# Energy in Orbit question

#### The_Journey

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
W = integral of F with respect to d

3. 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

GPEfinal + KEfinal = GPEinitial + KEinitial + Workof external force ?

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