Derive the formula for escape velocity of a particle from a planet of mass M and radius R .
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Escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. It is the speed needed to "break free" from the gravitational attraction of a massive body, without further propulsion, i.e., without spending more fuel.
For a spherically symmetric massive body such as a (non-rotating) star or planet, the escape velocity at a given distance is calculated by the formula given below.
V
e
=
R
2GM
,
where
G is the universal gravitational constant,
M the mass of the body, and
R the distance from the point in space to its center of mass.
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