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How to derive the formula for Gravitational Potential Energy?

  1. Dec 9, 2012 #1
    How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?
     
  2. jcsd
  3. Dec 9, 2012 #2
    Experimental observation and number fudging to find the constant of proportionality G.
     
  4. Dec 9, 2012 #3
    not "G"...
     
  5. Dec 9, 2012 #4

    jtbell

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    Staff: Mentor

    They used integral calculus.

    $$PE_{grav} = - \int^r_\infty {F_{grav} dr^\prime}
    = - \int^r_\infty {\left( -\frac{GmM}{{r^\prime}^2} \right) dr^\prime}
    = - \frac{GmM}{r}$$
     
  6. Dec 9, 2012 #5
    Newton's law of graviation is emperical - it can't be derived from some other fundamental law or set of equations. This is the case with all the basic laws of physics - nature is the way it is.

    If you want to read more about the history try here and related pages:

    http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
     
  7. Dec 9, 2012 #6
    Thanks ya'll!
     
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