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Escape velocity

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Escape velocity diagram
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Escape velocity is calculated here as (2G m/r)^0.5 without taking friction (i.e. atmospheric resistance) into account. It is derived from the Newtonian equations for gravitational potential energy and kinetic energy.
Mass of body
Distance from center

Escape velocity
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notes
The "escape velocity" of an unpowered object with respect to a massive body is the speed that the object needs to be traveling at in order to escape the gravitational field of the body from its current distance from the body center of mass. It is independant of the object mass or direction of movement (and therefore is not truly a "velocity" at all).
Note that a powered object may escape the gravity of a body at any speed desired.