How to Calculate Work for Lunar Lander Orbit Change

[sam2k2002]

Homework Statement

A 6000 kg lunar lander is in orbit 10 km above the surface of the moon. It needs to move out to a 100 km-high orbit in order to link up with the mother ship that will take the astronauts home.
How much work must the thrusters do?

Homework Equations

U_s = -GMm/r
F_g = GMm/r^2

The Attempt at a Solution

I tried to calculate the difference in force between the two orbits and then calculate the change in energy to get the work, but I've had no luck.

 

[mgb_phys]

You would need to integrate the force over the distqance the object moves, or
use the formula for the potential energy at a a distance 'r' , pe= -GMm/r

Remember r is the total distance from the centre of the moon

 

[sam2k2002]

I'm not sure how to do that.. I get:

U_g(10km) = -2.67*10^17
U_g(100km) = -2.67*10^16

the difference is only 26.7J... that can't be right.

 

[kamerling]

I'm not sure how to do that.. I get:

U_g(10km) = -2.67*10^17
U_g(100km) = -2.67*10^16

the difference is only 26.7J... that can't be right.

I can't see why you think the difference is only 26.7 J. But this does not matter because:

The r in -GMm/r is the distance to the center of the moon, not the distance to the surface.

You'll need to calculate the orbital speed at 10 and 100 km as well and account for the
difference in kinetic energy.

 

[sam2k2002]

How do I calculate the orbital speed?

I assume after I get that, i can compute the change in kinetic energy?

 

[kamerling]

How do I calculate the orbital speed?

I assume after I get that, i can compute the change in kinetic energy?

For a circular orbit: centripetal acceleration = gravity

 

[sam2k2002]

so g=v^2/r ?

 

[kamerling]

so g=v^2/r ?

Yes. Of course you have g = GM/r^2 here for the acceleration of gravity
(M is mass of moon)