Chapter 13, Problem 42P

Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about $8.0\times {10}^{11}$ solar masses. A star orbiting on the galaxy’s periphery is about $6.0\times {10}^4$ light-years from its center. (a) What should the orbital period of that star be? (b) If its period is $6.0\times {10}^7$ years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.