Orbital Motion and Kepler's Third Law

When a satellite or planet moves in a circular orbit, it is constantly accelerating toward the center of its circular path. This centripetal acceleration requires a centripetal force directed radially inward. For objects in orbit, gravity provides this centripetal force.

Consider a satellite of mass $m$ orbiting a planet of mass $M$ at orbital radius $r$. The gravitational force between them is given by Newton's law of universal gravitation:

For circular motion, the required centripetal force is:

where $v$ is the orbital speed. Since gravity is the only force acting on the satellite (ignoring air resistance in space), we set these equal: