- #1

- 6

- 0

## 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.