Energy to Increase Orbital Radius

[omegas]

Homework Statement

An Earth (mass M) satellite of mass m is in a circular orbit of radius r₁. It is moved to an orbit with a larger radius r₂ by way of an intermediate elliptical orbit. This is achieved by firing rockets for a short period when it is in the inner orbit, and then firing the rocket again when it has reached the maximum distance from M. Determine the total mechanical energy for each of the three orbits and the energy increase for each orbit transfer.

Homework Equations

I was not given any equations for this problem or any hints to what equations I need. I had a guess at using
F = GMm/r²

The Attempt at a Solution

I am completely lost on this one. I know I am supposed to equate some equations, but I don't know which ones or how to go about it. I am sure somethings cancel out somewhere. Please help.

 

[Filip Larsen]

You may want to search for "Hohmann transfer orbit". If you want to derive the energy yourself, you should find some equations in your textbook that relates the specific mechanical energy (also known as orbital energy) with the position and speed of a particle in an elliptical orbit. Alternatively you can search for "elliptic orbit" and see if you can find something related to energy.