Orbital Velocity Calculator
Find the speed of a satellite in a circular or elliptical orbit around Earth, the Moon, Mars, Venus or Jupiter from its periapsis and apoapsis altitudes, using the vis-viva equation.
Speed is set by the orbit, not by the satellite
An object in orbit is falling around the planet: gravity pulls it towards the centre, and its sideways speed carries it far enough that the ground curves away beneath it. For a circular orbit of radius r the required speed is v = √(μ/r), where μ is the standard gravitational parameter of the central body, its mass times the gravitational constant. Mass of the satellite does not appear anywhere. A 420-tonne space station and a loose bolt at the same altitude travel at exactly the same speed, which is why debris shares orbits with working spacecraft.
The calculator uses μ = 398,600.4418 km³/s² for Earth and the WGS-84 equatorial radius of 6,378.137 km, so an altitude of 400 km is a radius of 6,778.137 km. The circular speed there is 7.669 km/s, about 27,607 km/h, and one lap takes 92.56 minutes, so a station at that height circles the Earth 15.56 times a day. Every number on this page is a speed relative to the centre of the planet; the speed relative to the ground below differs by the rotation of the Earth, up to 0.465 km/s at the equator.
Elliptical orbits and the vis-viva equation
Most real orbits are slightly or strongly elliptical. The vis-viva equation gives the speed at any point: v = √(μ(2/r − 1/a)), where r is the current distance from the centre and a is the semi-major axis, half of the long axis of the ellipse. For a circle r equals a and the formula collapses to √(μ/r). An orbit is fully described here by two altitudes: the periapsis, the lowest point, and the apoapsis, the highest. The semi-major axis is the average of the two radii.
A geostationary transfer orbit from a 200 km periapsis to a 35,786 km apoapsis has a semi-major axis of 24,371 km and an eccentricity of 0.730. At periapsis the spacecraft moves at 10.239 km/s; it then coasts up, trading speed for height, and crawls through apoapsis at only 1.597 km/s before falling back. The whole loop takes about 10.5 hours. That slow point at the top is where engineers put burns that change the shape or the plane of an orbit, because they are cheapest there.
Common misconceptions
Higher orbits are slower, not faster. Speed falls with the square root of radius, so a geostationary satellite moves at only 3.075 km/s. Yet getting there costs far more energy than reaching low orbit, because the climb is uphill against gravity. A second mistake is to expect that firing an engine forward makes a spacecraft catch up with one ahead. Speeding up raises the far side of the orbit, the longer orbit takes more time, and the chaser falls behind; rendezvous is done by briefly dropping lower. A third is to treat orbital speed as the launch requirement. Gravity losses, air drag and steering add roughly 1.5 to 2 km/s, which is why the total Δv to reach low Earth orbit is about 9.4 km/s rather than 7.7.
How to use it
- Choose the central body. The Moon, Mars, Venus and Jupiter use their own μ and mean radius, shown under the result.
- Enter the periapsis altitude above the surface in kilometres. The default 400 km is the height band of the International Space Station.
- Enter the apoapsis altitude. Use the same value as the periapsis for a circular orbit, or a larger value for an ellipse.
- Read the speed at periapsis and apoapsis, the eccentricity and the period. For the default inputs the result is 7.669 km/s and a 92.56-minute orbit.
- Compare the circular speed at the periapsis radius with the periapsis speed of an ellipse to see how much a burn there would raise the far side.
Questions from the flight desk
How fast does the International Space Station travel?
At an altitude of about 400 km the station moves at roughly 7.67 km/s relative to the centre of the Earth, which is about 27,600 km/h or 17,150 mph. It completes one orbit in about 92.6 minutes, close to 15.5 orbits a day. Its altitude drifts between reboosts, so the exact figure changes slightly from week to week.
Does the mass of a satellite change its orbital speed?
No. The circular speed √(μ/r) depends only on the gravitational parameter of the planet and the distance from its centre. A heavy station and a small cubesat at the same altitude move at the same speed. Mass matters for how much propellant a spacecraft needs to change its orbit, not for the speed the orbit itself requires.
What is the vis-viva equation?
It relates speed to position on any Keplerian orbit: v² = μ(2/r − 1/a), where r is the distance from the centre of the body and a is the semi-major axis. It comes from conservation of energy. For a circle r = a and it gives √(μ/r); at r → infinity with a negative a it describes the hyperbolic speed of an escaping probe.
Why do satellites in higher orbits move more slowly?
Gravity weakens with the square of distance, so less sideways speed is needed to keep falling around the planet. Circular speed falls with the square root of radius: about 7.67 km/s at 400 km but only 3.07 km/s at geostationary altitude. Reaching the higher orbit still takes more total energy, because the spacecraft must climb out of the gravity well first.
Disclaimer: Orbital mechanics results are ideal two-body figures with instantaneous burns, computed from the values you enter and the constants stated on each page. They are not mission analysis, flight dynamics or launch safety advice. Real orbits are perturbed by Earth’s oblateness, the Moon, the Sun and atmospheric drag, and real burns carry gravity and steering losses. Never use these numbers to operate a spacecraft or to fly a rocket; follow the safety code of your rocketry association and the advice of qualified engineers.