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Proving t^2/r^3

  1. Nov 18, 2015 #1
    1. The problem statement, all variables and given/known data
    In our unit on centripetal force, a large portion of the unit has been focusing on gravity and how the orbit is related to centripetal force. Our teacher told us to prove t^2/r^3 using F=(mv^2)/r and F=G(mM/r^2) as a small side part of our homework

    2. Relevant equations
    t^2/r^3
    F=(mv^2)/r
    F=G(mM/r^2)

    where G = 6.67*10^-11
    M and m are the objects' masses

    3. The attempt at a solution
    (mv^2)/r = G(mM/r^2)
    mv^2 = G(mM/r)
    v^2 = GM/r

    giving

    4(pi^2)(r^2)/t^2 = GM/r
    and
    GM = v^2 / r = 4(pi^2)r

    GM/r = (4pi^2)r / r = 4pi^2

    4(pi^2)(r^2)/t^2 = (4pi^2)

    leaving the ratio
    r^2 / t^2

    When it should be r^2 / t^3. What did I do wrong? Was there something I forgot?
     
  2. jcsd
  3. Nov 18, 2015 #2

    SammyS

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    It's just bad algebra.
     
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