Orbital velocity is the speed an object needs to maintain a stable circular orbit around a larger body. It comes straight from balancing two forces: the central body's gravitational pull and the centripetal force required to keep the orbiting object moving in a circle rather than falling straight in or flying off in a straight line.

How the Orbital Velocity Calculator works

Setting gravitational force (F = GMm/r²) equal to the centripetal force needed for circular motion (F = mv²/r) and solving for v gives v = √(GM/r). Notice the orbiting object's own mass cancels out entirely — a feather and a space station need the same orbital velocity at the same radius around the same central body. Escape velocity follows from an energy argument: an object needs enough kinetic energy to offset its negative gravitational potential energy entirely, which works out to v_escape = √(2GM/r) — exactly √2 times faster than the circular orbital speed at that radius.

Inputs and what they mean

The calculator takes two inputs: the central body's mass in kilograms, and the orbital radius in meters, measured from the center of the body (not its surface). For Earth orbits, remember to add Earth's radius (~6,371 km) to the satellite's altitude above the surface to get the correct orbital radius. Because masses and radii for astronomical bodies span many orders of magnitude, both fields accept scientific notation (e.g. 5.972e24). The four preset chips — Earth, the Moon, Mars, and the Sun — fill in reasonable reference values so you can see realistic results immediately.

Limits and edge cases

This calculator assumes a perfectly circular orbit and a spherically symmetric, non-rotating central body — real orbits are often elliptical, and effects like atmospheric drag, oblateness (Earth bulges at the equator), and third-body perturbations (the Moon and Sun tugging on satellites) all cause real orbital speeds to deviate slightly from this idealized formula. The formula also breaks down at extremely small radii approaching a black hole's photon sphere, where general relativity — not Newtonian mechanics — governs the motion. For everyday satellite, planetary, and orbital-mechanics estimates, though, v = √(GM/r) is accurate to within a fraction of a percent.