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A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earth's equator (0° latitude), with a period equal to the Earth's rotational period and an orbital eccentricity of approximately zero. From locations on the surface of the Earth, geostationary objects appear motionless in the sky, making the GEO an orbit of great interest to operators of communications and weather satellites. Due to the constant 0° latitude and circularity of geostationary orbits, satellites in GEO differ in location by longitude only.

The notion of a geosynchronous satellite for communication purposes was first published in 1928 (but not widely so) by Herman Potočnik. The idea of a geostationary orbit was first published on a wide scale in a paper entitled "Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?" by Arthur C. Clarke, published in Wireless World magazine in 1945. In this paper, Clarke described it as a useful orbit for communications satellites. As a result this is sometimes referred to as the Clarke Orbit. Similarly, the Clarke Belt is the part of space approximately above sea level, in the plane of the equator, where near-geostationary orbits may be implemented. The Clarke Orbit is about long.

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 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.

Technically, a "geostationary" orbit is the special case of a geosynchronous orbit which is circular and in the equatorial plane. In practice, however, the terms geosynchronous and geostationary are mostly used interchangeably. Some people in the industry dislike the term "geostationary," because the orbit is not actually stationary (in fact, the term stationary orbit would be an oxymoron), and prefer to use "geosynchronous" because it emphasizes the key point that the orbit is not actually stationary, but synchronized with the motion of the Earth.

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 is used to provide visible and infrared images of Earth's surface and atmosphere. These satellite systems include:

- the US GOES
- Meteosat, launched by the European Space Agency and operated by the European Weather Satellite Organization, EUMETSAT
- the Japanese GMS
- India's INSAT series

Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits. (Russian television satellites have used elliptical Molniya and Tundra orbits due to the high latitudes of the receiving audience.) The first satellite placed into a geostationary orbit was the Syncom-3, launched by a Delta-D rocket in 1964.

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

In any circular orbit, the centripetal acceleration required to maintain the orbit is provided by the gravitational force on the satellite. To calculate the geostationary orbit altitude, one begins with this equivalence, and uses the fact that the orbital period is one sidereal day.

- $mathbf\{F\}\_text\{c\}\; =\; mathbf\{F\}\_text\{g\}$

By Newton's second law of motion, we can replace the forces F with the mass m of the object multiplied by the acceleration felt by the object due to that force:

- $m\; mathbf\{a\}\_text\{c\}\; =\; m\; mathbf\{g\}$

We note that the mass of the satellite m appears on both sides — geostationary orbit is independent of the mass of the satellite. So calculating the altitude simplifies into calculating the point where the magnitudes of the centripetal acceleration required for orbital motion and the gravitational acceleration provided by Earth's gravity are equal.

The centripetal acceleration's magnitude is:

- $|mathbf\{a\}\_text\{c\}|\; =\; omega^2\; r$

where ω is the angular speed, and r is the orbital radius as measured from the Earth's center of mass.

The magnitude of the gravitational acceleration is:

- $|mathbf\{g\}|\; =\; frac\{G\; M\}\{r^2\}$

Equating the two accelerations gives:

- $r^3\; =\; frac\{G\; M\}\{omega^2\}\; to\; r\; =\; sqrt[3]\{frac\{G\; M\}\{omega^2\}\}$

The product GM is known with much greater accuracy than either factor; it is known as the geocentric gravitational constant μ = :

- $r\; =\; sqrt[3]\{fracmu\{omega^2\}\}$

The angular speed ω is found by dividing the angle travelled in one revolution (360° = 2π rad) by the orbital period (the time it takes to make one full revolution: one sidereal day, or seconds). This gives:

- $omega\; approx\; frac\{2\; mathrmpi~mathrm\{rad\}\}\; \{86,164~mathrm\{s\}\}\; approx\; 7.2921\; times\; 10^\{-5\}~mathrm\{rad\}\; /\; mathrm\{s\}$

The resulting orbital radius is . Subtracting the Earth's equatorial radius, , gives the altitude of .

Orbital speed (how fast the satellite is moving through space) is calculated by multiplying the angular speed by the orbital radius:

- $v\; =\; omega\; r\; approx\; 3.0746~mathrm\{km\}/mathrm\{s\}\; approx\; 11,068~mathrm\{km\}/mathrm\{h\}\; approx\; 6877.8~mathrm\{mph\}text\{.\}$

For example, for ground stations at latitudes of φ=±45° on the same meridian as the satellite, the one-way delay can be computed by using the cosine rule, given the above derived geostationary orbital radius r, the Earth's radius R and the speed of light c, as

- $2\; frac\; \{sqrt\{R^2+r^2-2\; R\; r\; cosvarphi\}\}\; c\; approx253,mathrm\{ms\}$

This presents problems for latency-sensitive applications such as voice communication or online gaming.

- Graphical derivation of the geostationary orbit radius for the Earth
- ORBITAL MECHANICS (Rocket and Space Technology)
- List of satellites in geostationary orbit
- Clarke Belt Snapshot Calculator
- 3D Real Time Satellite Tracking

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Last updated on Sunday August 31, 2008 at 15:14:59 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Sunday August 31, 2008 at 15:14:59 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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