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


   Vorb = √[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


   Vorb = √(GM/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.