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Geostationary Orbit Calculator

Work out geostationary orbit instantly with clear inputs, formula shown and shareable results.

About Geostationary Orbit Calculator

A geostationary satellite must orbit with a period equal to the sidereal day of 23h 56m 4s, which puts it at 42,164 km radius or 35,793 km altitude, moving at 3.07 km/s. From there it sees about 162 degrees of longitude, so three satellites can cover the whole equatorial belt - the basis of global broadcast and weather coverage.

Formulas

Geostationary radius

a = cbrt(GM T(sidereal)^2 / 4 pi^2)

Visible longitude span

2 arccos(R / a)

Worked example

With the default values below, Geostationary Orbit Calculator returns Geostationary Altitude of 35,793.2. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rotation period of the bodyminimum 0 h
23.93447 h
Body massminimum 0 kg
5,972,200,000,000,000,000,000,000 kg
Body radiusminimum 0 km
6,371 km

Results

Geostationary Altitude
35,793.2 km
Orbital Radius
42,164.2 km
Orbital Velocity
3.075 km/s
Longitude Span Visible
162.6 deg

Step by step

  1. 1Values used
  2. 2Geostationary radius
  3. 3Visible longitude span
  4. 4Geostationary Altitude= 35,793.2 km
  5. 5Orbital Radius= 42,164.2 km
  6. 6Orbital Velocity= 3.075 km/s
  7. 7Longitude Span Visible= 162.6 deg

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax or fees or charges into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why the sidereal day and not 24 hours?

Because the satellite must match Earth's rotation against the stars. Using 24 hours would put it about 80 km too high and let it drift.

Why must geostationary orbits be equatorial?

Any inclination makes the satellite oscillate north and south of the equator daily, so it is geosynchronous but not geostationary.

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