# Binary w/ black hole - semi-major axis?

## Main Question or Discussion Point

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! :)

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Janus
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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.

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! :)