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Graviational Force

  • Thread starter SArnab
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Homework Statement


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.

Homework 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]


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.
 

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