Kepler's Laws, two large bodies

[bbbl67]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Here is something that some one asked me, as their homework question, and it stumped me.

A star is seen orbiting a black hole. The black hole's mass is 6.0E30 kg (approx, 3 solar masses). The star has an orbital period of 2.4 hours. The questions are:

(A) What is the star’s orbital radius in meters?
(B) What is the star’s orbital speed in m/s?

For #A, they were given the answer to be 5.7E8 m. But they couldn't match how they got that answer. My feeling is since it's a stellar mass black hole and a star, the two objects are relatively close in mass to each other, so you can't use the simplified Kepler equations, you have to use the general Kepler equations:

T² = (4 Π² r³)/(G (M₁ + M₂))

But I'm not sure about how to solve this, given that there are two unknowns here, the orbital radius, and the mass of the star. How do you go about solving for the star mass?

 

[mfb]

You cannot determine the mass, the radius or anything else without additional assumptions. As the question asks for radius, I guess you have to make some assumption about the star's mass.

 

[bbbl67]

You cannot determine the mass, the radius or anything else without additional assumptions. As the question asks for radius, I guess you have to make some assumption about the star's mass.

That's what I figured, but I thought I might be missing something. Maybe an assumed equation that let's you simultaneously solve both variables together?

 

[mfb]

The star is just at the Roche limit? That would give an interesting question.
The star is our sun?
The star is very light compared to the black hole?

I don't know.