A geostationary orbit, geostationary Earth orbit or geosynchronous equatorial orbit,
is an orbit whose position in the sky remains the same for a stationary observer on earth.
This effect is achieved with a circular orbit 35,786 kilometres above the Earth's equator
and following the direction of the Earth's rotation. An object in such an orbit has an
orbital period equal to the Earth's rotational period, 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 move 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)
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 geosynchronous satellite for
communication purposes was first published in 1928 by Herman Potočnik. The first appearance
of a geostationary orbit in popular literature was in the first Venus Equilateral story by
George O. Smith, but Smith did not go into details. British science fiction author Arthur
C. Clarke disseminated the idea widely, with more details on how it would work, in a 1945
paper entitled "Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?",
published in Wireless World magazine. Clarke acknowledged the connection in his introduction
to The Complete Venus Equilateral. 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 35,786 km above sea level, in the plane of
the Equator, where near-geostationary orbits may be implemented. The Clarke Orbit is about
265,000 km long.
Practical uses
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 into a geostationary orbit. The first satellite placed into a geostationary
orbit was the Syncom-3, launched by a Delta D rocket in 1964.
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 Meteosat, launched by the European Space Agency
and operated by the European Weather Satellite Organization, EUMETSAT
the Japanese MTSAT India's INSAT series
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.
Orbital stability A geostationary orbit can only be achieved
at an altitude very close to 35,786 km, 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 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. 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 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 manoeuvres
are necessary, amounting to a delta-v of approximately 50 m/s per year.
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 and two unstable equilibrium
points. Any geostationary object placed between the equilibrium points would 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 delta-v of about 2 m/s per
year, depending on the desired longitude. Solar wind and radiation pressure also exert
small forces on satellites which, over time, cause them to slowly drift away from their
prescribed orbits. In the absence of servicing missions from
the Earth or a renewable propulsion method, 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 significant — about a quarter
of a second for a trip from one ground-based transmitter to the satellite and back to another
ground-based transmitter; close to half a second for a round-trip communication from
one Earth station to another and then back to the first.
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,
the Earth's radius R and the speed of light c, as
(Note that r is the orbital radius, the distance from the centre of the Earth, not the height
above the Equator.) This delay presents problems for latency-sensitive
applications such as voice communication. 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, line-of-sight 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.
Orbit allocation Satellites in geostationary orbit must all
occupy a single ring above the Equator. 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 and radio frequencies. These disputes are addressed
through the International Telecommunication Union's allocation mechanism. 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. Limitations to usable life of geostationary
satellites 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 N-S station keeping, some satellites can continue to be used in
inclined orbits, or else be elevated to a "graveyard" disposal orbit.
Derivation of geostationary altitude
In any circular orbit, the centripetal force 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:
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:
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:
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, 5.9736 × 1024 kg, and G is the gravitational constant, 6.67428
± 0.00067 × 10−11 m3 kg−1 s−2. 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 = 398,600.4418 ± 0.0008 km3 s−2:
The angular speed ω is found by dividing the angle travelled in one revolution by the
orbital period. In the case of a geostationary orbit, the orbital period is one sidereal
day, or 86,164.09054 seconds). This gives:
The resulting orbital radius is 42,164 kilometres. Subtracting the Earth's equatorial radius,
6,378 kilometres, gives the altitude of 35,786 kilometres.
Orbital speed is calculated by multiplying the angular speed by the orbital radius:
By the same formula we can find the geostationary-type orbit of an object in relation to Mars. The
geocentric gravitational constant GM for Mars has the value of 42,828 km3s−2, and the
known rotational period 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 we have 17,031 km.
See also
Geostationary transfer orbit List of orbits
List of satellites in geosynchronous orbit Orbital stationkeeping
Space elevator Notes
References
This article incorporates public domain material from the General Services Administration
document "Federal Standard 1037C". External links
Orbital Mechanics 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.