Maximum distance in orbit from center of a planet

[gcfve]

Homework Statement

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 45^o 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 v_o in terms of G, M, R.

Homework Equations

E=$$\frac{1}{2}$$mv_r²+L²/2mr²+V(r)

The Attempt at a Solution

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

 

[Delphi51]

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

 

[gcfve]

Well, L=mrv or L=mbv₀
and i guess V=-GmM/r but i don't know how to use these at this point..