Escape velocity

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In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is the speed needed to "break free" from a gravitational field without further propulsion. The term escape velocity is actually a misnomer, as the concept refers to a scalar speed which is independent of direction.

In practice the escape velocity sets the bar for any rocket aiming to bring a satellite beyond earth orbit. It gives a minimum delta-v budget for rockets when no benefit can be obtained from the speeds of other bodies, for example on interplanetary missions where a gravitational slingshot may be applied.

When escape velocity is calculated by the gravitational potential energy (Ug) equation

atmospheric friction or air drag is neglected.

Contents

Overview

A barycentric velocity is a velocity of one body relative to the center of mass of a system of bodies. A relative velocity is the velocity of one body with respect to another. Relative escape velocities exist only in systems with two bodies. For systems of two bodies the term "escape velocity" is ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields "escape velocity" refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field.

The phenomenon of escape velocity is a consequence of conservation of energy. For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity field) it is only possible for the object to reach combinations of places and speeds which have that total energy; and places which have a higher potential energy than this cannot be reached at all.

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