Geostationary orbit
A geostationary orbit, geostationary Earth orbit or geosynchronous equatorial orbit^{[1]} (GEO) is a circular orbit 35,786 kilometres (22,236 mi) above the Earth's equator and following the direction of the Earth's rotation.^{[2]} An object in such an orbit has an orbital period equal to the Earth's rotational period (one sidereal day), and thus appears motionless, at a fixed position in the sky, to ground observers. Communications satellites and weather satellites are often placed in geostationary orbits, so that the satellite antennas which communicate with them do not have to rotate to track them, but can be pointed permanently at the position in the sky where they stay. Using this characteristic, ocean color satellites with visible sensors (e.g. the Geostationary Ocean Color Imager (GOCI)) can also be operated in geostationary orbit in order to monitor sensitive changes of ocean environments.
A geostationary orbit is a particular type of geosynchronous orbit, the distinction being that while an object in geosynchronous orbit returns to the same point in the sky at the same time each day, an object in geostationary orbit never leaves that position.
The notion of a
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 Astrodynamics
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 Artificial satellites in geosynchronous orbit

 Orbital Mechanics (Rocket and Space Technology)
 List of satellites in geostationary orbit
 Clarke Belt Snapshot Calculator
 3D Real Time Satellite Tracking
 Geostationary satellite orbit overview
 Daily animation of the Earth, made by geostationary satellite 'Electro L' photos Satellite shoots 48 images of the planet every day.
External links
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MILSTD188).
 ^ "Ariane 5 User's Manual Issue 5 Revision 1". arianespace. July 2011. Retrieved 28 July 2013.
 ^ A geostationary Earth orbit satellite model using Easy Java Simulation Loo Kang Wee and Giam Hwee Goh 2013 Phys. Educ. 48 72
 ^ Noordung, Hermann; et al. (1995) [1929]. The Problem With Space Travel. Translation from original German. DIANE Publishing. p. 72.
 ^ "(Korvus's message is sent) to a small, squat building at the outskirts of Northern Landing. It was hurled at the sky. … It … arrived at the relay station tired and worn, … when it reached a space station only five hundred miles above the city of North Landing." Smith, George O. (1976). The Complete Venus Equilateral. New York: Ballantine Books. pp. 3–4.
 ^ "It is therefore quite possible that these stories influenced me subconsciously when … I worked out the principles of synchronous communications satellistes …", op. cit, p. x
 ^ "ExtraTerrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?". Arthur C. Clark. October 1945. Archived from the original on 18 March 2009. Retrieved 4 March 2009.
 ^ "Basics of Space Flight Section 1 Part 5, Geostationary Orbits". NASA. Retrieved 21 June 2009.
 ^ The Teledesic Network: Using LowEarthOrbit Satellites to Provide Broadband, Wireless, RealTime Internet Access Worldwide
 ^ p. 123
 ^ [1]
 ^ ITU Space Services Division
 ^ Oduntan, Gbenga. "The Never Ending Dispute: Legal Theories on the Spatial Demarcation Boundary Plane between Airspace and Outer Space". Hertfordshire Law Journal, 1(2), p. 75.
 ^ Shi HuLi, Han YanBen, Ma LiHua, Pei Jun, Yin ZhiQiang and Ji HaiFu (2010). Beyond LifeCycle Utilization of Geostationary Communication Satellites in EndofLife, Satellite Communications, Nazzareno Diodato (Ed.), ISBN 9789533071350, InTech, "Beyond LifeCycle Utilization of Geostationary Communication Satellites in EndofLife".
 ^ "Inclined orbit operation".
 ^ "Newton's Second Law". http://www.physicsclassroom.com.
 ^ Edited by P. Kenneth Seidelmann, "Explanatory Supplement to the Astronomical Almanac", University Science Books,1992, pp. 700
References
 ^ Orbital periods and speeds are calculated using the relations 4π²R³ = T²GM and V²R = GM, where R = radius of orbit in metres, T = orbital period in seconds, V = orbital speed in m/s, G = gravitational constant ≈ 6.673×10^{−11} Nm²/kg², M = mass of Earth ≈ 5.98×10^{24} kg.
 ^ Approximately 8.6 times when the moon is nearest (363 104 km ÷ 42 164 km) to 9.6 times when the moon is farthest (405 696 km ÷ 42 164 km).
