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Question about the gravitational Potential Energy Law Proof

  1. Nov 16, 2011 #1
    In the Proof of the Gravitational Potential Energy Law , it says :

    Consider two point masses , body . mass "m" and earth mass "M" , where M remains fixed. The work done to move the mass "m" from point 1 to point 2 is given by :

    W(1-2) = ∫FG . dr (All in vectors) = ∫FG Cos 180° dr ( All in Magnitudes ) where ...
    and the proof just goes on until we reach Ur = - G (Mm/r)

    Now my question is , why do we consider the direction of motion of the point mass opposite to the direction of the gravitational force and at the end of the law we say r1 ( which is the initial position ) is ∞ and r2 ( which is the final position ) is = to the distance between the point mass and the earth , This means the direction of motion of the point mass should be in the same direction of the earth's gravitational force not opposite to it and so we shouldn't add this Cos 180 and the law at the end is : Ur = - G (Mm/r) .

    Thanks in advance
  2. jcsd
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