# Work to move from one orbit to another

1. Apr 23, 2007

### doopokko

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

U=-GMm/r

3. 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.

2. Apr 24, 2007

### 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?

3. Apr 24, 2007

### doopokko

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

4. Apr 24, 2007

### 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)?