# Maximum distance in orbit from center of a planet

1. Oct 21, 2009

### gcfve

1. The problem statement, all variables and given/known data
Consider a spherical, nonrotating planet of mass M, and radius R, with no atmosphere. A satellite is fired from the surface of the planet with speed v0 at 45o from the local vertical. In its subsequent orbit the satellite reaches a maximum distance of 5R/3 from the centre of the planet. Use conservation of energy and angular momentum to find vo in terms of G, M, R.

2. Relevant equations

E=$$\frac{1}{2}$$mvr2+L2/2mr2+V(r)

3. The attempt at a solution
so far all I have is a=GM/R^2, which I probably don't even need.

2. Oct 21, 2009

### Delphi51

Have you got a formula for V(r)?
Also need to work on momentum:
Angular momentum at start = angular momentum at apogee

3. Oct 22, 2009

### gcfve

Well, L=mrv or L=mbv0
and i guess V=-GmM/r but i dont know how to use these at this point..