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Graviational Force

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data
    A satellite of mass m moves in an elliptical around Earth with r and R, the closest and farthest distances from the center of Earth. An identical satellite moves in a circular orbit radius r. The elliptical satellite has energy [tex]E[/tex] = [tex]-G[/tex][tex]\frac{mM}{6r}[/tex].

    Derive an equation that would allow you to solve for R in terms of the given quantities.

    2. Relevant equations

    Potential Energy from Gravitation:
    [tex]U[/tex] = [tex]-G[/tex][tex]\frac{mM}{r}[/tex]

    Centripetal Force
    [tex]F[/tex] = [tex]\frac{mv^{2}}{r}[/tex]

    Gravitational Force
    [tex]F[/tex] = [tex]G[/tex][tex]\frac{mM}{r^{2}}[/tex]


    3. The attempt at a solution
    Set centripetal force and gravitational force equal to each other. Solve for R and you get:

    [tex]R[/tex] = [tex]\frac{GM}{v^{2}}[/tex]

    But now how would I get rid of the velocity from the equation. =|

    And to introduce myself, my name is Shafique. ^.^ I'm a senior at Deer Park High, currently taking AP Physics C.
     
  2. jcsd
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