# Find gravitational potential energy if at point

1. Oct 9, 2011

### jono240

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Eg = -G*M*m / r

3. 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 cant figure out how to do that with just the gravitational potential energy given. Please help with a hint on where to start. I dont want the question answered. Thanks

Last edited: Oct 9, 2011
2. Oct 9, 2011

### Pi-Bond

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.

3. Oct 9, 2011

### jono240

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 thats algebraically correct

4. Oct 10, 2011

### Pi-Bond

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)

5. Oct 10, 2011

### jono240

lol alright. I wasnt sure about the algebra there.
thanks alot man!