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Question about the Derivation of the Gravitational Law

  1. Dec 28, 2014 #1
    The derivation of the law have been put up in the forums but I have a question regarding its derivation.

    I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step:

    [tex] \frac{m}{k} = \frac{M}{k'} [/tex].

    This is similar to

    [tex] \frac{C}{M} = \frac{c}{m} = \frac{k}{4 \pi^2} [/tex]

    at this site, http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml.

    According to the same site, the next step requires the force to be squared. Why is this so? Is it merely to acquire the force ##F## between the two bodies? Aren't there any other ways to calculate the force other than multiplication?
     
  2. jcsd
  3. Dec 29, 2014 #2

    Nugatory

    User Avatar

    Staff: Mentor


    It's just a convenient algebra trick to get both ##m## and ##M## into the equation for ##f##. We have ##f=f'## so we can multiply both sides of that equation by ##f## to get one equation that can be solved for ##f## in terms of ##k##, ##m##, and ##M##.
     
  4. Dec 29, 2014 #3
    Alright. Thank you for your help. :D
     
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