Synchronous orbit

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.[1]

## Contents

* 1 Simplified meaning
* 2 Properties
* 3 Nomenclature
* 4 Formula
* 5 Examples
* 6 See also
* 7 References

## 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 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.

## Nomenclature

## Formula

For a stationary synchronous orbit:

Rsyn=G(m2)T24π23[2]
G = Gravitational constant
m2 = Mass of the celestial body
T = Sidereal rotational period of the body
Rsyn = 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.[3]

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.[4] This is universal and irrespective of the masses and distances involved.

## Examples

An astronomical example is Pluto's largest moon Charon.[5] Much more commonly, synchronous orbits are employed by artificial satellites used for communication, such as geostationary satellites.

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):

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[6] | 0.33010×1024 | 1407.6 h | 242,895 km | 240,454 km  | No
Venus[7] | 4.8673×1024 | 5832.6 h | 1,536,578 km | 1,530,526 km  | No
Earth[8] | 5.9722×1024 | 23.9345 h | 42,164 km | 35,786 km  | Yes
Moon[9] | 0.07346×1024 | 655.72 h | 88,453 km | 86,715 km  | No
Mars[10] | 0.64169×1024 | 24.6229 h  | 20,428 km  | 17,031 km  | Yes
Ceres[11] | 0.09393×1022 | 9.074 h  | 1,192 km  | 723 km  | Yes
Jupiter[12] | 1898.13×1024 | 9.925 h  | 169,010 km  | 88,518 km  | Yes
Saturn[13] | 568.32×1024 | 10.656 h  | 112,239 km  | 51,971 km  | Yes
Uranus[14] | 86.811×1024 | 17.24 h  | 82,686 km  | 57,127 km  | Yes
Neptune[15] | 102.409×1024 | 16.11 h  | 83,508 km  | 58,744 km  | Yes
Pluto[16] | 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

1. ↑ Holli, Riebeek (2009-09-04). "Catalog of Earth Satellite Orbits : Feature Articles" (in en). http://earthobservatory.nasa.gov/Features/OrbitsCatalog/.
2. ↑ "Calculating the Radius of a Geostationary Orbit - Ask Will Online" (in en-GB). Ask Will Online. 2012-12-27. https://www.askwillonline.com/2012/12/calculating-radius-of-geostationary.html.
3. ↑ see Circular motion
4. ↑ "Is it possible to achieve a stable "selenostationary" orbit around the Moon?" (in en). https://astronomy.stackexchange.com/questions/20499/is-it-possible-to-achieve-a-stable-selenostationary-orbit-around-the-moon/55436#55436.
5. ↑ S.A. Stern (1992). "The Pluto-Charon system". Annual Review of Astronomy and Astrophysics 30: 190. doi:10.1146/annurev.aa.30.090192.001153. Bibcode: 1992ARA&A..30..185S. "Charon's orbit is (a) synchronous with Pluto's rotation and (b) highly inclined to the plane of the ecliptic.".
6. ↑ "Mercury Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html.
7. ↑ "Venus Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html.
8. ↑ "Earth Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html.
9. ↑ "Moon Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html.
10. ↑ "Mars Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html.
11. ↑ "Asteroid Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html.
12. ↑ "Jupiter Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html.
13. ↑ "Saturn Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/saturnfact.html.
14. ↑ "Uranus Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html.
15. ↑ "Neptune Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html.
16. ↑ "Pluto Fact Sheet". https://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html.

* v
* t
* e

Gravitational orbits

Types|

| General|

* Box
* Capture
* Circular
* Elliptical / Highly elliptical
* Escape
* Horseshoe
* Hyperbolic trajectory
* Inclined / Non-inclined
* Lagrangian point
* Osculating
* Parabolic trajectory
* Parking
* Prograde / Retrograde
* 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
* Tundra

About other points|

* Mars
* Areosynchronous
* Areostationary
* Lagrange points
* Distant retrograde
* Halo
* Lissajous
* Lunar
* Sun
* Heliocentric
* Earth's orbit
* Heliosynchronous

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

Maneuvers|

* Bi-elliptic transfer
* Collision avoidance (spacecraft)
* Delta-v
* Delta-v budget
* Gravity assist
* Gravity turn
* Hohmann transfer
* Inclination change
* Low energy transfer
* Oberth effect
* Phasing
* Rocket equation
* Rendezvous
* Transposition, docking, and extraction

Orbital mechanics|

* Celestial coordinate system
* Characteristic energy
* Escape velocity
* Ephemeris
* Equatorial coordinate system
* Ground track
* Hill sphere
* Interplanetary Transport Network
* Kepler's laws of planetary motion
* Lagrangian point
* n-body problem
* Orbit equation
* Orbital state vectors
* Perturbation
* Retrograde motion
* Specific orbital energy
* Specific relative angular momentum
* Two-line elements

* List of orbits

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