Find gravitational potential energy if at point

[jono240]

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

 

[Pi-Bond]

If r_A is the distance from the center of the Earth to A, and r_b 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.

 

[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 that's algebraically correct

 

[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)

 

[jono240]

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