Orbital Velocity Calculator – Speed, Period and Delta-v
The Orbital Velocity Calculator works out how fast a satellite, moon or planet has to travel to stay in orbit around a central body. Choose a planet, moon or star from the presets — or enter your own mass and radius — give an altitude, a radius or a target period, and the tool returns the orbital velocity, the orbital period, the escape velocity at the same radius and the delta-v that separates the two.
Where the Formula Comes From
An orbit is a permanent free fall: gravity supplies exactly the centripetal acceleration the curved path demands. Setting GMm/r² = mv²/r and cancelling the satellite mass m leaves the circular relation:
v_o = √(GM / r) circular orbital speed
T = 2πr / v_o orbital period
v_e = √2 · v_o escape speed at the same radius
G gravitational constant, 6.6743 × 10⁻¹¹ m³/(kg·s²)
M mass of the central body (kg)
r distance from the central body's centre (m)Two consequences follow at once. Orbital speed does not depend on the satellite's mass — a loose bolt and a 420-tonne space station at 400 km altitude both travel at about 7.67 km/s and lap the planet every 92 minutes. And because speed falls off as 1/√r, higher orbits are slower: geostationary satellites at 35,786 km drift along at just 3.07 km/s.
Elliptical Orbits and the Vis-Viva Equation
Real orbits are usually ellipses, and the general speed law is the vis-viva equation v = √(GM(2/r − 1/a)), where a is the semi-major axis. The circular case is simply a = r, so the calculator implements the elliptical form once and lets circular orbits call it. A geostationary transfer orbit with a 200 km periapsis and a 35,786 km apoapsis has a = 24,368 km and eccentricity e = 0.73: it races through periapsis at 10.24 km/s and crawls through apoapsis at 1.60 km/s. The ratio of those speeds equals the inverse ratio of the radii, which is Kepler's second law expressed as conservation of angular momentum.
Solving Backwards: Radius, Period and Planet Masses
Kepler's third law, T = 2π√(a³/GM), inverts in two useful directions. Fix the period and you get the radius that produces it — feed in one sidereal day, 86,164 s, and the tool returns the geostationary radius of 42,164 km. Fix the radius and period of an observed satellite and you get the central mass from M = 4π²r³/(GT²). Measuring the Moon at 384,400 km with a 27.32-day period recovers Earth's mass to within about 1%, which is how astronomers weigh planets, stars and black holes they will never visit.
Delta-v, Transfers and Orbital Energy
Because v_e = √2 · v_o, a craft already in a circular orbit needs only 41.4% more speed to escape — about 3.18 km/s from low Earth orbit. Moving between two circular orbits is cheapest with a Hohmann transfer: one burn raises apoapsis onto an ellipse touching the target, a second burn circularises there. From a 200 km parking orbit to geostationary that costs roughly 2.46 km/s plus 1.48 km/s, about 3.93 km/s in total, over a 5.3-hour coast. Supply a satellite mass and the calculator also reports kinetic, potential and total orbital energy E = −GMm/2a, which stays negative for every bound orbit and rises toward zero as the orbit climbs.
Limits of the Model
Results assume an ideal two-body problem with a spherical, point-mass central body. Real orbits are perturbed by planetary oblateness, third bodies, solar radiation pressure and — below roughly 200 km — by atmospheric drag strong enough to decay an unpowered orbit within days. Treat the figures as accurate to three or four significant digits and as the starting point that mission analysts refine numerically.