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# Orbital period

The orbital period is the time it takes a planet (or another object) to make one full orbit.

There are two main kinds of orbital periods of objects orbiting the sun:

• The sidereal period is the time that it takes the object to make one full orbit around the sun, relative to the stars. This is considered to be an object's true orbital period.
• The synodic period is the time that it takes for the object to reappear at the same spot in the sky, relative to the sun, as observed from Earth. This is the time that elapses between two successive conjunctions with the sun and is the object's apparent orbital period. The synodic period differs from the sidereal period since Earth itself revolves around the sun.

## Relation between sidereal and synodic period

Copernicus devised a mathematical formula to relate a planet's sidereal period with its synodic period.

Using the abbreviations

P = planet's sidereal period
S = planet's synodic period
E = the sidereal period of Earth

During the time S, the Earth moves over an angle of (360°/E)S (assuming a circular orbit) and the planet moves (360°/P)S.

Let us consider the case of an inferior planet, i.e. a planet that will complete one orbit more than Earth before the two return toe the same position relative to the sun.

(360°)/P)S = (360°/E)S + 360°

and using algebra we obtain

1/P = 1/E + 1/S

For a superior planet one derives likewise:

1/P = 1/E - 1/S