Can You Determine a Star's Mass Using Its Orbital Period Around a Black Hole?

[nicholas123]

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

 

[rock.freak667]

Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.

 

[nicholas123]

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

 

[rock.freak667]

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 )

 

[rwisz]

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.