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Escape speed

The escape speed can be derived from the definition of potential gravitational energy $$E_{\text{p}}$$. $$E_{\text{p}}$$ of an object is defined as the work done in bringing an object from infinity to its current location.

Escaping a gravitational field means moving to a point where the gravitational field strength is zero (i.e. to infinity).

For most practical purposes, this is the distance at which the field strength at the point is so weak as to be almost zero. This happens when the object is at a great distance from the source of the gravitational field.

The object needs to be given sufficient kinetic energy $$E_{\text{k}}$$ (i.e. it needs to have sufficient speed) to offset the potential energy.

Using this requirement and the equations for potential and kinetic energy, the equation for the escape speed can be derived.

The energy contained within rocket fuel gives the rocket enough kinetic energy to escape the gravitational field of the earth.