A geostationary orbit is a circular orbit 35,786 km above the equator where a satellite circles once per Earth rotation, so it seems to hang still over one spot.
Earth turns once on its axis, measured against the stars, every 23 hours 56 minutes 4 seconds. A satellite 35,786 km above the equator, moving eastward, takes exactly that long to go round once. Satellite and ground turn together, so from the ground the satellite never seems to move.
That is why a DTH dish on a roof can be bolted in place. The satellite it points at stays in the same part of the sky day and night.
Matching Earth's spin is not enough on its own. If the orbit were tilted, the satellite would swing north and south of the equator every day. If the orbit were stretched, the satellite would run ahead and fall behind.
So a geostationary orbit must be circular (eccentricity zero) and lie in the equator's plane (inclination close to zero). The pull of the Sun and Moon slowly spoils both, so operators fire small thrusters from time to time to hold the satellite in its slot. This is called station-keeping.
Three of NavIC's seven navigation satellites are geostationary, parked at 32.5°E, 83°E and 129.5°E.
India's weather satellite INSAT-3DS is another. Its catalogue entry shows a low point of 35,781 km, a high point of 35,792 km and an inclination of just 0.10° — about as close to a perfect geostationary orbit as real satellites get.
A geostationary satellite watches the same part of the globe all the time, which suits communication and weather satellites. ESA notes that three satellites spaced evenly around the ring can cover nearly the whole globe. The polar regions stay out of view, though.
The price is distance. At 35,786 km, a GEO satellite is about 70 times farther from the ground than Cartosat-3 at 509 km, so it sees far less fine detail.
It only looks still. Its distance from Earth's centre is 42,164 km, so each lap is 2π × 42,164 ≈ 265,000 km long. Covering that in one sidereal day (86,164 s) means a speed of about 3.07 km/s — over 11,000 km/h.
INSAT-3DS's estimated position stays over the same point on the equator, while low-orbit satellites race past it. Watch INSAT-3DS in geostationary orbit
Start from Kepler's third law for a circular orbit, T = 2π√(r³/GM), and demand T = Earth's sidereal rotation period. With T = 23.9345 h = 86,164 s and GM = 398,600 km³/s²:
r = (GM·T² / 4π²)^(1/3) = (398,600 × 86,164² / 39.48)^(1/3) ≈ 42,164 km.
Subtract the equatorial radius, 6,378 km, and the height is 35,786 km. The speed is v = √(GM/r) = 3.07 km/s.
Why the sidereal day (23 h 56 min) and not the 24-hour solar day? The orbit has to keep pace with Earth's rotation in space. Earth's 24-hour day is a little longer because Earth also moves along its path around the Sun.
How much of Earth can a GEO satellite see? A line from the satellite that just grazes Earth meets the surface at an angle θ from the point directly below, where cos θ = R/r = 6,378 / 42,164 = 0.151, so θ ≈ 81.3°. A geostationary satellite therefore sees at most out to about 81° latitude, with the region near that edge right on its horizon. The polar regions are never in view, and ESA notes that three evenly spaced GEO satellites give near-global coverage.
Keeping the slot costs fuel. NASA notes that a geostationary satellite needs propulsion for station-keeping, and the Sun's and Moon's pull changes the inclination of orbits over time.
Only an orbit in the equator's plane keeps the satellite at a fixed latitude. Any tilt would make it swing north and south every day, so it would not stay over one spot.
The satellite must match Earth's rotation measured against the stars, which is one sidereal day of 23 h 56 min 4 s. The 24-hour solar day is longer because Earth also moves around the Sun.
The satellite it receives from is geostationary, so it stays in the same direction in the sky all the time.