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

AI Thread Summary
To determine a star's mass using its orbital period around a black hole, the method involves using gravitational and centripetal force equations. The equation F=(mv^2)/r can be combined with v=(2 pi r)/T, where T is the orbital period. However, when equating this with the gravitational force equation G(Mm/r^2), the star's mass cancels out, leaving only the mass of the black hole. Therefore, the calculations will yield the mass of the black hole, not the star. This highlights the limitation of the method for directly finding the star's mass.
nicholas123
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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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Equating those two equations, you will only be able to get the mass of the black hole. The star's mass will cancel out.
 
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
 
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:)
 

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