Orbital and Escape Velocity Calculator
Pick Earth, the Moon, Mars, Venus, Jupiter or the Sun, or enter your own mass and radius. Add a height to get the orbital speed, period and escape speed.
A circular orbit around a spherical body with no air. 400 km above Earth is about the height of the International Space Station.
Worked examples
Space station
Earth at a height of 400 km
7.67 km/s and 92.6 minutes per orbit
v = sqrt(GM / r) with r = 6,771 km.
Leaving Earth
Earth surface
11.19 km/s escape speed
sqrt(2GM / R).
About Orbital and Escape Velocity Calculator
An object stays in a circular orbit when gravity provides exactly the inward force needed to keep it moving in a circle. That fixes the speed: the square root of the gravitational constant times the mass of the body, divided by the distance from the centre. Close to the Earth that is about 7.7 kilometres per second, and an orbit at the height of the International Space Station takes about 92 minutes. This calculator works it out for six bodies or for any mass and radius you enter.
The speed needed to escape from a body altogether, never to fall back, is the square root of two times the orbital speed at the same distance. For the surface of the Earth that is 11.2 kilometres per second. The page shows the orbital speed, the time for one orbit, the escape speed and the strength of gravity at the surface and at your height. Heights are measured above the surface, and the page adds the body's radius for you.
How to use Orbital and Escape Velocity Calculator
- Choose the central body, or pick custom and enter its mass and radius.
- Enter the height above the surface, such as 400 kilometres.
- Read the orbital speed, orbit time and escape speed.
- Compare the gravity at the surface with the gravity at your height.
Common uses
- Understanding how satellites and space stations move
- Astronomy and physics coursework
- Comparing escape speeds of planets
- Estimating the period of a low orbit around the Moon or Mars
Frequently asked questions
What is the orbital velocity formula?
v = the square root of (G x M / r), where G is the gravitational constant, M the mass of the central body and r the distance from its centre.
What is escape velocity?
It is the speed needed to leave a body's gravity without further push. It equals the square root of 2 x G x M / r, which is 1.414 times the orbital speed at the same distance.
Why does a higher orbit take longer?
The period rises with the distance to the power of 1.5, and the orbital speed falls with distance, so a higher orbit is slower and longer.
Where do the planet figures come from?
The masses and mean radii are from the NASA planetary fact sheets. They are rounded, and the planets are treated as spheres.