Orbital Period Calculator

This calculator finds the orbital period of a satellite, moon or planet using Kepler's third law, from the size of its orbit and the mass it orbits. Kepler's third law, given its physical basis by Newton, relates how long an object takes to complete one orbit to the size of that orbit and the mass at the centre. The larger the orbit, the longer the period, and the more massive the central body, the shorter it. This single relationship governs everything from the low-Earth orbits of satellites and the International Space Station, to the Moon around the Earth, to the planets around the Sun. This tool computes it. You enter the semi-major axis of the orbit, which for a circular orbit is just its radius from the centre of the central body, and the mass of the central body, using scientific notation for these large values, and the calculator returns the orbital period, expressed in seconds, minutes and hours, along with the orbital speed. The results update as you type, so you can compare different orbits. Use it for astronomy and physics study, for understanding satellites and orbits, or out of curiosity about other worlds. The period is two pi times the square root of the semi-major axis cubed divided by the gravitational constant times the central mass. The orbital speed for a circular orbit is the square root of the gravitational constant times the mass divided by the radius. A striking feature is the dependence on the cube of the orbit size under the square root: doubling the orbital radius increases the period by a factor of about 2.83. As a check, entering the Earth's mass and a radius a few hundred kilometres above its surface gives a period of around ninety minutes, matching real low-Earth-orbit satellites. The calculation assumes a small object orbiting a much larger mass.

Kepler's third law: period = 2 pi x square root of (a³ / (G M)), with G = 6.674 x 10^-11. Orbital speed = square root of (G M / a). Scientific notation supported.