How much work is done by the thrusters on a shuttle changing distances of orbit

[nickhuf098]

Homework Statement

a 2000kg lunar lander is in orbit 40km above the surface of the moon. it needs to move out to a 500km orbit in oder to link up with a mothership that will take the astronauts home. it wants the answer in joules

Homework Equations

??E2-E1=Work done by non conservative forces

The Attempt at a Solution

I get answers like 9.91*10^9 joules or negative 9.91*10^9

i thought that Total energy in an orbit=0 so i solved E(@40km)=mv1^2-GMm/r1=2000(v1^2-GM/40000+Rmoon)

 

[jackiefrost]

Does the topic happen to be work/energy (as in "potential energy")?

If so maybe m*g_moon(h2-h1)... is worth thinking about

 

[jackiefrost]

Ooops - the distances are km! (I was thinking meters).

You'd probably need to integrate f(r)dr [force as a function of distance times incremental change in distance to center of moon - i.e. work] from (40000+R_moon) to (500000+R_moon), where f(r)=Gm1m2/r^2

m1=mass of moon
m2=mass of lander
R=radius of moon

 

[nickhuf098]

Thanks for the help but i finally figured it out.

I had to take the total energy of the second orbit minus the total energy of the first orbit to get the work done by non conservative forces aka the thrusters. Thanks for your assistance though especially about changing it to meters from km