Binary w/ black hole - semi-major axis?

In summary, the X-ray binary system consists of a B2 main-sequence star and an unseen companion (black hole) with a separation of 20 million km and an orbital period of 4 days. To find the sum of the masses of the two bodies, the semi-major axis must be calculated using the formula M_{1} + M_{2} = (4π²)÷G × (a³)÷(p²), where G is the gravitational constant and p is the period. The semi-major axis in this case is equal to the separation between the two bodies.
  • #1
accountkiller
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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! :)
 
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  • #2
mbradar2 said:
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! :)
 

Related to Binary w/ black hole - semi-major axis?

1. What is a binary system with a black hole and what is a semi-major axis?

A binary system with a black hole is a system in which two objects, one of which is a black hole, orbit around their common center of mass. The semi-major axis is the distance between the center of mass and the furthest point of the orbit.

2. How is the semi-major axis of a binary system with a black hole measured?

The semi-major axis of a binary system with a black hole can be measured by observing the orbital period of the objects and using Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis.

3. What is the significance of the semi-major axis in a binary system with a black hole?

The semi-major axis is important because it determines the size and shape of the orbit of the objects in the binary system. It also plays a crucial role in determining the stability and dynamics of the system.

4. Can the semi-major axis of a binary system with a black hole change over time?

Yes, the semi-major axis can change over time due to various factors such as tidal forces, gravitational interactions with other objects, and even the emission of gravitational waves.

5. How does the semi-major axis affect the gravitational pull in a binary system with a black hole?

The semi-major axis directly affects the gravitational pull between the objects in the binary system. The closer the objects are to each other, the stronger the gravitational pull will be. As the semi-major axis increases, the gravitational pull decreases.

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