 ^ In the small body approximation, the geostationary orbit is independent of the satellite's mass. For satellites having a mass less than M μ_{err}/μ≈10^{15} kg, that is, over a billion times that of the ISS, the error due to the approximation is smaller than the error on the universal geocentric gravitational constant (and thus negligible).
Notes
 Geostationary transfer orbit
 List of orbits
 List of satellites in geosynchronous orbit
 Orbital stationkeeping
 Space elevator
See also
By the same formula we can find the geostationarytype orbit of an object in relation to Mars (this type of orbit above is referred to as an areostationary orbit if it is above Mars). The geocentric gravitational constant GM (which is μ) for Mars has the value of 42,828 km^{3}s^{−2}, and the known rotational period (T) of Mars is 88,642.66 seconds. Since ω = 2π/T, using the formula above, the value of ω is found to be approx 7.088218×10^{−5} s^{−1}. Thus, r^{3} = 8.5243×10^{12} km^{3}, whose cube root is 20,427 km; subtracting the equatorial radius of Mars (3396.2 km) we have 17,031 km.
 v = \omega r \approx 3.0746~\mathrm{km}/\mathrm{s} \approx 11\,068~\mathrm{km}/\mathrm{h} \approx 6877.8~\mathrm{mph}\text{.}
Orbital speed (how fast the satellite is moving through space) is calculated by multiplying the angular speed by the orbital radius:
The resulting orbital radius is 42,164 kilometres (26,199 mi). Subtracting the Earth's equatorial radius, 6,378 kilometres (3,963 mi), gives the altitude of 35,786 kilometres (22,236 mi).
 \omega \approx \frac{2 \mathrm\pi~\mathrm{rad}} {86\,164~\mathrm{s}} \approx 7.2921 \times 10^{5}~\mathrm{rad} / \mathrm{s}
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). In the case of a geostationary orbit, the orbital period is one sidereal day, or 86,164.09054 seconds).^{[16]} This gives:
 r = \sqrt[3]{\frac\mu{\omega^2}}
The product GM is known with much greater precision than either factor alone; it is known as the geocentric gravitational constant μ = 398,600.4418 ± 0.0008 km^{3} s^{−2}:
 r^3 = \frac{G M}{\omega^2} \to r = \sqrt[3]{\frac{G M}{\omega^2}}
Equating the two accelerations gives:
where M is the mass of Earth, 5.9736 × 10^{24} kg, and G is the gravitational constant, 6.67428 ± 0.00067 × 10^{−11} m^{3} kg^{−1} s^{−2}.
 \mathbf{g} = \frac{G M}{r^2}
The magnitude of the gravitational acceleration is:
where ω is the angular speed, and r is the orbital radius as measured from the Earth's center of mass.
 \mathbf{a}_\text{c} = \omega^2 r
The centripetal acceleration's magnitude is:
We note that the mass of the satellite m appears on both sides — geostationary orbit is independent of the mass of the satellite.^{[3]} 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.
 m \mathbf{a}_\text{c} = m \mathbf{g}
By Newton's second law of motion,^{[15]} 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:
 \mathbf{F}_\text{c} = \mathbf{F}_\text{g}
In any circular orbit, the centripetal force required to maintain the orbit (F_{c}) is provided by the gravitational force on the satellite (F_{g}). To calculate the geostationary orbit altitude, one begins with this equivalence:
Derivation of geostationary altitude
When they run out of thruster fuel, the satellites are at the end of their service life as they are no longer able to keep in their allocated orbital position. The transponders and other onboard systems generally outlive the thruster fuel and, by stopping NS station keeping, some satellites can continue to be used in inclined orbits (where the orbital track appears to follow a figureeight loop centred on the Equator),^{[13]}^{[14]} or else be elevated to a "graveyard" disposal orbit.
