Geostationary orbit
Overview
 
A geostationary orbit (or Geostationary Earth Orbit - GEO) is a geosynchronous orbit
Geosynchronous orbit
A geosynchronous orbit is an orbit around the Earth with an orbital period that matches the Earth's sidereal rotation period...

 directly above the Earth's equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

 (0° latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

), with a period equal to the Earth's rotational period and an orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

 of approximately zero. An object in a geostationary orbit appears motionless, at a fixed position in the sky, to ground observers. Communications satellite
Communications satellite
A communications satellite is an artificial satellite stationed in space for the purpose of telecommunications...

s and weather satellite
Weather satellite
The weather satellite is a type of satellite that is primarily used to monitor the weather and climate of the Earth. Satellites can be either polar orbiting, seeing the same swath of the Earth every 12 hours, or geostationary, hovering over the same spot on Earth by orbiting over the equator while...

s are often given geostationary orbits, so that the satellite antennas that communicate with them do not have to move to track them, but can be pointed permanently at the position in the sky where they stay.
Encyclopedia
A geostationary orbit (or Geostationary Earth Orbit - GEO) is a geosynchronous orbit
Geosynchronous orbit
A geosynchronous orbit is an orbit around the Earth with an orbital period that matches the Earth's sidereal rotation period...

 directly above the Earth's equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

 (0° latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

), with a period equal to the Earth's rotational period and an orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

 of approximately zero. An object in a geostationary orbit appears motionless, at a fixed position in the sky, to ground observers. Communications satellite
Communications satellite
A communications satellite is an artificial satellite stationed in space for the purpose of telecommunications...

s and weather satellite
Weather satellite
The weather satellite is a type of satellite that is primarily used to monitor the weather and climate of the Earth. Satellites can be either polar orbiting, seeing the same swath of the Earth every 12 hours, or geostationary, hovering over the same spot on Earth by orbiting over the equator while...

s are often given geostationary orbits, so that the satellite antennas that communicate with them do not have to move to track them, but can be pointed permanently at the position in the sky where they stay. Due to the constant 0° latitude and circularity of geostationary orbits, satellites in GEO differ in location by longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

 only.

The notion of a geosynchronous satellite
Geosynchronous satellite
A geosynchronous Satellite is a satellite whose orbit on the Earth repeats regularly over points on the Earth over time. If such a satellite's orbit lies over the equator, the orbit is circular and its angular velocity is the same as the earth's, then it is called a geostationary satellite...

 for communication purposes was first published in 1928 (but not widely so) by Herman Potočnik
Herman Potocnik
Herman Potočnik was an Austro-Hungarian rocket engineer and pioneer of cosmonautics . He is chiefly remembered for his work addressing the long-term human habitation of space.- Early life :Potočnik was born in Pola, southern Istria, Austria-Hungary...

. The idea of a geostationary orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

 was first disseminated on a wide scale in a 1945 paper entitled "Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?" by British science fiction writer Arthur C. Clarke
Arthur C. Clarke
Sir Arthur Charles Clarke, CBE, FRAS was a British science fiction author, inventor, and futurist, famous for his short stories and novels, among them 2001: A Space Odyssey, and as a host and commentator in the British television series Mysterious World. For many years, Robert A. Heinlein,...

, published in Wireless World
Wireless World
Wireless World was the pre-eminent British magazine for radio and electronics enthusiasts. It was one of the very few "informal" journals which were tolerated as a professional expense.- History :...

magazine. The orbit, which Clarke first described as useful for broadcast and relay communications satellites, is sometimes called the Clarke Orbit. Similarly, the Clarke Belt is the part of space about 35786 km (22,236.4 mi) above sea level, in the plane of the equator, where near-geostationary orbits may be implemented. The Clarke Orbit is about 265000 km (164,663.8 mi) long.

Geostationary orbits are useful because they cause a satellite to appear stationary with respect to a fixed point on the rotating Earth, allowing a fixed antenna to maintain a link with the satellite. The satellite orbits in the direction of the Earth's rotation, at an altitude of 35786 km (22,236 mi)
1 E7 m
To help compare different orders of magnitude, this page lists lengths starting at 107 metres .Distances shorter than 107 metres- Conversions :10 megametres is* 6,215 miles....

 above ground, producing an orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

 equal to the Earth's period of rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

, known as the sidereal day.

Introduction

A geostationary transfer orbit is used to move a satellite from low Earth orbit
Low Earth orbit
A low Earth orbit is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km...

 (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 United States GOES
    Goes
    Goes is a municipality and a city in the southwestern Netherlands in Zuid-Beveland, in the province Zeeland. The city of Goes has approximately 27,000 residents.-History of Goes:...

  • Meteosat
    Meteosat
    The Meteosat series of satellites are geostationary meteorological satellites operated by EUMETSAT under the Meteosat Transition Programme and the Meteosat Second Generation program....

    , launched by the European Space Agency
    European Space Agency
    The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...

     and operated by the European Weather Satellite Organization, EUMETSAT
  • the Japan
    Japan
    Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

    ese MTSAT
  • India
    India
    India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

    's INSAT series


Most commercial communications satellite
Communications satellite
A communications satellite is an artificial satellite stationed in space for the purpose of telecommunications...

s, broadcast satellites and SBAS satellites operate in geostationary orbits. (Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n television satellites have used elliptical
Elliptic orbit
In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1; this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 . In a...

