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 planets:

   * The sidereal period is the time that it takes an object to make one
     full orbit, relative to the stars. This is considered to be an object's
     true orbital period. (See also: sidereal year)
   * The synodic period is the time that it takes for an object to make one
     full orbit, relative to the sun (as observed from Earth). This is the
     time which elapses between two successive conjunctions and is the
     object's apparent orbital period. (See also: synodic month)

History of the Orbital Period

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

P = planet's sidereal period in years

S = planet's synodic period in years

E = the sidereal period of Earth in years

   * Earth moves around its orbit at 360¡/E per day.
   * A planet moves around its orbit at 360¡/P per day.
        o During a time, S, the Earth moves (360¡/E)S and the planet moves
          (360¡/P)S

Let us consider the case of an inferior planet.

   * The inferior planet will complete one full orbit before the Earth has
     completed its orbit.
        o (360¡)/P)S = (360¡/E)S + 360¡

Using algebra...

     1/P = 1/E + 1/S

For a superior planet we would obtain:

     1/P = 1/E - 1/S

For example:

Jupiter has a synodic period of 1.092 years but a sidereal period of 11.87
years. Thus, every 1.092 years the Earth orbits 360¡+ and "laps" Jupiter.

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