# escape velocity

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Related to First cosmic velocity: Third cosmic velocity

## escape velocity,

the velocity a body must be given in order to escape the gravitational hold of some other larger body, e.g., the earth, moon, or sun. A body given less than the escape velocity will fall back toward the surface of the larger body; a body given a velocity equal to or greater than the escape velocity will still be attracted by the larger body, but this force will not be sufficient to cause it to return. Escape velocity depends on the mass of the larger body and the distance of the smaller body from its center, being proportional to the square root of the ratio of these two quantities. The velocity of escape from the earth at its surface is about 7 mi (11.3 km) per sec, or 25,000 mi per hr; from the moon's surface it is 1.5 mi (2.4 km) per sec; and for a body at the earth's distance from the sun to escape from the sun's gravitation, the velocity must be 26 mi (41 km) per sec.## escape velocity

The minimum velocity required for an object to enter a parabolic trajectory around a massive body and hence escape from its vicinity. The object will keep moving away from the body although it travels at decreasingly lower speeds as the massive body's gravitational attraction continues to slow it down. If the object does not attain escape velocity it will enter an elliptical orbit around the body. If escape velocity is exceeded the object will follow a hyperbolic path. The escape velocity at a distance*r*from the center of a massive body, mass

*m*, is given by √(2

*Gm*/

*r*), where

*G*is the gravitational constant. The escape velocity from the Earth's surface is about 11.2 km s

^{–1}, from the Moon 2.4 km s

^{–1}, and from the Sun 617.7 km s

^{–1}. For a massive body to retain an atmosphere the average velocity of the gas molecules must be well below escape velocity.

## escape velocity

[ə′skāp və‚läs·əd·ē] (astronomy)

The minimum speed away from a parent body that a particle must acquire to escape permanently from the gravitational attraction of the parent.

## escape velocity

the minimum velocity that a body must have in order to escape from the gravitational field of the earth or other celestial body

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