Orbital Period Calculator

The orbital period is the time it takes for one astronomical body to complete a full orbit around another. For example, Earth's orbital period around the Sun is approximately 365.25 days (one year). The period depends on the orbital separation and the mass of the central body — larger orbits and less massive central bodies result in longer periods.

Kepler's Third Law states that the square of a planet's orbital period is proportional to the cube of its semi-major axis: T² = (4π² / GM) × R³. This calculator applies that exact formula — you supply the orbital radius and the central mass, and it solves for T. For planets in AU and solar masses, the gravitational constant simplifies such that T (years) = R (AU)^(3/2) / √M.

The calculator supports three scenarios: (1) planets or exoplanets orbiting a star, using AU and solar masses; (2) artificial satellites in Low Earth Orbit (LEO) or Geostationary Orbit (GEO), using km and kg; and (3) binary star systems, where two stars orbit their common centre of mass. For binary systems, the total mass of both stars is used in Kepler's formula.

Low Earth Orbit is a region roughly 160 km to 2,000 km above Earth's surface. Satellites in LEO have orbital radii from about 6,531 km to 8,371 km from Earth's centre. A typical LEO satellite at 400 km altitude (the ISS) orbits Earth in approximately 92 minutes. The calculator returns this result when you enter the radius in km mode.

A geostationary orbit (GEO) is a special circular equatorial orbit at about 42,164 km from Earth's centre where a satellite's orbital period exactly matches Earth's rotation — 24 hours (1 sidereal day). Enter 42,164 km in the satellite mode of this calculator to verify that result. Geostationary satellites appear stationary from the ground, making them ideal for communications and weather observation.

For a binary star system, Kepler's Third Law still applies using the total mass of both stars. The formula is T = 2π × √(R³ / (G × (M₁ + M₂))), where R is the separation between the two stars and M₁, M₂ are their individual masses. Select 'Binary Star System' mode, enter both masses and the separation, and the calculator handles the rest.

Mean orbital velocity is the average speed of the orbiting body along its circular (or near-circular) orbit. It is calculated as the orbital circumference divided by the period: v = 2πR / T. For Earth orbiting the Sun, this is roughly 29.78 km/s. The calculator displays this alongside the period so you can understand both the timing and the speed of the orbit.

As of the mid-2020s, there are over 8,000 active satellites orbiting Earth, with thousands more pieces of debris tracked by space agencies. The majority reside in LEO (below 2,000 km), particularly mega-constellations like Starlink. Others occupy medium Earth orbit (MEO) used by GPS constellations, or geostationary orbit (GEO) at 35,786 km altitude.