Binary w/ black hole - semi-major axis?

AI Thread Summary
In an X-ray binary system with a B2 main-sequence star and an unseen black hole, the separation of 20 million km corresponds to the sum of the semi-major axes of both bodies around their barycenter. To apply Kepler's Version of Newton's Third Law, this separation can be used directly as the value for 'a' in the formula. The orbital period of 4 days is also necessary for calculations. Clarification was provided that 'a' represents the total distance between the two objects, not just one semi-major axis. Understanding this distinction is crucial for accurately determining the sum of the masses in the system.
accountkiller
Messages
118
Reaction score
0
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! :)
 
Last edited:
Astronomy news on Phys.org
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:

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! :)
 

Thread 'Potential biosignature found in Mars rock'

Publication: Redox-driven mineral and organic associations in Jezero Crater, Mars Article: NASA Says Mars Rover Discovered Potential Biosignature Last Year Press conference The ~100 authors don't find a good way this could have formed without life, but also can't rule it out. Now that they have shared their findings with the larger community someone else might find an explanation - or maybe it was actually made by life.
View full post »

Thread 'Does it make sense to build new radio telescopes?'

TL;DR Summary: In 3 years, the Square Kilometre Array (SKA) telescope (or rather, a system of telescopes) should be put into operation. In case of failure to detect alien signals, it will further expand the radius of the so-called silence (or rather, radio silence) of the Universe. Is there any sense in this or is blissful ignorance better? In 3 years, the Square Kilometre Array (SKA) telescope (or rather, a system of telescopes) should be put into operation. In case of failure to detect...
View full post »
Thread 'Could gamma-ray bursts have an intragalactic origin?'

Thread 'Could gamma-ray bursts have an intragalactic origin?'

This is indirectly evidenced by a map of the distribution of gamma-ray bursts in the night sky, made in the form of an elongated globe. And also the weakening of gamma radiation by the disk and the center of the Milky Way, which leads to anisotropy in the possibilities of observing gamma-ray bursts. My line of reasoning is as follows: 1. Gamma radiation should be absorbed to some extent by dust and other components of the interstellar medium. As a result, with an extragalactic origin, fewer...
View full post »

Similar threads

I Are Two Supermassive Black Holes on a Collision Course?
Replies
2
Views
2K
I Where Are the Missing Black Holes in the Milky Way?
2
Replies
87
Views
9K
B The Semi-Major Axis of Binary Stars
Replies
4
Views
3K
I What do high-mass X-ray binaries, or HMXBs, tell us?
Replies
1
Views
2K
I Is there a plan for a search for nearby black holes?
2
Replies
55
Views
8K
A Take FFT to find time period for eclipsing binaries
Replies
1
Views
2K
I Calculating semi-major axis and minimum mass of an exoplanet
Replies
1
Views
2K
Stargazing What is the true extent of the semi-major axis for companion stars?
Replies
11
Views
6K
Finding the mass of a super-massive Black Hole?
Replies
1
Views
2K
What is the Semi Major Axis of a Binary Star System?
Replies
5
Views
6K

Hot Threads

Recent Insights

Back
Top