Binary w/ black hole - semi-major axis?

  • #1

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:

[tex]M_{1} + M_{2}[/tex] = (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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  • #2
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:

[tex]M_{1} + M_{2}[/tex] = (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.
 
  • #3
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! :)
 

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