# Synchronous orbit

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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]

## 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

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 ]

## Formula

For a stationary synchronous orbit:

${\displaystyle R_{syn}={\sqrt[{3}]{G(m_{2})T^{2} \over 4\pi ^{2}}}}$ [2]
G = Gravitational constant
m2 = Mass of the celestial body
T = rotational period of the body
${\displaystyle R_{syn}}$ = 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.[ citation needed ]

1. Holli, Riebeek (2009-09-04). "Catalog of Earth Satellite Orbits : Feature Articles". earthobservatory.nasa.gov. Retrieved 2016-05-08.
2. "Calculating the Radius of a Geostationary Orbit - Ask Will Online". Ask Will Online. 2012-12-27. Retrieved 2017-11-21.

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A geosynchronous orbit is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds. The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km (22,236 mi).

A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude above Earth's equator and following the direction of Earth's rotation.

A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never more than about one-third of the radius of Earth.

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