Solving the Shuttle's Orbital Recovery: Angular Momentum

[negatifzeo]

Homework Statement

A space shuttle S and a satellite A are in the circular orbits shown. In order for the shuttle to recover the satellite, the shuttle is first placed in an elliptical path BC by increasing it's speed by deltaVb=280 ft/s as it passes through B. As the shuttle approaches C, it's speed increases by DeltaVc=260 ft/s to insert it into a second elliptical orbit CD. Knowing that the distance from O to C is 4289 mi, determine the amount by which the speed of the shuttle should increase as it approaches D to insert it into the circular orbit of the satellite.

Homework Equations

I know this uses conservation of angular momentum for elliptical orbits, but I can't get a workable equation.

The Attempt at a Solution

The equations for angular momentum involve mass(which cancels here), velocity and radius. The radius is known in one position, the velocity isn't known in any position, only the change in velocity. As a result, I'm confused.

 

[magwas]

You might try to mix in Newton't law of gravity and mass of Earth to get the speeds.