A collapsing gas cloud of 1M⊙ of gas contracts from an initial radius of R1 = 100R⊙, to R2 = 10R⊙. The gravitational self-energy of a spherical mass is (in SI units) E = −3GM2/5R
(a) Find the gravitational energy difference ΔE = Efinal −Einitial between the large and smaller states of the gas cloud
(b) If the average luminosity of this cloud during collapse is L = 10L⊙, how long would it take to radiate this amount of energy?