How Does the Energy Principle Help Calculate Work Needed to Move a Satellite?

[Kibbel]

Homework Statement

In certain cases, using both the momentum principle and energy principle to analyze a system is useful, as they each can reveal different information. You will use the both momentum principle and the energy principle in this problem.

A satellite of mass 7000 kg orbits the Earth in a circular orbit of radius of 8.6 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the magnitude of the gravitational force on the satellite due to the earth?
F = 37,714 N

Using the momentum principle, find the speed of the satellite in orbit.
v = 6906.93 m/s

Using the energy principle, find the minimum amount of work needed to move the satellite from this orbit to a location very far away from the Earth. (You can think of this energy as being supplied by work due to something outside of the system of the Earth and the satellite.)
work = ?

Homework Equations

for this problem, I seriously don't know, I was working with escape speed (mv^2)/2 + (-Gmm/R) = 0, but that includes the planet as the system, which I am not sure I should

The Attempt at a Solution

help, like my attempt probably was wrong. and would lead off track

 

[The legend]

it's ok if it's wrong, just post the attempt and it can be corrected.

 

[Kibbel]

okay here's my attempt

I said that (V being the initial velocity) (mv^2)/2 + (-Gmm/R) = 0 would give the initial velocity to escape the pull of gravity. Which in turn means that moving Gmm/r to the other side would give us the necessary kinetic energy to escape Earth's gravitational pull. (or the energy that gravity is applying)

So if I subtract the initial kinetic energy the spaceship has from the initial kinetic energy required to hit escape velocity, would that be correct?

 

[Kibbel]

couldn't get it :/ bummer