Putting a satellite into an elliptical orbit

[Keano16]

Homework Statement

It is required to put a satellite into an orbit with apogee of 5R/2, where R is the radius of the planet. The satellite is to be launched from the surface with a speed Vo at 30degrees to the local vertical. If M is the mass of the planet, show that (Vo)^2 = 5GM/4R. Assume zero rotation.

Homework Equations

The Attempt at a Solution

I tried to use conservation of energy first i.e., 1/2*m*Vo^2 - GMm/R = 2GmM/3R
3R/2 - distance between planet's surface and apogee).

Needless to say, that doesn't yield the right answer, I was wondering perhaps elliptical orbits have some other requirements -- perhaps the inclusion of angular momentum?

Thanks, I appreciate any nudge towards the right direction.

 

[Redbelly98]

The Attempt at a Solution

I tried to use conservation of energy first i.e., 1/2*m*Vo^2 - GMm/R = 2GmM/3R
3R/2 - distance between planet's surface and apogee).

Needless to say, that doesn't yield the right answer, I was wondering perhaps elliptical orbits have some other requirements -- perhaps the inclusion of angular momentum?

Thanks, I appreciate any nudge towards the right direction.

I haven't worked on elliptical orbit problems myself, but I see nobody else has responded so I'll go ahead and comment on two issues I see with what you've done:

1. For potential energy, use the distance from the satellite to the center of the Earth, not the Earth's surface.

2. At the apogee of the elliptical orbit, v is not zero. So there should be a kinetic energy term in your expression for the total energy at apogee.

And, as you said, using angular momentum may be useful here.