Geostationary Orbit Altitude Calculator
A geostationary orbit is the circular equatorial orbit whose period matches a planet's sidereal rotation, so a satellite hovers over one spot on the equator. The radius is set by Kepler's third law once you fix the period to the rotation period. This calculator takes the sidereal rotation period, the gravitational parameter, and the planet radius, then returns the orbit radius, the altitude above the surface, and the orbital speed. The defaults reproduce Earth's geostationary belt near 35,786 kilometers. All inputs are user-editable so you can find the synchronous orbit of any rotating body.
Geostationary orbit formula
orbit radius a = cube root( mu * T^2 / (4 * pi^2) )
T = sidereal rotation period (seconds)
altitude = a - planet radius
orbital speed = sqrt( mu / a )
miles = km * 0.621371
This is Kepler's third law with the period locked to the planet's sidereal rotation. The satellite then orbits at exactly the planet's spin rate and appears stationary over the equator.
Geostationary notes
- Earth's geostationary altitude is about 35,786 km above the surface.
- Use the sidereal rotation period (about 86,164 s for Earth), not the solar day.
- The orbit must be circular and equatorial to be truly stationary.
- Geosynchronous orbits share the period but may be inclined or eccentric.
- Edit mu, period, and radius to model other planets.
Geostationary orbit: frequently asked questions
What is a geostationary orbit?
A geostationary orbit is a circular equatorial orbit whose period exactly matches a planet's sidereal rotation period, so the satellite stays fixed over one point on the equator. For Earth this requires a specific altitude of roughly 35,786 kilometers above the surface.
How is the geostationary altitude calculated?
Set the orbital period equal to the body's sidereal rotation period and apply Kepler's third law: the orbit radius equals the cube root of the gravitational parameter times the period squared, divided by four pi squared. Subtracting the planet's radius gives the altitude. This calculator does both steps.
Why use the sidereal day, not the solar day?
The satellite must keep pace with the planet's rotation relative to the stars, which is the sidereal period. Earth's sidereal day is about 86,164 seconds (23 hours 56 minutes 4 seconds), slightly shorter than the 86,400-second solar day. The period is a user-editable input.
What is the difference between geostationary and geosynchronous?
Geosynchronous orbits have a period equal to the rotation period but can be inclined or eccentric, so the satellite traces a figure-eight or oscillates. A geostationary orbit is the special geosynchronous case that is circular and equatorial, so the satellite appears truly fixed in the sky.
Can other planets have geostationary orbits?
Yes. Any rotating body has a synchronous orbit radius set by its rotation period and gravitational parameter. Enter the body's sidereal rotation period, gravitational parameter, and radius to find its geostationary altitude. All three are user-editable.
Official sources
- NASA Glenn Beginner's Guide to Aeronautics: Kepler's laws and orbits.
- NASA NSSDCA: planetary rotation and radii.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.