Orbital Velocity Calculator

Orbital velocity is the sideways speed an object needs to remain in a circular path around a much more massive central body. Gravity continually pulls the orbiting object inward, while its forward motion keeps it falling around the body rather than directly toward the surface. This calculator uses the standard two-body approximation: orbital velocity equals the square root of the gravitational constant multiplied by central mass and divided by orbital radius. The radius must be measured from the center of the central body, not from its surface. The calculator also finds orbital period, the time needed to complete one revolution. The period follows from the circumference of the orbit divided by orbital speed and is equivalent to Kepler's circular-orbit equation. Escape velocity is included for comparison. It is the minimum ideal speed at the same radius that gives an object enough kinetic energy to escape the central body's gravity without further propulsion. At any given radius, escape velocity is the square root of two times circular orbital velocity. Use SI units for consistent results: kilograms for central mass and metres for radius. For a satellite above Earth, add Earth's mean radius, approximately 6,371,000 metres, to the altitude above sea level. For example, a spacecraft 400 kilometres above Earth has an orbital radius near 6,771 kilometres. The calculation assumes a spherical central body, a circular orbit, negligible satellite mass, and no atmospheric drag. Real spacecraft may have elliptical orbits, experience perturbations from other bodies, and require corrections for an uneven gravity field. Orbital velocity decreases as orbital radius increases, while orbital period grows rapidly. This explains why low Earth orbit satellites travel several kilometres each second and circle Earth in roughly ninety minutes, whereas geostationary satellites move more slowly and take one sidereal day. The same formulas apply to moons, planets, and artificial satellites whenever one mass dominates the system. Engineers can use these results for quick mission estimates, students can check orbital mechanics exercises, and astronomy learners can compare motion around different planets or stars. For precision mission design, use complete ephemerides and numerical trajectory models rather than this idealized circular calculation.