Calculating Work with Kinetic Energy in Orbit

[The_Journey]

Homework Statement

A 62kg satellite orbits the Earth with a radius of 3.3*10^7 m. A net external force acts on the satellite to an orbit of 7.7*10^6 m, what work must the external force do?

Homework Equations

W = integral of F with respect to d

The Attempt at a Solution

Integrate F which in this case is GMm/r^2 which becomes -GMm/r, then plug in the radii. However, the answer that I got was -2.46*10^9, which is incorrect.

 

[willem2]

You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger

 

[The_Journey]

You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger

How would I include the kinetic energy?

Would I approach it as this?

GPE = gravitational potential energy
KE = kinetic energy


GPE_final + KE_final = GPE_initial + KE_initial + Work_{of external force} ?