Orbital Period Calculator

About this calculator

Kepler's third law, in its full Newtonian form, gives the orbital period of any body orbiting a central mass as T = 2π√(a³ / GM), where a is the semi-major axis of the orbit, G is the gravitational constant, and M is the mass of the body being orbited. This works for anything from a satellite circling Earth to a planet circling the Sun to a moon circling a planet — only the central mass and orbital distance matter, not the orbiting body's own mass (as long as it's much smaller than M).

Astronomers and aerospace engineers use this formula to plan satellite orbits (a geostationary satellite is placed at the specific altitude that gives exactly a 24-hour period), to determine the masses of stars and planets by observing the orbital periods of their companions, and to predict how long a spacecraft transfer orbit or a newly discovered exoplanet's "year" will last. Enter the semi-major axis and central mass to find the orbital period.