The work necessary is equal to force x distance.

However, in this problem, the force is not constant since it will change depending on the height of the satellite. Consequently, we will need to use integrals to calculate the total work.

W = F x d

F = (GMm / r^2)

We will simplify GMm into a general proportionality constant, k.

F = (k / r^2)

At the surface of the Earth (r = 4000 mi), the satellite weighs 184 lbs. Therefore

184 = k / (4000)^2

k = (184)(4000)^2

The distance, d, is given by r

lower limit of integration: 4000

upper limit of integration: 4139

integrand: F x d = ( (184)(4000)^2 / r^2 ) x r

10^8 mile-pounds of work.