Satellite Orbit Altitude Calculator
Find the orbital radius and altitude a satellite needs to have a chosen orbital period — including geostationary orbit.
How it works
a = ∛(G·M·T² ÷ 4π²) · altitude = a − R_planet
Rearranging Kepler’s third law for the orbital radius gives a = ∛(GMT²/4π²): pick a period and this returns the radius that produces it. Subtracting the planet’s radius yields the altitude above the surface. Setting the period equal to Earth’s sidereal rotation (about 23.9345 hours) yields the famous geostationary altitude of roughly 35,786 km.
Worked example
For Earth (M = 5.972×10²⁴ kg, R = 6,371 km) and a 23.9345 h period: a = ∛(6.674×10⁻¹¹ × 5.972×10²⁴ × 86,164² ÷ 4π²) ≈ 42,164 km, so altitude ≈ 42,164 − 6,371 = 35,793 km — the geostationary belt.
Sources: Geostationary orbit — Wikipedia
Frequently asked questions
What is geostationary orbit?
It is the orbit whose period matches Earth’s rotation, so a satellite appears fixed over one spot on the equator. This tool reproduces its ~35,786 km altitude when you enter a 23.9345 h period.
Why can a period be too short to orbit?
A very short period demands a radius smaller than the planet itself, which is physically impossible — the "orbit" would be underground. The calculator flags this case in its summary.
Does the satellite’s mass matter?
No. As with all Keplerian orbits, the satellite’s own mass cancels out; only the planet’s mass and the chosen period set the altitude.
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This calculator is for educational purposes. Double-check important results before acting on them.