A synchronous orbit is an

orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...

in which an orbiting body (usually a

satellite A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scient ...

) 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.

Simplified meaning

A synchronous

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 The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

ial and circular will appear to be suspended motionless above a point on the orbited planet's equator. For synchronous satellites orbiting

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

, this is also known as a

geostationary orbit A geostationary orbit, also referred to as a geosynchronous equatorial orbit''Geostationary orbit'' and ''Geosynchronous (equatorial) orbit'' are used somewhat interchangeably in sources. (GEO), is a circular orbit, circular geosynchronous or ...

. 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 In astronomy, an analemma (; ) is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same Solar time#Mean solar time, mean solar time over the course of a year. The change of position is a result ...

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

that is circular and lies in the equatorial plane is called a

. 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 Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...

are areostationary and areosynchronous orbits.

Formula

For a stationary synchronous orbit: :

R_ = \sqrt /math>
: G =

Gravitational constant The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...

: m₂ = Mass of the celestial body : T = Sidereal rotational period of the body :

R_

= 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. Due to obscure quirks of

orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal ...

, 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 The Hill sphere is a common model for the calculation of a Sphere of influence (astrodynamics), gravitational sphere of influence. It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical ...

. This is universal and irrespective of the masses and distances involved.

Examples

An astronomical example is

Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of Trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Su ...

's largest moon Charon. 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. 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):

References