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.

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.