Question

Hey, I'm a bit stuck on this question. "It has been observed that a certain star (S2) in the Sagittarius A* (meaning in the direction of the constellation Sagittarius) is orbiting a supermassive black hole. If the period of S2 is 16year and the distance between the two is 1.79e13m. What is the mass of this black hole? (be careful with your units)" I think I know which equation to use, but other than that I don't know how to go about solving it.

Answer 1

force gravity=centripetal force
GMm/r^2=m v^2/r= but v=2PIr/period
= m(2PI)^2 r/period

GM=r^3/T^2 * (2PI)^2

M = (1.79e13)^3 * (2PI)^2/period squared.
so convert 16 years to seconds and solve. In my head, I get period to be 31.6e6 * 16 seconds
so calculate.