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Encyclopedia > Geostationary orbit
Geostationary orbit

The idea of a geosynchronous satellite for communication purposes was first published in 1928 by Herman Potočnik. The geostationary orbit was first popularised by science fiction author Arthur C. Clarke in 1945 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 35,786 km above mean sea level in the plane of the equator where near-geostationary orbits may be achieved. A geosynchronous satellite is a satellite whose orbital track on the Earth repeats regularly over points on the Earth over time. ... Herman PotoÄnik (pseudonym Hermann Noordung) (December 22, 1892 - August 27, 1929) was a Slovene rocket engineer and pioneer of cosmonautics (astronautics). ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ... Sir Arthur Charles Clarke (born December 16, 1917) is a British science-fiction author and inventor, most famous for his novel 2001: A Space Odyssey, and for collaborating with director Stanley Kubrick on the film of the same name. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...

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. A yagi antenna Most simply, an antenna is an electronic component designed to send or receive radio waves. ... Altitude is the elevation of an object from a known level or datum. ... To help compare different orders of magnitude, this page lists lengths starting at 107 m (10,000 km). ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... A sphere rotating around its axis. ... On a prograde planet like the Earth, the sidereal day is shorter than the solar day. ...

## Contents

Geostationary orbits can only be achieved very close to the ring 35,786 km directly above the equator. This equates to an orbital velocity of 3.07 Km/s or a period of 1436.06 minutes which equates to almost exactly one earth day or 23.934 hours. This makes sense considering that the satellite must be locked to the earths rotational period in order to have a stationary footprint. This can be calculated and verified here: [1]. In practice this means that all geostationary satellites have to exist on this ring, which poses problems for satellites that will be decommissioned at the end of their service life (e.g. when they run out of thruster fuel). Such satellites will either continue to be used in inclined orbits (where the orbital track appears to follow a figure-of-eight loop centered on the Equator) or be raised to a "graveyard" disposal orbit. Satellites with bad figure 8 movements that wobble, may cause the tracking actuators on antennas that have an autotracking pointing and control unit to fail prematurely. This is due to the fact the actuators that position the antenna are in continous motion while they are always positioning to seek the strongest signal from the satellite. An example of an elliptical footprint with a receipt area of Germany, Austria and Switzerland. ... A geostationary orbit occurs when an object (satellite) is placed 37,000 km (22,300 miles) above the Earths equator with the characteristic that, from a fixed observation point on the Earths surface, it appears motionless. ... A graveyard orbit is an orbit where spacecraft are intentionally placed at the end of their operational life. ... Rotating magnetic field as a sum of magnetic vectors from 3 phase coils An electric motor converts electrical energy into mechanical energy. ...

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 are used to provide visible, as well as infrared images of Earth's surface and atmosphere. These satellite systems include: A geostationary transfer orbit (GTO) is a Hohmann transfer orbit around the Earth between a low Earth orbit (LEO) and a geostationary orbit (GEO). ... A low Earth orbit (LEO) is an orbit in which objects such as satellites are below intermediate circular orbit (ICO) and far below geostationary orbit, but typically around 350 - 1400 km above the Earths surface. ...

Most commercial communications satellites and television 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 Syncom-3, launched by a Delta-D rocket in 1964. Motto: (Out Of Many, One) (traditional) In God We Trust (1956 to date) Anthem: The Star-Spangled Banner Capital Washington D.C. Largest city New York City None at federal level (English de facto) Government Federal constitutional republic  - President George Walker Bush (R)  - Vice President Dick Cheney (R) Independence from... Goes is a municipality and a city in the southwestern Netherlands, in Zuid-Beveland. ... This article needs cleanup. ... Established: 1974 Administrator: Jean-Jacques Dordain Budget: â‚¬2. ... EUMETSAT is an intergovernmental organisation created through an international convention agreed by 19 European Member States: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland, Turkey, and the United Kingdom. ... Image taken by INSAT 2-E Indian National Satellite System (INSAT) is a series of multipurpose satellites launched by ISRO for telecommunications, broadcasting, meteorology, and search and rescue services. ... U.S. military MILSTAR communications satellite A communications satellite (sometimes abbreviated to comsat) is an artificial satellite stationed in space for the purposes of telecommunications. ... Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. ... Molniya orbit is a class of a highly elliptic orbit with inclination of +/-63. ... Tundra orbit is a class of a highly elliptic orbit with inclination of 63. ... Syncom (for synchronous communication satellite) started as a 1961 NASA program for active geosynchronous communication satellites, all of which were developed and manufactured by Hughes Space and Communications. ... The Delta family of rockets is used in an expendable launch system that has provided space launch capability for the United States since 1960. ...

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 statite is a hypothetical type of artificial satellite that employs a solar sail to continuously modify its orbit in ways that gravity alone would not allow. ... This article does not cite any references or sources. ...

## Derivation of geostationary altitude

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. The centripetal force is the external force required to make a body follow a circular path at constant speed. ... On a prograde planet like the Earth, the sidereal day is shorter than the solar day. ...

Fcentripetal = Fgravitational

By Newton's second law of motion, we can replace the forces F with the mass of the object multiplied by the acceleration felt by the object due to that force: Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point basicly. ...

$m_mathrm{sat} cdot a_mathrm{centripetal} = m_mathrm{sat} cdot a_mathrm{gravitational}$

We note that the mass of the satellite, msat, 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 derived from orbital motion and the gravitational acceleration provided by Earth's gravity are equal. A centripetal force is a force pulling an object toward the center of a circular path as the object goes around the circle. ... Gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. ...

