Find gravitational potential energy if at point

AI Thread Summary
To find the gravitational potential energy at point B, the relationship between the distances from the center of the Earth to points A and B is crucial, with B being twice the distance of A. The gravitational potential energy at A is given as -2MJ, which can be expressed using the formula Eg = -G*M*m / r. By substituting the distance for B (2rA) into the potential energy formula, the potential energy at B can be derived. The algebraic manipulation confirms that the potential energy at B is -MJ, reflecting the change in distance. This approach effectively clarifies the relationship between gravitational potential energy and distance in a gravitational field.
jono240
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Homework Statement


An object is moved from A to B in the gravitational field of earth. The distance between the center of Earth and B is twice that of A. If the gravitational potential energy of the object at A is -2MJ, what is the gravitational potential energy of the object at B?

Homework Equations


Eg = -G*M*m / r

The Attempt at a Solution


Im stumped for where I should start. I need to find the mass or radius of orbit of this object but I can't figure out how to do that with just the gravitational potential energy given. Please help with a hint on where to start. I don't want the question answered. Thanks
 
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If rA is the distance from the center of the Earth to A, and rb the same for B, then you know

\frac{GMm}{r_A} = -2MJ

\frac{GMm}{r_B} = ?

Use the relation between the two lengths and the first formula to get the potential energy at B.
 
I know that rb is 2ra

so if I just substitute the 2ra in the first equation, do I get GMm/2ra = -2MJ/2

Im not sure if that's algebraically correct
 
That's correct, you basically substituted the value for the potential energy at A into the expression for it at B (with the additional half factor)
 
lol alright. I wasnt sure about the algebra there.
thanks a lot man!
 

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