Grav. Force - Mass of an object

[ecthelion4]

Homework Statement

A proton moving at 0.999 of the speed of light orbits a black hole 4362km from the center of the attractor. What is the mass of the black hole?

Homework Equations

F=(Gm1*m2)/d^2

The Attempt at a Solution

Assuming the above is correct, a proton I think has constant mass of 1.6726*[(10)^(-27)], I know the distance, and G is constant. Since what I need is mass of black hole I'm assuming there's a way to find the force using the proton's speed.

 

[hage567]

The gravity of the black hole is acting as the central force. So what is the definition of a central force? Think Newton's second law for circular motion.

 

[ecthelion4]

super, i figured put the problem, the force would be equal to (m*v^2)/r

now the only thing I am missing is v, which is .999 of the speed of light, but what does that mean?

 

[hage567]

Do you know what the speed of light is in a vacuum? It's a constant. The 0.999 is how much of the speed of light the proton is moving at.

 

[ecthelion4]

ok, so if the speed of light is 299,792,458 m/s, then the proton's speed would be that times .999 right?

 

[hage567]

ok, so if the speed of light is 299,792,458 m/s, then the proton's speed would be that times .999 right?

That's right.