Let’s try a generalization of Exercise 41. Experimental evidence strongly indicates the existence of a huge black hole at the center of our galaxy (the Milky Way). This black hole is absorbing stars and increasing in mass and radius. Assuming that this black hole currently has a mass of 109 solar masses,
(a) Determine its current Schwarzschild radius. Compare this to the radius of our galaxy (about 30,000 light-years). Does this black hole take up a significant portion of the galaxy?
(b) Suppose it is “gobbling” stars (each with a mass equal to that of our Sun) at one per Earth-year. At what rate is its Schwarzschild radius increasing?
(c) Assuming it could “swallow” all of the stars (about 200 billion) in the galaxy, each with the mass of our Sun, how long would this process take and what would be the eventual Schwarzschild radius of the black hole? Compare this to the radius of the galaxy now.