1. Gravitational Potential and Escape Velocity
Additional necessary info 

2. Gravitational Potential (V)
A field, defined at every point in space, but a scalar quantity
Defined as:
The work done per unit mass to bring a small point mass (m) from infinity to a point P.

4. Escape velocity…
Defined as: the velocity required for an object of mass m to be launched so that it escapes from the pull of the larger mass, M, and will move very far away from it. (assume that “very far away” means that the distance approaches infinity)
Imagine that a satellite, when it is sitting at the surface of the Earth, is modeled as something sitting at the bottom of an infinitely deep “potential well”
In order to escape the “well”, it must gain enough energy in order to get higher than the depth of the well…

5. Escape Velocity… The “depth” of the potential well is:
If the satellite (mass = m) gets enough potential energy to raise it out of the well, it will have
The satellite really isn’t at “infinity”, but it is far enough away that it is no longer affected by the gravitational force

6. Calculating Escape Velocity…
The change in potential energy is equal to the change in kinetic energy…
For Earth:
(where g0 = 9.81 m·s-2…)