 Molniya
Molniya orbit
Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of -90 degree and an orbital period of one half of a sidereal day...

 and Tundra
Tundra orbit
Tundra orbit is a type of highly elliptical geosynchronous orbit with a high inclination and an orbital period of one sidereal day . A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as apogee dwell...

 orbits due to the high latitudes of the receiving audience.) The first satellite placed into a geostationary orbit was the Syncom
Syncom
Syncom started as a 1961 NASA program for active geosynchronous communication satellites, all of which were developed and manufactured by Hughes Space and Communications...

-3, launched by a Delta-D rocket in 1964.

A statite
Statite
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. Typically, a statite would use the solar sail to "hover" in a location that would not otherwise be available as a stable geosynchronous...

, a hypothetical satellite that uses a solar sail
Solar sail
Solar sails are a form of spacecraft propulsion using the radiation pressure of light from a star or laser to push enormous ultra-thin mirrors to high speeds....

 to modify its orbit, could theoretically hold itself in a "geostationary" orbit with different altitude and/or inclination from the "traditional" equatorial geostationary orbit.

Derivation of geostationary altitude

In any circular orbit, the centripetal force
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

 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.


By Newton's second law of motion, we can replace the forces F with the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 m of the object multiplied by the acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

 felt by the object due to that force:


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
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

 provided by Earth's gravity are equal.

The centripetal acceleration
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

's magnitude is:


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:

where M is the mass of Earth, , and G is the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

,
.

Equating the two accelerations gives:


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


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:


The resulting orbital radius is 42164 kilometres (26,199.6 mi). Subtracting the Earth's equatorial radius
Earth radius
Because the Earth is not perfectly spherical, no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km...

, 6378 kilometres (3,963.1 mi), gives the altitude of 35786 kilometres (22,236.4 mi).

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


Now, by the same formula, let us find the geostationary-type orbit of an object in relation to Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

 (this type of orbit above is referred to as an areostationary orbit
Areostationary orbit
An areostationary orbit is a circular areo­synchronous orbit in the Martian equatorial plane about above the surface, any point on which revolves about Mars in the same direction and with the same period as the Martian surface...

 if it is above Mars). The geocentric gravitational constant GM (which is μ) for Mars has the value of 42,828 km3s-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, r3 = 8.5243×1012 km3, whose cube root is 20,427 km; subtracting the equatorial radius of Mars (3396.2 km) we have 17,031 km.

Practical limitations

A geostationary orbit can only be achieved at an altitude very close to 35786 km (22,236 mi), and directly above the equator. This equates to an orbital velocity of 3.07 km/s or a period of 1,436 minutes, which equates to almost exactly one sidereal day or 23.934461223 hours. This makes sense considering that the satellite must be locked to the Earth's rotational period in order to have a stationary footprint
Footprint (satellite)
The footprint of a communications satellite is the ground area that its transponders offer coverage, and determines the satellite dish diameter required to receive each transponder's signal...

 on the ground. 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 lives (e.g., when they run out of thruster fuel). Such satellites will either continue to be used in inclined orbit
Inclined orbit
A satellite is said to occupy an inclined orbit around the Earth if the orbit exhibits an angle other than zero degrees with the equatorial plane. This angle is called the orbit's inclination...

s (where the orbital track appears to follow a figure-eight loop centered on the equator), or else be elevated to a "graveyard" disposal orbit.

A combination of lunar
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

 gravity, solar
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 gravity, and the flattening of the Earth at its poles is causing a precession motion of the orbit plane of any geostationary object with a 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
Orbital stationkeeping
In astrodynamics orbital station-keeping is a term used to describe the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit.For many Earth satellites the effects of the non-Keplerian forces, i.e...

 maneuvers are necessary, amounting to a delta-v of approximately 50 m/s per year.

The 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
Orbital stationkeeping
In astrodynamics orbital station-keeping is a term used to describe the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit.For many Earth satellites the effects of the non-Keplerian forces, i.e...

 maneuvers with a maximum delta-v of about 2 m/s per year, depending on the desired longitude.

In the absence of servicing missions from the Earth, the consumption of thruster propellant for station-keeping places a limitation on the lifetime of the satellite.

Communications

Satellites in geostationary orbits are far enough away from Earth that communication latency becomes very high — about a quarter of a second for a one-way trip from one ground based transmitter to another via the geostationary satellite; close to half a second for round-trip communication between two earth stations.

For example, for ground stations at latitudes of φ=±45° on the same meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 c, as


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

Orbit allocation

Satellites in geostationary orbit must all occupy a single ring above the equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

. The requirement to space these satellites apart to avoid harmful radio-frequency 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 at the same longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

 but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union
International Telecommunication Union
The International Telecommunication Union is the specialized agency of the United Nations which is responsible for information and communication technologies...

's allocation mechanism. Countries located at the Earth's equator have also asserted their legal claim to control the use of space above their territory.

See also

  • Geostationary transfer orbit
    Geostationary transfer orbit
    A geosynchronous transfer orbit or geostationary transfer orbit is a Hohmann transfer orbit used to reach geosynchronous or geostationary orbit....

  • List of orbits
  • List of satellites in geosynchronous orbit
  • Orbital stationkeeping
    Orbital stationkeeping
    In astrodynamics orbital station-keeping is a term used to describe the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit.For many Earth satellites the effects of the non-Keplerian forces, i.e...

  • Space elevator
    Space elevator
    A space elevator, also known as a geostationary orbital tether or a beanstalk, is a proposed non-rocket spacelaunch structure...


External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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