# Graviational Force

1. Feb 6, 2010

### SArnab

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 $$E$$ = $$-G$$$$\frac{mM}{6r}$$.

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

2. Relevant equations

Potential Energy from Gravitation:
$$U$$ = $$-G$$$$\frac{mM}{r}$$

Centripetal Force
$$F$$ = $$\frac{mv^{2}}{r}$$

Gravitational Force
$$F$$ = $$G$$$$\frac{mM}{r^{2}}$$

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

$$R$$ = $$\frac{GM}{v^{2}}$$

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.