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Synchronous orbit

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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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Asynchronous orbit is anorbit 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.^[2]

Formula

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For a stationary synchronous orbit:^[3]

$R_{syn}={\sqrt[{3}]{G(m_{2})T^{2} \over 4\pi ^{2}}}$ where:

${\textstyle G}$ is thegravitational constant
${\textstyle m_{2}}$ is the mass of the celestial body
${\textstyle T}$ is thesidereal rotational period of the body
${\textstyle R_{syn}}$ is the radius of orbit

By this formula, one can find the synchronous orbital radius of a body, given its mass and sidereal rotational period.

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius.^[4]

Due to obscure quirks oforbital mechanics, notidally locked body in a 1:1 spin-orbit resonance (i.e. a moon locked to a planet or a planet locked to a star) can have a stable satellite in a synchronous orbit, as the synchronous orbital radius lies outside the body'sHill sphere.^[5] This is universal and irrespective of the masses and distances involved.

Examples

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An astronomical example isPluto's largest moonCharon.^[6]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]}

The following table lists selectSolar System bodies' masses, sidereal rotational periods, and the semi-major axises and altitudes of their synchronous orbital radii (calculated by the formula in the above section):

Body	Body's Mass (kg)	Sidereal Rotation period	Semi-major axis of synchronous orbit (km)	Altitude of synchronous orbit (km)	Synchronous orbit withinHill sphere?
Mercury^[7]	0.33010×10²⁴	1407.6 h	242,895 km	240,454 km	No
Venus^[8]	4.8673×10²⁴	5832.6 h	1,536,578 km	1,530,526 km	No
Earth^[9]	5.9722×10²⁴	23.9345 h	42,164 km	35,786 km	Yes
Moon^[10]	0.07346×10²⁴	655.72 h	88,453 km	86,715 km	No
Mars^[11]	0.64169×10²⁴	24.6229 h	20,428 km	17,031 km	Yes
Ceres^[12]	0.09393×10²²	9.074 h	1,192 km	723 km	Yes
Jupiter^[13]	1898.13×10²⁴	9.925 h	169,010 km	88,518 km	Yes
Saturn^[14]	568.32×10²⁴	10.656 h	112,239 km	51,971 km	Yes
Uranus^[15]	86.811×10²⁴	17.24 h	82,686 km	57,127 km	Yes
Neptune^[16]	102.409×10²⁴	16.11 h	83,508 km	58,744 km	Yes
Pluto^[17]	0.01303×10²⁴	153.2928 h	18,860 km	17,672 km	Yes

References

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^Holli, Riebeek (2009-09-04)."Catalog of Earth Satellite Orbits : Feature Articles".earthobservatory.nasa.gov. Retrieved2016-05-08.
^"A Proposed Communication and Navigation Infrastructure at Mars".Mars Network. NASA JPL. 1999-11-24. Archived fromthe original on 2007-06-21.
^"Calculating the Radius of a Geostationary Orbit - Ask Will Online".Ask Will Online. 2012-12-27. Retrieved2017-11-21.
^seeCircular motion#Formulas
^"Is it possible to achieve a stable "selenostationary" orbit around the Moon?".Astronomy Stack Exchange. Retrieved2025-05-29.
^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.
^"Mercury Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Venus Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Earth Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Moon Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Mars Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Asteroid Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Jupiter Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Saturn Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Uranus Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Neptune Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.
^"Pluto Fact Sheet".nssdc.gsfc.nasa.gov. Retrieved2025-05-30.

This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22.

Gravitationalorbits

Types

General	Box Circular Elliptical /Highly elliptical Horseshoe Hyperbolic trajectory Inclined /Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous semi sub Transfer orbit
Geocentric	Geosynchronous Geostationary Geostationary transfer Graveyard High Earth Low Earth Medium Earth Molniya Near-equatorial Orbit of the Moon Polar Sun-synchronous Transatmospheric Tundra Very low Earth
About other points	Mars Areocentric Areosynchronous Areostationary Lagrange points Distant retrograde Halo Lissajous Libration Lunar Sun Heliocentric Earth's orbit Mars cycler Heliosynchronous Other Lunar cycler

Parameters

Shape Size	e Eccentricity a Semi-major axis b Semi-minor axis Q, q Apsides
Orientation	i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis
Position	M Mean anomaly ν,θ,f True anomaly E Eccentric anomaly L Mean longitude l True longitude
Variation	T Orbital period n Mean motion v Orbital speed t₀ Epoch