Can You Determine a Star's Mass Using Its Orbital Period Around a Black Hole?

[nicholas123]

Hi
I have to describe a method to solve a problem involving a black hole. The only information given is the period of the orbiting star and the radius of the orbit. I have to find the stars mass.

Would i use the equation F=(mv^2)/r and then substitute in v=(2 pi r)/T for the radius where T is the period? Then would i set the original equation equal to G(Mm/r^2) where the first two masses would cancel out and then solve for the final mass?

Thanks

 

[rock.freak667]

Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.

 

[nicholas123]

Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.

ok. but the mass i get will be for the star?
thanks

 

[rock.freak667]

ok. but the mass i get will be for the star?
thanks

If the star's mass will cancel out, you will only be left with one mass (and it's not the mass of the star )