# orbital velocity

The orbital velocity is the velocity of an object at a given point in its orbit. If the orbit is perfectly circular, the magnitude of the velocity is constant and given by

*V*_{orb} = √[*G*(*M* + *m*)/*r*],

where *G* is the gravitational
constant, *M* is the mass of the primary gravitating body, *m* is the mass of the orbiting object, and *r* is the radius of the orbit.
In this special case, orbital velocity is the same as circular
velocity.

If the *m* is negligible compared with *M*, as it is, for
example, in the case of a spacecraft orbiting the Earth, then this equation
reduces to

*V*_{orb} = √(*G**M*/*r*).

An object moving faster than circular velocity will enter an elliptical orbit with a velocity at any point determined by Kepler's laws of planetary motion. If the object moves faster still, it will travel at escape velocity along a parabolic orbit or beyond escape velocity in a hyperbolic orbit.