# Grav. Force - Mass of an object

## 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?

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
Homework Helper
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.

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

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

hage567
Homework Helper
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.

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
Homework Helper
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.