Answer Happy

3. When a star of mass M is devoid of a nuclear energy source it will keep the same luminosity L for quite a while by consuming its gravitational energy through contraction. Assume the star can remain in a state of hydrostatic equilibrium and its gravitational energy is given by: GM2 Ω = -α R where G is the gravitational constant, a is a constant and R is the radius of the star. (a) Prove that the rate of contraction of its radius R can be expressed by: Ro T 2 dR dt (1+) where Ro is the star's initial radius when it starts to contract and: T = AGM2 2R0L (b) Calculate how long a star with a luminosity of 1000 LO, mass of 8 M., an initial radius of 3 Ro, that has exhausted its reserve of hydrogen, would be able to continue to shine assuming its energy output remains the same. You can assume that a = 0.5.