Limitations to usable life of geostationary satellites
Satellites in geostationary orbit must all occupy a single ring above the Equator. The requirement to space these satellites apart to avoid harmful radiofrequency interference during operations means that there are a limited number of orbital "slots" available, thus only a limited number of satellites can be operated in geostationary orbit. This has led to conflict between different countries wishing access to the same orbital slots (countries near the same longitude but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union's allocation mechanism.^{[10]}^{[11]} In the 1976 Bogotá Declaration, eight countries located on the Earth's equator claimed sovereignty over the geostationary orbits above their territory, but the claims gained no international recognition.^{[12]}
Orbit allocation
Geostationary satellites are directly overhead at the Equator, and become lower in the sky the further north or south one travels. As the observer's latitude increases, communication becomes more difficult due to factors such as atmospheric refraction, Earth's thermal emission, lineofsight obstructions, and signal reflections from the ground or nearby structures. At latitudes above about 81°, geostationary satellites are below the horizon and cannot be seen at all.^{[9]}
This delay presents problems for latencysensitive applications such as voice communication.^{[8]}
(Note that r is the orbital radius, the distance from the centre of the Earth, not the height above the Equator.)
 \Delta t = \frac{2}{c} \sqrt{R^2 + r^2  2 R r \cos\varphi} \approx253\,\mathrm{ms}
For example, for ground stations at latitudes of φ = ±45° on the same meridian as the satellite, the time taken for a signal to pass from Earth to the satellite and back again can be computed using the cosine rule, given the geostationary orbital radius r (derived below), the Earth's radius R and the speed of light c, as
Satellites in geostationary orbits are far enough away from Earth that communication latency becomes significant — about a quarter of a second for a trip from one groundbased transmitter to the satellite and back to another groundbased transmitter; close to half a second for a roundtrip communication from one Earth station to another and then back to the first.
Communications
In the absence of servicing missions from the Earth or a renewable propulsion method, the consumption of thruster propellant for stationkeeping places a limitation on the lifetime of the satellite.
Solar wind and radiation pressure also exert small forces on satellites which, over time, cause them to slowly drift away from their prescribed orbits.
A second effect to be taken into account is the longitude drift, caused by the asymmetry of the Earth – the Equator is slightly elliptical. There are two stable (at 75.3°E, and at 104.7°W) and two unstable (at 165.3°E, and at 14.7°W) equilibrium points. Any geostationary object placed between the equilibrium points would (without any action) be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation. The correction of this effect requires orbit control manoeuvres with a maximum deltav of about 2 m/s per year, depending on the desired longitude.
A combination of lunar gravity, solar gravity, and the flattening of the Earth at its poles causes a precession motion of the orbital plane of any geostationary object, with an orbital period of about 53 years and an initial inclination gradient of about 0.85 degrees per year, achieving a maximum inclination of 15 degrees after 26.5 years. To correct for this orbital perturbation, regular orbital stationkeeping manoeuvres are necessary, amounting to a deltav of approximately 50 m/s per year.
A geostationary orbit can only be achieved at an altitude very close to 35,786 km (22,236 mi), and directly above the Equator. This equates to an orbital velocity of 3.07 km/s (1.91 mi/s) or an orbital period of 1,436 minutes, which equates to almost exactly one sidereal day or 23.934461223 hours. This ensures that the satellite is locked to the Earth's rotational period and has a stationary footprint on the ground. All geostationary satellites have to be located on this ring.
Orbital stability
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.
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:
Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits. A geostationary transfer orbit is used to move a satellite from low Earth orbit (LEO) into a geostationary orbit. (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 Syncom3, launched by a Delta D rocket in 1964.
Practical uses
Contents

Practical uses 1
 Orbital stability 1.1
 Communications 1.2
 Orbit allocation 1.3
 Limitations to usable life of geostationary satellites 1.4
 Derivation of geostationary altitude 2
 See also 3
 Notes 4
 References 5
 External links 6
, in the plane of the Equator, where neargeostationary orbits may be implemented. The Clarke Orbit is about 265,000 km (165,000 mi) long. sea level is the part of space about 35,786 km (22,236 mi) above Clarke Belt Similarly, the ^{[7]}.Clarke Orbit is sometimes called the ^{[6]} The orbit, which Clarke first described as useful for broadcast and relay communications satellites,^{[5]}.The Complete Venus Equilateral magazine. Clarke acknowledged the connection in his introduction to Wireless World disseminated the idea widely, with more details on how it would work, in a 1945 paper entitled "ExtraTerrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?", published in Arthur C. Clarke science fiction author but Smith did not go into details. British [4]