Orbital Velocity Calculator

The vis-viva equation gives the orbital speed at any point in an elliptical orbit: v^2 = GM(2/r - 1/a), where r is the current distance from the focus and a is the semi-major axis. At periapsis r = a(1-e) and at apoapsis r = a(1+e). It reduces to v = sqrt(GM/r) for circular orbits (where r = a).

A Hohmann transfer orbit is the most fuel-efficient trajectory for moving between two circular orbits around the same body. It uses two engine burns: the first to leave the inner orbit onto an elliptical transfer orbit that just touches the outer orbit, and the second to circularize at the outer orbit. Mars missions typically use Hohmann-like transfers, which take about 8.5 months to travel from Earth to Mars.

A satellite's orbital period depends on its altitude (through Kepler's third law). The International Space Station at ~400 km altitude orbits every 90 minutes. GPS satellites at ~20,200 km orbit every 12 hours (completing exactly 2 orbits per sidereal day). Geostationary satellites at 35,786 km orbit every 23 hours 56 minutes (one sidereal day), appearing stationary over a fixed point on Earth.

A geosynchronous orbit has a period equal to Earth's rotation period (23h 56m). A geostationary orbit is a special case at the equatorial plane at exactly 35,786 km altitude, where the satellite remains fixed above one point on Earth's surface. All geostationary orbits are geosynchronous, but not vice versa — inclined geosynchronous orbits trace a figure-eight over Earth.

Gravity assists (slingshot maneuvers) use a planet's gravity to change a spacecraft's speed and direction without expending fuel. As the spacecraft approaches the planet, it gains speed from the planet's gravity; as it flies away, it loses the same amount relative to the planet. But because the planet itself moves, the spacecraft's heliocentric velocity changes. Voyager 2 used gravity assists from Jupiter, Saturn, Uranus, and Neptune to reach interstellar space.

Orbital resonance occurs when two orbiting bodies have orbital periods in a simple integer ratio. Jupiter's moons Io, Europa, and Ganymede are in a 1:2:4 resonance, meaning Io orbits 4 times for every one orbit of Ganymede. This resonance pumps eccentricity into Io's orbit, driving intense tidal heating. Neptune and Pluto are in a 3:2 resonance, which protects Pluto from close encounters with Neptune despite their apparently crossing orbits.

Periapsis is the generic term for the closest point in an orbit around any body. Perihelion is the specific term for the closest point in an orbit around the Sun (helios = Sun). Similarly, apoapsis is the generic farthest point; aphelion is the specific term for orbits around the Sun. For orbits around Earth, the terms are perigee and apogee. For orbits around black holes, the terms are periastron and apastron.

In theory, yes — in the absence of drag or other perturbations, a satellite in orbit around the Sun would maintain its orbit indefinitely. In practice, gravitational perturbations from Jupiter and other planets slowly modify orbital elements over millions of years. Some asteroids are gradually nudged out of stable orbits into Earth-crossing trajectories over tens of millions of years through this process.

The Sun orbits the Galactic center at about 220-230 km/s at a distance of about 8.5 kpc from the center, completing one galactic orbit every 225-250 million years (a galactic year or cosmic year). This velocity is measured from the kinematics of nearby stars and the rotation curve of the Galaxy, which remains flat out to large radii — evidence for the presence of a dark matter halo.