42,164.2
km
35,793.2
km
3.0747
km/s
7.6726
km/s
10.0721
km/s
1.6174
km/s
2.3995
km/s
1.4572
km/s
3.8567
km/s
5.29
h
42,164.2
km
35,793.2
km
3.0747
km/s
7.6726
km/s
10.0721
km/s
1.6174
km/s
2.3995
km/s
1.4572
km/s
3.8567
km/s
5.29
h
The Geosynchronous Orbit Calculator determines the altitude and speed of a geosynchronous orbit — the special orbit where a satellite's orbital period exactly matches the rotation period of the central body. For Earth, this produces the familiar geostationary orbit (GEO) at 35,786 km altitude where satellites appear fixed in the sky, enabling satellite TV, weather monitoring, and communications.
A geosynchronous orbit has an orbital period equal to the body's sidereal rotation period (the rotation period relative to distant stars, not to the Sun). For Earth, this is 23 hours, 56 minutes, and 4 seconds (23.9345 hours) — about 4 minutes shorter than the 24-hour solar day. The radius of this orbit is determined by equating Kepler's orbital period formula with the body's rotation period: r = (GM * T^2 / (4*pi^2))^(1/3).
A geosynchronous orbit is only geostationary (fixed over one spot on Earth's surface) if it is also circular and in the equatorial plane (0 degrees inclination). A geosynchronous orbit with inclination traces a figure-8 pattern (analemma) in the sky as seen from the ground. Most practical communications satellites seek true geostationary orbits: circular, equatorial, and geosynchronous.
The calculator also supports computing geosynchronous orbits around other planets and moons. Mars rotates in 24.62 hours — very close to Earth — so its geosynchronous orbit is at about 20,428 km altitude. The Moon's geosynchronous orbit would be at about 88,000 km, but since the Moon is tidally locked to Earth (its rotation period equals its orbital period around Earth), a true geosynchronous orbit above the Moon would be unstable.
From Kepler's Third Law: T = 2*pi*sqrt(r^3/GM). Solving for r: r_geo = (GM * T^2 / (4*pi^2))^(1/3), where T is the body's sidereal rotation period in seconds. Altitude = r_geo - body_radius. Speed = sqrt(GM/r_geo). Delta-v estimate uses Hohmann transfer from 400 km LEO to GEO altitude.
Earth GEO: 35,786 km altitude, 3.075 km/s orbital speed. Mars geosynchronous: ~17,042 km altitude. Jupiter geosynchronous: ~160,000 km (Jupiter rotates in just 9.9 hours, so its geosynchronous orbit is at moderate altitude relative to its enormous radius of 71,492 km). Planets that rotate quickly have lower geosynchronous orbits relative to their size.
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Earth's GEO is at 35,793 km altitude (commonly rounded to 35,786 km). Reaching it from LEO requires about 3.9 km/s delta-v via Hohmann transfer.
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Mars's geosynchronous orbit is at about 17,038 km altitude. Satellites here would appear stationary over a fixed Martian location.
Geosynchronous means the orbital period matches the planet's rotation period. Geostationary is a special case of geosynchronous where the orbit is also circular and in the equatorial plane. A geostationary satellite appears fixed in the sky. A geosynchronous satellite with inclination traces a figure-8 (analemma) as seen from the ground.
A satellite at GEO appears stationary to ground observers, eliminating the need for tracking antennas. One GEO satellite can cover about 40% of Earth's surface (excluding polar regions). Three GEO satellites at 120-degree spacing provide nearly global coverage (except poles). This makes GEO ideal for broadcast TV, weather satellites (GOES), and broadband communications (ANIK, INTELSAT).
GEO satellites hover above the equator. From high latitudes (above about 75-80 degrees), the satellite is below the horizon or at very low elevation angles, making the signal path through a thick atmosphere (high airmass) unusable. Polar regions use elliptical high-inclination orbits (Molniya, Tundra) for communications instead.
Retired GEO satellites are boosted to a graveyard orbit about 300 km above GEO (at roughly 36,100 km altitude). This preserves the valuable GEO orbital slots for operational satellites. International regulations require satellite operators to remove satellites from GEO slots within a few years of end-of-life using residual propellant for the graveyard boost maneuver.
A satellite slightly above GEO has a longer orbital period than the Earth's rotation — it drifts slowly westward relative to the ground. One slightly below GEO drifts eastward. Operators use these drifting maneuvers to reposition GEO satellites to new longitude slots using minimal propellant.
As of 2024, there are over 500 active satellites in geostationary orbit, plus hundreds of defunct ones. The equatorial GEO arc is administered by the ITU (International Telecommunication Union), which assigns orbital slots (by longitude) and radio frequencies. Popular longitudes over high-population regions are heavily contested.
A sidereal day is Earth's rotation period relative to distant stars: 23h 56m 4s. A solar day (24 hours) is relative to the Sun and is longer because Earth also orbits the Sun. For geosynchronous orbit, we use the sidereal rotation period because the orbit must repeat relative to inertial space (the stars), not relative to the Sun.
The Moon rotates once per month (its rotation is tidally locked to its orbital period around Earth). A lunar geosynchronous orbit would have an altitude of about 88,400 km, far outside the Moon's sphere of influence (about 66,000 km from the Moon). Lunar geosynchronous orbits are not stable in practice due to Earth and Sun perturbations.
A semi-synchronous orbit has a period of exactly half the planet's rotation period, so the satellite passes over the same ground points twice per day (at 12-hour intervals). GPS satellites are in semi-synchronous orbits at 20,200 km altitude (period 11.97 hours, approximately half Earth's sidereal day of 23.93 hours). This repeating ground track simplifies GPS receiver predictions.
All GEO satellites are at the same altitude (35,786 km) but at different longitudes around the equator. Station keeping — small thruster burns every 1-2 weeks — corrects for perturbations from the Moon, Sun, and Earth's non-uniform gravity that would otherwise cause longitude drift and inclination change. Each maneuver uses a small amount of propellant; the satellite's operational lifetime is limited by its propellant budget for station keeping.
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