Show that the altitude of the pole star is equal to the latitude of the observer.

Calculate the magnitude of the faintest object that a 3·5 m telescope can detect.

Explain the Sunspot cycle.

Derive the equation of Hydrostatic Equilibrium.

List the four components of Interstellar gas. Explain how H-I region was detected.

Write the expression for Schwarzschild radius and calculate its value for the Earth.

A galaxy of absolute magnitude M -20 is at a distance of 700 kpc. Would it be visible to the naked eye? Explain.

How is the presence of dark matter in the universe inferred on the basis of virial theorem?

Define apparent and absolute magnitudes of a star and derive an expression for the distance modulus.
The distance modulus of star Vega is -0·5. At what distance is it from us

Define right ascension and declination «n. Explain why these coordinates remain unchanged during the daily motion of stars.
Determine the coordinates ex and for the Sun on March 22 and September 23.

Sketch H-R diagram indicating the location of the major types of stars.
Suppose that the surface temperature of two stars A and B is the same and the luminosity of A is higher than B. Which of the two stars is bigger in size? Why?

Explain astrometric and radial velocity methods for detecting extra-solar planets.
Calculate the total angular momentum of Sun-Jupiter system assuming that Jupiter has a circular orbit of radius 5·2 AU and its orbital period is 11·86 years. Assume that the Sun interacts only with Jupiter.

Describe the evolution of 1 solar mass star. It is estimated that after its life on the main sequence, the Sun will swell about 200 times the present radius. If, at that time, its surface temperature is half of its present value, calculate the luminosity of the Sun.

Draw the rotation curve of the Milky Way galaxy. Explain how the presence of dark matter is inferred from this rotation curve.

State Hubble's law. Explain the significance of Hubble's constant.

Define an active galaxy. State the properties of Star Burst galaxies.