Geostationary orbit

A geostationary apogee (or Geostationary Earth Apogee - GEO) is a geosynchronous apogee anon aloft the Earth's equator (0° latitude), with a aeon according to the Earth's rotational aeon and an alternate aberration of about zero. An article in a geostationary apogee appears motionless, at a anchored position in the sky, to arena observers. Communications satellites and acclimate satellites are generally accustomed geostationary orbits, so that the accessory antennas that acquaint with them do not accept to move to clue them, but can be acicular assuredly at the position in the sky area they stay. Due to the connected 0° breadth and circularity of geostationary orbits, satellites in GEO alter in area by breadth only.

The angle of a geosynchronous accessory for advice purposes was aboriginal arise in 1928 (but not broadly so) by Herman Potočnik.[1] The abstraction of a geostationary apogee was aboriginal advertisement on a advanced calibration in a 1945 cardboard advantaged "Extra-Terrestrial Relays — Can Rocket Stations Give Worldwide Radio Coverage?" by British science fiction biographer Arthur C. Clarke, arise in Wireless World magazine. The orbit, which Clarke aboriginal declared as advantageous for advertisement and broadcast communications satellites,[2] is sometimes alleged the Clarke Orbit.[3] Similarly, the Clarke Belt is the allotment of amplitude about 35,786 km (22,000 mi) aloft sea level, in the even of the equator, area near-geostationary orbits may be implemented. The Clarke Apogee is about 265,000 km (165,000 mi) long.

Geostationary orbits are advantageous because they account a accessory to arise anchored with account to a anchored point on the alternating Earth, acceptance a anchored antenna to advance a articulation with the satellite. The accessory orbits in the administration of the Earth's rotation, at an distance of 35,786 km (22,236 mi) aloft ground, bearing an alternate aeon according to the Earth's aeon of rotation, accepted as the sidereal day.

Introduction

A geostationary apogee can alone be accomplished at an distance actual abutting to 35,786 km (22,236 mi), and anon aloft the equator. This equates to an alternate acceleration of 3.07 km/s (1.91 mi/s) or a aeon of 1,436 minutes, which equates to about absolutely one sidereal day or 23.934461223 hours. This makes faculty because that the accessory charge be bound to the Earth's rotational aeon in adjustment to accept a anchored brand on the ground. In practice, this agency that all geostationary satellites accept to abide on this ring, which poses problems for satellites that will be decommissioned at the end of their account lives (e.g., back they run out of thruster fuel). Such satellites will either abide to be acclimated in absorbed orbits (where the alternate clue appears to chase a figure-eight bend centered on the equator), or abroad be animated to a "graveyard" auctioning orbit.

A geostationary alteration apogee is acclimated to move a accessory from low Earth apogee (LEO) into a geostationary orbit.

A common arrangement of operational geostationary meteorological satellites is acclimated to accommodate arresting and bittersweet images of Earth's apparent and atmosphere. These accessory systems include:

the United States GOES

Meteosat, launched by the European Space Agency and operated by the European Weather Accessory Organization, EUMETSAT

the Japanese MTSAT

India's INSAT series

Most bartering communications satellites, advertisement satellites and SBAS satellites accomplish in geostationary orbits. (Russian television satellites accept acclimated egg-shaped Molniya and Tundra orbits due to the aerial latitudes of the accepting audience.) The aboriginal accessory placed into a geostationary apogee was the Syncom-3, launched by a Delta-D rocket in 1964.

A statite, a academic accessory that uses a solar captain to adapt its orbit, could apparently authority itself in a "geostationary" apogee with altered distance and/or affection from the "traditional" close geostationary orbit.

Derivation of geostationary altitude

In any annular orbit, the centripetal force appropriate to advance the apogee is provided by the gravitational force on the satellite. To account the geostationary apogee altitude, one begins with this equivalence, and uses the actuality that the alternate aeon is one sidereal day.

\mathbf{F}_\text{c} = \mathbf{F}_\text{g}

By Newton's additional law of motion, we can alter the armament F with the accumulation m of the article assorted by the dispatch acquainted by the article due to that force:

m \mathbf{a}_\text{c} = m \mathbf{g}

We agenda that the accumulation of the accessory m appears on both abandon — geostationary apogee is absolute of the accumulation of the satellite.[4] So artful the distance simplifies into artful the point area the magnitudes of the centripetal dispatch appropriate for alternate motion and the gravitational dispatch provided by Earth's force are equal.

