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# Geostationary orbit

A geostationary orbit (abbreviated GEO) is a circular orbit in the Earth's equatorial plane, any point on which revolves about the Earth in the same direction and with the same period as the Earth's rotation. It is a special case of the geosynchronous orbit (abbreviated GSO), and the one which is of most interest to operators of artificial satellite.

Geosynchronous and geostationary orbits were first popularised by science fiction author Arthur C. Clarke in 1945 as useful orbits for communications satellites. As a result they are sometimes referred to as Clarke orbits. Similarly, the "Clarke Belt" is the part of space approximately 35,786 km above mean sea level in the plane of the equator where near-geostationary orbits may be achieved.

Geostationary orbits are useful because they cause a satellite to appear stationary with respect to a fixed point on the rotating Earth. As a result, an antenna can point in a fixed direction and maintain a link with the satellite. The satellite orbits in the direction of the Earth's rotation, at an altitude of approximately 35,786 km (22,240 statute miles) above ground. This altitude is significant because it produces an orbital period equal to the Earth's period of rotation, known as the sidereal day.

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## Use in artificial satellites

Geostationary orbits can only be achieved very close to the ring 35,786 km directly above the equator. All other circular non-active geosynchronous orbits will cross the geostationary orbit and possibly collide with satellites there. In practice this means that all geostationary satellites have to exist on this ring, which poses problems for satellites needing to be decommissioned at the end of their service life (for example when they run out of thruster fuel).

A geostationary transfer orbit is used to move a satellite from Low Earth orbit (LEO) into a geostationary orbit.

A worldwide network of operational geostationary meteorological satellites provides visible and infrared images of Earth's surface and atmosphere. These satellite systems include:

A statite, a hypothetical satellite that uses a solar sail to modify its orbit, can theoretically hold itself in a geostationary orbit with different altitude and/or inclination from the "traditional" equatorial geostationary orbit.

## Derivation of geostationary altitude

To calculate Earth's geostationary orbit altitude:

$r = \sqrt[3]{\frac{\mu}{\omega^2}} = \sqrt[3]{\frac{M \cdot G \cdot T^2}{4 \cdot \pi^2}}$
$=\;$ 42,164 km (the distance from the centre of the Earth). [1]

where μ is the geocentric gravitational constant.

Subtracting the Earth's equatorial radius, 6,378 km, gives the altitude of 35,786 km.