Escape velocity

Escape Velocity is the speed at which a vessel or other object needs to travel in order to leave the vicinity of a planet or other large object. This speed depends on the mass of the planet, and the distance from its center. Because escape velocity depends on distance from the planet, it can have any value, but the most commonly quoted value for escape velocity is defined relative to the surface of the planet.

To be precise, a vessel travelling at escape velocity is on a parabolic orbit, with an eccentricity of 1.0 exactly. Vessels travelling slower travel along an elliptical orbit, and vessels travelling faster travel along a hyperbolic orbit.

Also, a vessel or other object dropped from infinitely far away with zero initial speed, will impact the planet at precisely the surface escape velocity.

Escape velocity is calclated using the following formula:

$v_{esc}={\sqrt {\frac {2GM}{r}}}$