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Homework Help: Orbit related equations

  1. Jun 9, 2008 #1
    1. The problem statement, all variables and given/known data
    I'm just trying to rearrange a few equations for gravity, period, radius etc., and am a tad confused.

    2. Relevant equations
    (G*M)/R^2 = (4*pi^2*R)/T^2

    Want to rearrange for T and R. :)

    3. The attempt at a solution
    I got T to a point of...

    T^2 = (4*pi^2*R)*(R^2)/GM
    I think that's right, but I'm sure it can be further simplified.

    Any halp? :)
  2. jcsd
  3. Jun 9, 2008 #2


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    [tex]\frac{GM}{R^2} = \frac{4 \pi^2 R}{T^2}[/tex]

    [tex]\frac{GM}{R^3} = \frac{4 \pi^2}{T^2}[/tex]

    now re-arrange again.
  4. Jun 9, 2008 #3
    Thanks! Just what I needed! Can't believe I forgot it actually, silly me.

    ANYWAY, therefore...

    {T^2} = {4 \pi^2} \frac{R^3}{GM}



    {R^3} = {GM} \frac{4 \pi^2}{T^2}


    {M} = \frac{4 \pi^2 R^3}{G T^2}

    Just wondering if I could get these verified...
  5. Jun 10, 2008 #4
    The second equation is wrong...rest is fine!
  6. Jun 10, 2008 #5


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    When in doubt, check the units. The gravitational constant G has the units N·(m^2)/(kg^2) = (m^3)/[kg·(sec^2)].

    So the second equation couldn't be right, since the kg and the (sec^2) in the denominator of G have to be canceled out somehow in order to leave the (m^3) for R^3 on the left-hand side. The correct form must have the combination GM(T^2)...
  7. Jun 10, 2008 #6
    So it'd be ..

    R^3 = GMT^2? on 4pi^2

    Oh, and I just rearranged the lorentz factor to subject v^2

    v^2 = c^2(1-(1/lorentz)^2)

    How's that?

    Thanks guys
    Last edited: Jun 10, 2008
  8. Jun 10, 2008 #7


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    Both look fine.
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