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{{Short description|Orbit of an astronomical body equal to that body's average rotational period}}
A '''synchronous orbit''' is an [[orbit]] in which an orbiting body (usually a [[satellite]]) 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.<ref>{{Cite web|url=http://earthobservatory.nasa.gov/Features/OrbitsCatalog/|title=Catalog of Earth Satellite Orbits : Feature Articles|last=Holli|first=Riebeek|date=2009-09-04|website=earthobservatory.nasa.gov|language=en|access-date=2016-05-08}}</ref>

== Simplified meaning ==
A [[synchronous]] orbit 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 ==
A satellite in a synchronous orbit that is both [[equator]]ial and [[circle|circular]] will appear to be suspended motionless above a point on the orbited planet's equator. For synchronous satellites orbiting [[Earth]], this is also known as a [[geostationary 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 an [[ellipse|elliptical]] 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 an [[analemma]].

== Nomenclature ==
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 around [[Earth]] that is circular and lies in the equatorial plane is called a [[geostationary orbit]]. The more general case, when the orbit is inclined to Earth's equator or is non-circular is called a [[geosynchronous orbit]]. The corresponding terms for synchronous orbits around [[Mars]] are [[Areostationary orbit|areostationary]] and [[Areosynchronous orbit|areosynchronous]] orbits.<ref>{{cite web |title=A Proposed Communication and Navigation Infrastructure at Mars |url=http://marsnet.jpl.nasa.gov/what-is-it/what-is-it.html |website=Mars Network |publisher=NASA JPL |archive-url=https://web.archive.org/web/20070621171137/http://marsnet.jpl.nasa.gov/what-is-it/what-is-it.html |archive-date=2007-06-21 |date=1999-11-24 |url-status=dead}}</ref>

== Formula ==

For a stationary synchronous orbit:<ref>{{Cite news|url=https://www.askwillonline.com/2012/12/calculating-radius-of-geostationary.html|title=Calculating the Radius of a Geostationary Orbit - Ask Will Online|date=2012-12-27|work=Ask Will Online|access-date=2017-11-21|language=en-GB}}</ref>

<math display="block">R_{syn} = \sqrt[3]{{G(m_2)T^2\over 4 \pi^2}}</math>
where:
{{block indent |left=1.5 |text={{plainlist}}
* <math display="inline">G</math> is the [[gravitational constant]]
* <math display="inline">m_2</math> is the mass of the celestial body
* <math display="inline">T</math> is the [[Sidereal time|sidereal]] rotational period of the body
* <math display="inline">R_{syn}</math> is the radius of orbit
{{endplainlist}}}}

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.<ref>see [[Circular motion#Formulas]]</ref>

Due to obscure quirks of [[orbital mechanics]], no [[Tidal locking|tidally 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's [[Hill sphere]].<ref>{{Cite web |title=Is it possible to achieve a stable "selenostationary" orbit around the Moon? |url=https://astronomy.stackexchange.com/questions/20499/is-it-possible-to-achieve-a-stable-selenostationary-orbit-around-the-moon/55436#55436 |access-date=2025-05-29 |website=Astronomy Stack Exchange |language=en}}</ref> This is universal and irrespective of the masses and distances involved.

== Examples ==
An astronomical example is [[Pluto]]'s largest moon [[Charon (moon)|Charon]].<ref>{{cite journal |title = The Pluto-Charon system |author = S.A. Stern |year = 1992 |journal = Annual Review of Astronomy and Astrophysics |volume = 30 |page = 190 |quote=Charon's orbit is (a) synchronous with Pluto's rotation and (b) highly inclined to the plane of the ecliptic. |bibcode=1992ARA&A..30..185S|doi = 10.1146/annurev.aa.30.090192.001153 }}</ref>
Much more commonly, synchronous orbits are employed by artificial satellites used for communication, such as [[geostationary satellites]].

For natural satellites, which can attain a synchronous orbit only by [[tidal locking|tidally locking]] their parent body, it always goes in hand with [[synchronous 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.<ref>{{Cite web |date=2023-06-06 |title=Tidal Locking - NASA Science |url=https://science.nasa.gov/moon/tidal-locking/ |access-date=2026-03-09 |language=en-US}}</ref>

The following table lists select [[List of Solar System objects by size|Solar 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):

{| class="wikitable sortable"
|-
! Body !! Body's Mass (kg) !! Sidereal Rotation period !! Semi-major axis of synchronous orbit (km) !! Altitude of synchronous orbit (km)
!Synchronous orbit within [[Hill sphere]]?
|-
| [[Mercury (planet)|Mercury]]<ref>{{Cite web |title=Mercury Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>|| 0.33010×1024 || 1407.6 h || 242,895 km||240,454 km
|No
|-
| [[Venus]]<ref>{{Cite web |title=Venus Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>|| 4.8673×1024 || 5832.6 h|| 1,536,578 km||1,530,526 km
|No
|-
| [[Earth]]<ref>{{Cite web |title=Earth Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>|| 5.9722×1024|| 23.9345 h|| 42,164 km||35,786 km
|Yes
|-
| [[Moon]]<ref>{{Cite web |title=Moon Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>|| 0.07346×1024|| 655.72 h|| 88,453 km||86,715 km
|No
|-
|[[Mars]]<ref>{{Cite web |title=Mars Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|0.64169×1024
|24.6229 h
|20,428 km
|17,031 km
|Yes
|-
|[[Ceres (dwarf planet)|Ceres]]<ref>{{Cite web |title=Asteroid Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|0.09393×1022
|9.074 h
|1,192 km
|723 km
|Yes
|-
|[[Jupiter]]<ref>{{Cite web |title=Jupiter Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|1898.13×1024
|9.925 h
|169,010 km
|88,518 km
|Yes
|-
|[[Saturn]]<ref>{{Cite web |title=Saturn Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/saturnfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|568.32×1024
|10.656 h
|112,239 km
|51,971 km
|Yes
|-
|[[Uranus]]<ref>{{Cite web |title=Uranus Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|86.811×1024
|17.24 h
|82,686 km
|57,127 km
|Yes
|-
|[[Neptune]]<ref>{{Cite web |title=Neptune Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|102.409×1024
|16.11 h
|83,508 km
|58,744 km
|Yes
|-
|[[Pluto]]<ref>{{Cite web |title=Pluto Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html |access-date=2025-05-30 |website=nssdc.gsfc.nasa.gov}}</ref>
|0.01303×1024
|153.2928 h
|18,860 km
|17,672 km
|Yes
|}

== See also ==
* [[Subsynchronous orbit]]
* [[Supersynchronous orbit]]
* [[Graveyard orbit]]
* [[Tidal locking]] (synchronous rotation)
* [[Sun-synchronous orbit]]
* [[List of orbits]]

==References==
{{reflist}}
* {{FS1037C}}

{{orbits|state=expanded}}

[[Category:Astrodynamics]]
[[Category:Orbits]]

Synchronous orbit - Revision history

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