Binary w/ black hole - semi-major axis?

[accountkiller]

Say I have an X-ray binary system of a B2 main-sequence star with an unseen companion (i.e., black hole). They have a separation of 20 million km and an orbital period of 4 days.

How do I figure out what the semi-major axis is? I need it for the formula for Kepler's Version of Newton's Third Law:

M_{1} + M_{2} = (4π²)÷G × (a³)÷(p²)
where G is the gravitational constant, p is the period (which is given to me) and a is the semi-major axis. My question asks to find the sum of the masses, so I need to plug something in for a in the equation to get that answer. Can I just use the 20 million km separation?

Thanks! :)

 

[Janus]

Say I have an X-ray binary system of a B2 main-sequence star with an unseen companion (i.e., black hole). They have a separation of 20 million km and an orbital period of 4 days.

How do I figure out what the semi-major axis is? I need it for the formula for Kepler's Version of Newton's Third Law:

M_{1} + M_{2} = (4π²)÷G × (a³)÷(p²)
where G is the gravitational constant, p is the period (which is given to me) and a is the semi-major axis. My question asks to find the sum of the masses, so I need to plug something in for a in the equation to get that answer. Can I just use the 20 million km separation?

Thanks! :)

In the formula you listed, 'a' is the sum of the semi-major axes of the orbits of the the two bodies around the barycenter. So in this case, it is equal to the separation between the two bodies.

 

[accountkiller]

Oh, it's the SUM of both semi-major axes? I thought it was just one, which is why I was confused.

Well, thanks for clearing that up! :)