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Gravitational Potential Energy - Further=Smaller?

  1. Apr 20, 2009 #1
    I recently looked at wikipedia for gravitational potential energy

    For two masses; M and m, and distance; r between their centres,
    gravitational energy; Ep is:


    With this, the further away the masses, the smaller the potential energy the system has

    But this does not make sense to me because the further away the masses are,
    the more kinetic energy they will collide with (after accelerated for some time due
    to gravitational force between the masses).

    Other than gravitational potential energy, no other energy can be converted to this
    kinetic energy. Hence, the fact that GPE is small for further masses contadicts with
    the large KE they will collide with.

    Can somebody explain?

    The model Ep=GMMr-1 seems not right to me
    because if it is derived from:
    therefore the gravitational force throughout the acceleration of the two masses
    will be constant, whereas in real life it will not be, because the force will
    be bigger and bigger as the masses come nearer and nearer.

    Please help. Thank you
  2. jcsd
  3. Apr 20, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You left out an all-important minus sign:
    GPE = -GMm/r.

    GPE increases as they separate to a maximum value of 0 at infinity.
  4. Apr 20, 2009 #3
    Ah, i see :shy:

    So, if there are two masses, 5E+6 kg and 10E+5 kg, separated at 50 m at their centres
    hence: GPE of the system is -6.67 Joules

    does this mean to move from r=infinity to r=50m it has lost 6.67Joules of potential energy
    converted to EK?
  5. Apr 20, 2009 #4


    User Avatar

    That is correct (I didn't do the calculation to check though, so I'm assuming you got the value right).
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