Synchronous orbit is a spatial relation in which an object orbits a massive body (usually a planet) in the same period that the body rotates, and does so in the same direction. Many artificial satellites, especially those for communications, were put into such an orbit, and visiting spacecraft also found it useful on occasion to remain above the same part of a planetary surface.
To an observer standing on the equator of the rotating body, an object so orbiting would generally appear to oscillate north and south. The one synchronous orbit which did not deviate from the body's equatorial plane, known as stationary because the orbiting object would appear to that observer to be suspended motionless overhead, was yet often understood to be the type intended by the general term. The USS Enterprise maintained a stationary "synchronous orbit over the capital city of Gideon" in 2268. (TOS: "The Mark of Gideon")
A space elevator or orbital tether was a particular type of stationary space station, connected to the equatorial surface by an extremely long cable or tower. The Nezu of the Delta Quadrant used such structures in their colonizations. (VOY: "Rise")
Some special terms are used in the UFP home system. Satellites, stations and ships orbiting in lockstep with Earth rotation are said to be "geosynchronous"; those about Mars "areosynchronous". These objects when in perfect equatorial orbits are "geostationary" and "areostationary", respectively.
These terms can however be used loosely, to describe orbits about other planets. In the 2006 novel Captain's Glory by William Shatner and Garfield and Judith Reeves-Stevens, James T. Kirk found himself in geostationary orbit above Vulcan. The novel Spock's World used "hephaistosynchronous".
Geostationary orbit is also known as a "Clarke orbit", after the physicist and science fiction writer who proposed placing telecommunications satellites there. (Clarke also helped popularize the idea of space elevators).
Clarke orbit is at a radius of 42,164 km–from the Earth's center, meaning about 35,800 kilometers (22,300 miles) above the equatorial surface. Velocity at that altitude must be 6,877 mph to keep pace with rotation. The first communications satellite placed in a Clarke orbit was Syncom 2, launched in 1963. There is now a whole belt of satellites in the skies above the equator, bringing Humans their television broadcasts among other things. Cellular telephone and even internet is still partly dependent on stationary satellites in 2008.