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Find gravitational potential energy if at point

  1. Oct 9, 2011 #1
    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. jcsd
  3. Oct 9, 2011 #2
    If rA is the distance from the center of the earth to A, and rb the same for B, then you know

    [itex]\frac{GMm}{r_A} = -2MJ[/itex]

    [itex]\frac{GMm}{r_B} = ?[/itex]

    Use the relation between the two lengths and the first formula to get the potential energy at B.
  4. Oct 9, 2011 #3
    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
  5. Oct 10, 2011 #4
    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)
  6. Oct 10, 2011 #5
    lol alright. I wasnt sure about the algebra there.
    thanks alot man!
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