Star orbiting black hole

In summary, the method to solve for the mass of a black hole given the period and radius of an orbiting star involves using the equations F=(mv^2)/r and G(Mm/r^2) and equating them to solve for the mass of the black hole. The mass of the star will cancel out in this equation, leaving only the mass of the black hole to be determined.
  • #1
Hi
I have to describe a method to solve a problem involving a black hole. The only information given is the period of the orbiting star and the radius of the orbit. I have to find the stars mass.

Would i use the equation F=(mv^2)/r and then substitute in v=(2 pi r)/T for the radius where T is the period? Then would i set the original equation equal to G(Mm/r^2) where the first two masses would cancel out and then solve for the final mass?

Thanks
 
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  • #2
Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.
 
  • #3
rock.freak667 said:
Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.

ok. but the mass i get will be for the star?
thanks
 
  • #4
nicholas123 said:
ok. but the mass i get will be for the star?
thanks

If the star's mass will cancel out, you will only be left with one mass (and it's not the mass of the star :wink:)
 
  • #5
for your question! It sounds like you are on the right track. The equation you mentioned, F=(mv^2)/r, is known as the centripetal force equation and is commonly used to calculate the mass of an object orbiting around a central body. In this case, the central body is the black hole.

To solve for the mass of the star, you can use the equation you mentioned and substitute in the values given, such as the period and radius of the orbit. This will give you the centripetal force acting on the star.

Next, as you mentioned, you can set this force equal to the gravitational force between the star and the black hole, which is given by G(Mm)/r^2. Here, M represents the mass of the black hole, and m represents the mass of the star. By setting these two equations equal to each other, you can solve for the mass of the star.

One thing to keep in mind is that this method assumes that the orbit of the star is circular. If the orbit is elliptical, the equation will be slightly different and may require additional information. But for a circular orbit, this method should give you a good estimate of the mass of the star.

I hope this helps and good luck with your calculations! Remember to always double check your units and make sure they are consistent throughout the equation.
 

What is a black hole?

A black hole is an area in space with a strong gravitational pull that even light cannot escape from. It is formed when a massive star collapses under its own gravity.

How do stars orbit black holes?

Stars orbit black holes in the same way that planets orbit a star. The gravitational pull of the black hole causes the star to move in an elliptical orbit around it.

What happens to a star as it gets closer to a black hole?

As a star gets closer to a black hole, the gravitational pull becomes stronger, causing the star to accelerate. The intense gravity can also cause the star to stretch and eventually be torn apart by the black hole's tidal forces.

Can a star orbiting a black hole escape?

It is possible for a star to escape from the gravitational pull of a black hole, but it would require an immense amount of energy. This energy could come from a close encounter with another star or a gravitational slingshot effect.

How do scientists study stars orbiting black holes?

Scientists use a variety of techniques to study stars orbiting black holes, including observing changes in the star's light and tracking the star's movement using telescopes and other instruments. They also use computer simulations and mathematical models to better understand the dynamics of these systems.

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