Grav. Force - Mass of an object

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A proton is orbiting a black hole at a distance of 4362 km and moving at 0.999 times the speed of light. To determine the mass of the black hole, the gravitational force equation F=(Gm1*m2)/d^2 is applied, where G is the gravitational constant and m1 is the mass of the proton. The force acting on the proton can also be expressed using circular motion dynamics as F=(m*v^2)/r, where v is the proton's speed. The speed of the proton is calculated as 0.999 multiplied by the speed of light, which is 299,792,458 m/s. This approach combines gravitational and motion equations to solve for the black hole's mass.
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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.
 
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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 I am missing is v, which is .999 of the speed of light, but what does that mean?
 
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?
 
ecthelion4 said:
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.
 

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