Compute mass of black hole, gravitational and circular acceleration

[Maiia]

Homework Statement

Determine the mass of the black hole lurking at the center of our galaxy. Conveniently, Nature has arranged for a number of stars to be orbiting the black hole. Star S0-19 has an orbital period of 37 years, and a semimajor axis of 1720 AU. Assume circular orbit and compute the mass of the black hole. Express your answer in solar masses, Msun.

What I'm confused about in this problem is if the semi-major axis is the same as the orbital radius? and do I have to convert AU into seconds for solar masses?

 

[chrisk]

The problems states to assume a circular orbit. So, the radius is the semimajor axis in this case. It simplifies the problem but is can be solved using an elliptical orbit. AU is astronomical unit and is equal to the mean distance between our sun and the earth; it is not a unit of time.

 

[Maiia]

oh i see... thanks for your help!