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

## 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)

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

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

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