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Synchronous orbit

From Wikipedia, the free encyclopedia
Orbit of an astronomical body equal to that body's average rotational period

Asynchronous orbit is anorbit in which an orbiting body (usually asatellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body.[1]

Simplified meaning

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Asynchronousorbit is an orbit in which the orbiting object (for example, an artificial satellite or a moon) takes the same amount of time to complete an orbit as it takes the object it is orbiting to rotate once.

Properties

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A satellite in a synchronous orbit that is bothequatorial andcircular will appear to be suspended motionless above a point on the orbited planet's equator. For synchronous satellites orbitingEarth, this is also known as ageostationary orbit. However, a synchronous orbit need not be equatorial; nor circular. A body in a non-equatorial synchronous orbit will appear to oscillate north and south above a point on the planet's equator, whereas a body in anelliptical orbit will appear to oscillate eastward and westward. As seen from the orbited body the combination of these two motions produces a figure-8 pattern called ananalemma.

Nomenclature

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There are many specialized terms for synchronous orbits depending on the body orbited. The following are some of the more common ones. A synchronous orbit aroundEarth that is circular and lies in the equatorial plane is called ageostationary orbit. The more general case, when the orbit is inclined to Earth's equator or is non-circular is called ageosynchronous orbit. The corresponding terms for synchronous orbits aroundMars areareostationary andareosynchronous orbits.[citation needed]

Formula

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For a stationary synchronous orbit:

Rsyn=G(m2)T24π23{\displaystyle R_{syn}={\sqrt[{3}]{G(m_{2})T^{2} \over 4\pi ^{2}}}}[2]
G =Gravitational constant
m2 = Mass of the celestial body
T = rotational period of the body
Rsyn{\displaystyle R_{syn}} = Radius of orbit

By this formula one can find the stationary orbit of an object in relation to a given body.

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius.[3]

Examples

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An astronomical example isPluto's largest moonCharon.[4]Much more commonly, synchronous orbits are employed by artificial satellites used for communication, such asgeostationary satellites.

For natural satellites, which can attain a synchronous orbit only bytidally locking their parent body, it always goes in hand withsynchronous rotation of the satellite. This is because the smaller body becomes tidally locked faster, and by the time a synchronous orbit is achieved, it has had a locked synchronous rotation for a long time already.[citation needed]

OrbitBody's Mass (kg)Sidereal Rotation periodSemi-major axis (km)Altitude
Geostationary orbit (Earth)5.97237×10240.99726968 d42,164 km (26,199 mi)35,786 km (22,236 mi)
areostationary orbit (Mars)6.4171×102388,642 s20,428 km (12,693 mi)
Ceres stationary orbit9.3835×10209.074170 h1,192 km (741 mi)722 km (449 mi)
Pluto stationary orbit6.38680 d

See also

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References

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  1. ^Holli, Riebeek (2009-09-04)."Catalog of Earth Satellite Orbits : Feature Articles".earthobservatory.nasa.gov. Retrieved2016-05-08.
  2. ^"Calculating the Radius of a Geostationary Orbit - Ask Will Online".Ask Will Online. 2012-12-27. Retrieved2017-11-21.
  3. ^seeCircular motion#Formulas
  4. ^S.A. Stern (1992). "The Pluto-Charon system".Annual Review of Astronomy and Astrophysics.30: 190.Bibcode:1992ARA&A..30..185S.doi:10.1146/annurev.aa.30.090192.001153.Charon's orbit is (a) synchronous with Pluto's rotation and (b) highly inclined to the plane of the ecliptic.
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