Escape velocity

In celestial mechanics, escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body, assuming:

• Ballistic trajectory - no other forces are acting on the object, including propulsion and friction
• No other gravity-producing objects exist

Although the term escape velocity is common, it is more accurately described as a speed than a velocity because it is independent of direction. Because gravitational force between two objects depends on their combined mass, the escape speed also depends on mass. For artificial satellites and small natural objects, the mass of the object makes a negligible contribution to the combined mass, and so is often simply ignored (including by the formulas in this article).

In this idealized scenario, an object traveling at lower-than-escape speed will follow the curve of an ellipse (or straight line if going directly up), which will result in it orbiting the primary or colliding with its surface. An object headed outward faster than escape speed will continue moving away forever along a hyperbolic trajectory, continuing to slow down under weaker and weaker gravity, but asymptotically approaching a positive speed. An object traveling exactly at escape speed will have a parabolic trajectory. It has precisely balanced positive kinetic energy and negative gravitational potential energy; it will always be slowing down, asymptotically approaching zero speed, but never quite stop. The escape speed thus depends on the distance from the center of the primary body.

In practice, there are many massive bodies in the universe, so escape velocity calculations are typically used to determine whether an object will remain in the gravitational sphere of influence of a given body. For example, in solar system exploration, it is useful to know at what speed a probe will continue to orbit the Earth vs. escape to become a satellite of the Sun. It is also useful to know how much a probe will need to slow down in order to be gravitationally captured by its destination body. Rockets do not have to reach escape velocity in a single maneuver, and objects can also use a gravity assist to siphon kinetic energy away from large bodies. Accurate trajectory calculations require taking into account small forces like atmospheric drag, radiation pressure, and solar wind. A rocket under continuous or intermittent thrust (or an object climbing a space elevator) can attain escape at any non-zero speed, but the minimum amount of energy required to do so is always the same.