Orbital Period Calculator

Orbital period is the time an object takes to complete one revolution around a central body. This calculator uses Newton's form of Kepler's third law: period equals two pi times the square root of semi-major axis cubed divided by the gravitational constant and central mass. For a circular orbit, semi-major axis is simply the constant orbital radius. The calculator also reports circular orbital speed, found from the square root of gravitational constant times mass divided by radius. Semi-major axis is a center-to-center distance, not altitude above a planet's surface. To evaluate a low Earth satellite, add Earth's mean radius, roughly 6,371 kilometres, to the satellite altitude. The field accepts kilometres and converts them to metres internally so it is consistent with the SI gravitational constant. Central body mass is entered in kilograms. Scientific notation, such as 5.972e24 for Earth, is convenient for astronomical masses. Period increases as semi-major axis raised to the three-halves power, so moving an orbit outward makes its period much longer. Greater central mass shortens the period at a fixed radius because gravity is stronger. A geostationary satellite illustrates these relationships: at approximately 42,164 kilometres from Earth's center, its orbital period matches Earth's sidereal rotation. Low Earth satellites orbit much closer, travel faster, and circle Earth in roughly ninety minutes. The same physical relationship describes moons around planets and planets around stars. The implemented formula treats the orbiting object's mass as negligible relative to the central mass. More generally, the denominator contains the sum of both masses. It also uses the ideal two-body approximation and reports circular speed; speed varies around an elliptical orbit even though the period still depends on semi-major axis. Atmospheric drag, nonspherical gravity, third-body perturbations, radiation pressure, and relativistic effects are omitted. Use this calculator for education, quick mission estimates, and consistency checks. Operational trajectory planning requires precise ephemerides, an appropriate gravitational parameter, uncertainty analysis, and numerical propagation that includes relevant perturbations.