the following terms with the help of a diagram, wherever needed: celestial sphere, zenith, circumpolar stars, diurnal circle, resolving power of a telescope. 2. a) A main sequence star has mass 2 × 10^31 kg and radius 3 × 10^9 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) The mean distance of Mars from the Earth is 0.5 A.U. and its orbital period is 687 days. Calculate the orbital period of Jupiter given that its mean distance from the Earth is 4 A.U. d) A star has surface temperature of 25000 K. Which lines would be prominent in its spectrum and why? e) Derive the following expression for the mean temperature in a star: 3. a) Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds. b) Derive an expression for Jeans mass and discuss its significance in the formation of stars. c) A white dwarf star has a mass of 10^30 kg. Its luminosity is 10^24 Js−1. Calculate how long it can survive with its present luminosity if its internal temperature is 107 K. d) How long will a 5MΘ star burn hydrogen as fuel, given that the Sun will do so for about 10^10 years? 4. a) Distinguish between elliptical and spiral galaxies and give one example of each type of galaxy. b) What is an active galaxy? What is the source of its activity? Under what conditions does an active galaxy emit synchrotron radiation? c) What do you understand by cosmic distance ladder? Explain how it is used to estimate distance of stars.