synchronous orbit

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.

A satellite in a synchronous orbit that is both equatorial and 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 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.

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 and areosynchronous orbits. {{citation needed|date=November 2019}}

For a stationary synchronous orbit:

: $R\_\{syn\}\; =\; \backslash sqrt[3]\{\{G(m\_2)T^2\backslash over\; 4\; \backslash pi^2\}\}${{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}}

: G = Gravitational constant

: m₂ = Mass of the celestial body

: T = Sidereal rotational period of the body

:$R\_\{syn\}$ = 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.see Circular motion#Formulas

Due to obscure quirks of orbital mechanics, no 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.{{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}} This is universal and irrespective of the masses and distances involved.

An astronomical example is Pluto's largest moon Charon.{{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 }}

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 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.{{citation needed|date=November 2011}}

The following table lists select 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):

• Subsynchronous orbit
• Supersynchronous orbit
• Graveyard orbit
• Tidal locking (synchronous rotation)
• Sun-synchronous orbit
• List of orbits

{{reflist}}

• {{FS1037C}}

{{orbits|state=expanded}}

Category:Astrodynamics

Category:Orbits