Orbital Velocity Calculator
Find the speed an object must travel to maintain a stable circular orbit around a central body. Use it for satellites, moons, or planets given the central mass and orbital radius.
About this calculator
Orbital velocity is the speed a body needs to remain in a stable circular orbit around a more massive central object. It is derived by balancing gravitational attraction with the centripetal acceleration required for circular motion. The formula is: v = √(G × M / r), where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the central mass in kilograms, and r is the orbital radius in metres. Notice that orbital velocity decreases as the orbital radius increases — objects in higher orbits travel more slowly. This is why the International Space Station (~400 km altitude) orbits at roughly 7.66 km/s while the Moon (~384,400 km away) orbits at only about 1.02 km/s. The formula assumes a perfectly circular orbit and a point-mass central body.
How to use
Suppose you want the orbital velocity of a satellite 7,000 km from Earth's centre. Earth's mass M = 5.972 × 10²⁴ kg; orbital radius r = 7,000 km = 7,000,000 m. Plug into v = √(G × M / r): v = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 7,000,000) = √(5.692 × 10⁷) ≈ 7,544 m/s, or about 7.54 km/s. Enter 5.972 × 10²⁴ in Central Mass and 7000 in Orbital Radius, and the calculator returns the same result instantly.
Frequently asked questions
What is orbital velocity and why does it depend on altitude?
Orbital velocity is the precise speed a satellite must maintain so that the inward gravitational pull exactly provides the centripetal force needed for circular motion. As altitude (and therefore orbital radius) increases, gravity weakens, so less centripetal force is required and the required speed drops. This inverse-square relationship means doubling the orbital radius reduces orbital speed by a factor of √2. That is why geostationary satellites at 35,786 km orbit at only about 3.07 km/s compared with low-Earth-orbit satellites at roughly 7.8 km/s.
How do I convert orbital radius from kilometres to metres for this calculator?
The formula uses SI units, so the orbital radius must be in metres. Simply multiply the kilometre value by 1,000 — for example, 400 km becomes 400,000 m. The calculator accepts the radius in kilometres and handles the conversion internally, so you can enter 400 for a 400 km orbit without manual conversion. Always double-check whether you are measuring from the surface or from the planet's centre; the formula requires the distance from the centre of the central body.
Can this calculator be used for elliptical orbits or only circular orbits?
The formula v = √(G × M / r) strictly applies to circular orbits, where the speed is constant throughout. For elliptical orbits, the speed varies between a maximum at periapsis and a minimum at apoapsis, and the full vis-viva equation v² = G × M × (2/r − 1/a) is needed, where a is the semi-major axis. For a quick estimate, you can use the semi-major axis as r to obtain the mean orbital speed, but the result will not reflect the actual speed at any specific point along the ellipse.