Orbital Velocity Calculator

Orbital velocity is the speed an object must travel to maintain a stable orbit around a celestial body. It balances the inward pull of gravity with the outward centrifugal tendency of the moving object. For a circular orbit, it is calculated as v = √(GM/r), where G is the gravitational constant, M is the central body's mass, and r is the orbital radius.

Orbital velocity is the speed needed to stay in a stable circular orbit, while escape velocity is the minimum speed required to break free from the gravitational pull of a body entirely. Escape velocity is always √2 times greater than the circular orbital velocity at the same radius — approximately 1.414× faster.

An elliptical orbit is a closed orbit shaped like an ellipse, characterised by an eccentricity between 0 (circular) and 1 (parabolic escape). In an elliptical orbit, the orbiting body moves faster at periapsis (closest point) and slower at apoapsis (farthest point), as described by Kepler's second law.

Orbital velocity decreases as orbital radius increases. Objects in lower orbits must travel faster to counteract the stronger gravitational pull experienced at closer distances. For example, the ISS at ~400 km altitude orbits at about 7.66 km/s, while the Moon at ~384,000 km travels only about 1.02 km/s.

Kepler's third law states that the square of an orbit's period is proportional to the cube of its semi-major axis: T² ∝ a³. More precisely, T = 2π√(r³/GM). This means that planets or satellites farther from the central body take significantly longer to complete one orbit.

Specific orbital energy (also called vis-viva energy) is the total mechanical energy per unit mass of an orbiting object, combining its kinetic and potential energy. For a circular orbit it equals -GM/(2r). A negative value indicates a bound orbit; zero or positive values indicate escape trajectories.

Centripetal acceleration is the inward acceleration keeping the satellite on its curved orbital path, provided entirely by gravity. It equals GM/r² (or equivalently v²/r). At the ISS orbit altitude, this is approximately 8.69 m/s² — only slightly less than surface gravity due to the relatively small altitude difference.

Yes. By changing the central body mass and orbital radius you can model any gravitationally bound two-body system — artificial satellites around Earth, moons around planets, or planets around the Sun. Simply input the appropriate mass (e.g. Sun = 1.989×10³⁰ kg) and orbital radius for the body you want to analyse.