The centripetal acceleration's magnitude is: The centripetal force is the external force required to make a body follow a circular path at constant speed. ...

$|a_mathrm{centripetal}| = omega^2 cdot mathrm{r}$

where ω is the angular velocity in radians per second, and r is the orbital radius in meters as measured from the Earth's center of mass. Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... Some common angles, measured in radians. ... Look up second in Wiktionary, the free dictionary. ... The metre, or meter (symbol: m) is the SI base unit of length. ...

The magnitude of the gravitational acceleration is: Gravity is a force of attraction that acts between bodies that have mass. ...

$|a_mathrm{gravitational}| = frac{G cdot M_mathrm{Earth}}{r^2}$

where MEarth is the mass of Earth in kilograms, and G is the gravitational constant. The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. It was assigned to the United States in 1889 and is periodically recertified and traceable to the primary international standard, The Kilogram, held at the Bureau International des Poids et... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

Equating the two accelerations gives:

$r^3 = frac{G cdot M_mathrm{Earth}}{omega^2}$
$r = sqrt[3]{frac{G cdot M_mathrm{Earth}}{omega^2}}$

We can express this in a slightly different form by replacing $G cdot M_{Earth}$ by μ, the geocentric gravitational constant: In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...

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

The angular velocity ω is found by dividing the angle travelled in one revolution ($360^circ = 2 cdot pi mathrm{rad}$) by the orbital period (the time it takes to make one full revolution: one sidereal day, or 86164.09054[1] seconds). This gives: On a prograde planet like the Earth, the sidereal day is shorter than the solar day. ... Look up second in Wiktionary, the free dictionary. ...

$omega = frac{2 cdot pi}{86164 , mathrm{s}} = 7.29 cdot 10^{-5} , mathrm{rad} / mathrm{s}$

The resulting orbital radius is 42,164 km. Subtracting the Earth's equatorial radius, 6,378 km, gives the altitude of 35,786 km. A kilometre (American spelling: kilometer) (symbol: km) is a unit of length equal to 1000 metres (from the Greek words khilia = thousand and metro = count/measure). ... Since the Earth, like all planets, is not a perfect sphere, the radius of Earth can refer to various values. ...

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

$v = omega cdot r = 3.07466 , mathrm{km/s} = 11,068 , mathrm{km/h} = 6,877 , mathrm{mph}$

## Practical limitations

While a geostationary orbit should hold a satellite in fixed position above the equator, orbital perturbations cause slow but steady drift away from the geostationary location. Satellites correct for these effects with station keeping maneuvers. In the absence of servicing missions, consumption of thruster propellant for station keeping places a limitation on the lifetime of a satellite. In astrodynamics orbital perturbation is an effect on an objects orbit due to the range of external influences. ... In astrodynamics orbital stationkeeping is a term used to describe a particular set of orbital maneuvers used to keep a spacecraft in assigned orbit, either low earth orbit (LEO), or geostationary orbit (GEO). ...

In 2001 California, US, proposed applying property taxes on communications satellites over the state, however since no part of the state lies on the equator, there are none which are permanently, and few ever, over California. That point was missed by regulators who focused instead on their distance from the state.[2]

This is the derivation of the geosynchronous orbital distance for a body in circular orbit around the Earth. ... A geostationary transfer orbit (GTO) is a Hohmann transfer orbit around the Earth between a low Earth orbit (LEO) and a geostationary orbit (GEO). ... In astrodynamics orbital stationkeeping is a term used to describe a particular set of orbital maneuvers used to keep a spacecraft in assigned orbit, either low earth orbit (LEO), or geostationary orbit (GEO). ... A space elevator would consist of a cable anchored to the Earths surface, reaching into space. ... The following is a list of types of orbits: // Box orbit Circular orbit Ecliptic orbit Elliptic orbit Highly Elliptical Orbit Graveyard orbit Hohmann transfer orbit Hyperbolic trajectory Inclined orbit Osculating orbit Parabolic trajectory Capture orbit Escape orbit Semi-synchronous orbit Subsynchronous orbit Synchronous orbit Geocentric orbit Geosynchronous orbit Geostationary orbit...

## References

1. ^ Edited by P. Kenneth Seidelmann, "Explanatory Supplement to the Astronomical Almanac", University Science Books,1992, pp. 700
2. ^ Satellite Tax Out Of This World

Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ... MIL-STD-188 is a series of U.S. military standards relating to telecommunications. ...

Results from FactBites:

 Geostationary orbit - Wikipedia, the free encyclopedia (744 words) The geostationary orbit was first popularised by science fiction author Arthur C. Clarke in 1945 as a useful orbit for communications satellites. Geostationary orbits are useful because they cause a satellite to appear stationary with respect to a fixed point on the rotating Earth. To calculate the geostationary orbit altitude, one begins with this equivalence, and uses the fact that the orbital period is one sidereal day.
 Geostationary transfer orbit - Wikipedia, the free encyclopedia (686 words) After a typical launch the inclination of the LEO (the angle between the plane of the orbit and the plane of the equator) is determined by the latitude of the launch site and the direction of launch. Once in the GTO, it is usually the satellite itself that performs the conversion to geostationary orbit by firing a rocket at a tangent to the GTO at the apogee. The reason for this is that the GTO is an orbit cycling between a perigee tangent to LEO and an apogee tangent to a geostationary orbit.
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