The centripetal acceleration's consequence is:

|\mathbf{a}_\text{c}| = \omega^2 r

where ω is the angular speed, and r is the alternate ambit as abstinent from the Earth's centermost of mass.

The consequence of the gravitational dispatch is:

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

where M is the accumulation 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:

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

The artefact GM is accepted with abundant greater attention than either agency alone; it is accepted as the geocentric gravitational connected μ = 398,600.4418 ± 0.0008 km3 s−2:

r = \sqrt[3]{\frac\mu{\omega^2}}

The angular dispatch ω is begin by adding the bend travelled in one anarchy (360° = 2π rad) by the alternate aeon (the time it takes to accomplish one abounding revolution: one sidereal day, or 86,164.09054 seconds).[5] This gives:

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

The consistent alternate ambit is 42,164 kilometres (26,199 mi). Adding the Earth's close radius, 6,378 kilometres (3,963 mi), gives the distance of 35,786 kilometres (22,236 mi).

Orbital dispatch (how fast the accessory is affective through space) is affected by adding the angular dispatch by the alternate radius:

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

Now, by the aforementioned formula, let us acquisition the geostationary apogee of an article in affiliation to Mars (an areostationary orbit). The geocentric gravitational connected GM (which is μ) for Mars has the amount of 42,828 km3s-2, and the accepted rotational aeon (T) of Mars is 88,642.66 seconds. Since ω = 2π/T, application the blueprint above, the amount of ω is begin to be approx 7.088218×10-5 s-1. Thus, r3 = 8.5243×1012 km3, whose cube basis of is 20,427 km; adding the close ambit of Mars (3396.2 km) we accept 17,031 km.

Practical limitations

A aggregate of lunar gravity, solar gravity, and the flattening of the Apple at its poles is causing a antecedence motion of the apogee even of any geostationary article with a aeon of about 53 years and an antecedent affection acclivity of about 0.85 degrees per year, accomplishing a best affection of 15 degrees afterwards 26.5 years. To actual for this alternate perturbation, approved alternate stationkeeping assignment are necessary, amounting to a delta-v of about 50 m/s per year.

The additional aftereffect to be taken into annual is the breadth drift, acquired by the aberration of the apple - the equator is hardly elliptical. There are two abiding (at 75.3°E, and at 104.7°W) and two ambiguous (at 165.3°E, and at 14.7°W) calm points. Any geostationary article placed amid the calm credibility would (without any action) be boring accelerated appear the abiding calm position, causing a alternate breadth variation. The alteration of this aftereffect requires apogee ascendancy assignment with a best delta-v of about 2 m/s per year, depending on the adapted longitude.

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

Communications

Satellites in geostationary orbits are far abundant abroad from Apple that advice cessation becomes actual aerial — about a division of a additional for a one-way cruise from one arena based transmitter to addition via the geostationary satellite; abutting to bisected a additional for round-trip advice amid two apple stations.

For example, for arena stations at latitudes of φ=±45° on the aforementioned acme as the satellite, the one-way adjournment can be computed by application the cosine rule, accustomed the aloft acquired geostationary alternate ambit r, the Earth's ambit R and the acceleration of ablaze c, as

2 \frac {\sqrt{R^2+r^2-2 R r \cos\varphi}} c \approx253\,\mathrm{ms}

This presents problems for latency-sensitive applications such as articulation advice or online gaming.

Orbit allocation

Satellites in geostationary apogee charge all absorb a distinct arena aloft the equator. The affirmation to amplitude these satellites afar to abstain adverse radio-frequency arrest during operations agency that there are a bound cardinal of alternate "slots" available, appropriately alone a bound cardinal of satellites can be operated in geostationary orbit. This has led to battle amid altered countries adulatory admission to the aforementioned alternate slots (countries at the aforementioned breadth but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union's allocation mechanism.[7] Countries amid at the Earth's equator accept additionally asserted their acknowledged affirmation to ascendancy the use of amplitude aloft their territory.