Grav. Force - Mass of an object

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Homework Help Overview

The problem involves calculating the mass of a black hole based on the gravitational force acting on a proton that is orbiting it at a significant fraction of the speed of light. The context includes concepts from gravitational physics and circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between gravitational force and circular motion, referencing Newton's laws. There is an exploration of how to incorporate the speed of the proton into the calculations, with questions about the implications of using a relativistic speed.

Discussion Status

The discussion is active, with participants clarifying concepts related to speed and gravitational force. Some have provided insights into the definitions and relationships involved, while others are working through the implications of the proton's speed on the calculations.

Contextual Notes

There is a focus on understanding the constants involved, such as the speed of light, and how they relate to the problem. Participants are also considering the assumptions made regarding the mass of the proton and the nature of the forces at play.

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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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