Stephan hawkins worked extensively with theoretical gravitational physics. he is well known for his work with black holes. he passed on march 14th, 2018. 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)

The equation that relates the period of a body that orbits a greater body in space with the distance  between both bodies is:

(1)  

Where;  

is the mass of the Black Hole (the value we want to find)

is the Gravitational Constant and its value is  

is the distance from the Black Hole to the Star S2 (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit).  

is the orbital period of the Star S2

At this point, note we have to transform the units of from years to seconds:

is the orbital period of the Star S2 in seconds

If we want to find the mass of the black hole, we have to express equation (1) as written below and substitute all the values:  

(2)  

(3)  

(3)  

Finally we have the mass of the black hole:

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.

f is prop to m1xm2 double m1 double force