Escape velocity is the velocity required to launch an object to escape a planet's gravitational force (not just in orbit around the planet).
We have seen that gravitational potential at a point is the work required to move a unit mass from that point to infinity. Potential has units of energy/mass. We found that gravitational potential, U, is given by
where M is the mass of the point mass for which we are finding potential (in this case, mass of the planet, insofar as a planet is spherically symmetric) and R is the distant from the point mass (or from the center of the planet).
To escape a planet's gravitational field, it must have kinetic energy equal to the gravitational potential energy. Kinetic energy of an object, with mass m, is given by
or, per unit mass,
Escape velocity is obtained by setting these equal and solving for V:
