Work to move from one orbit to another

[doopokko]

Homework Statement

A spacecraft of mass 2500kg is in a circular orbit a distance 2560km above the surface of Mars.

How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4660km above the surface?

Take the gravitational constant to be = 6.67×10^?11 N*M^2/kg^2, the mass of Mars to be = 6.42×10^23 kg, and the radius of Mars to be = 3.40×10^6 m.

Homework Equations

U=-GMm/r

The Attempt at a Solution

r1 = 3.4x10^6m + 2560km = 5960000m

r2 = 3.4x10^6m + 4660km = 8060000m

U1=-GMm/r1=6.67x10^-11 * 6.42x10^23 * 2500 / 5960000 = -1.796x10^10

U2=-GMm/r2=6.67x10^-11 * 6.42x10^23 * 2500 / 8060000 = -1.328x10^10

U2-U1=4.68x10^9

But that isn't the right answer. Can anyone help point out what I'm doing wrong? Thank you.

 

[e(ho0n3]

You seem to be calculating the difference of the graviational potential energies at the two orbits. How is that related to the work the spacecraft 's engines do?

 

[doopokko]

I'm not sure. Can you recommend an alternate way to approach this problem?

 

[mezarashi]

You've calculated the difference in gravitational potential of the two orbits. That's a good start. Now have you thought about the difference in the kinetic energies of the two orbits (due to the difference in speed needed to maintain orbit)?