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Orbital period
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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:

Relation between sidereal and synodic period

Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period.

Using the abbreviations

E = the sidereal period of Earth (a sidereal year, not the same as a tropical year)
P = the sidereal period of the other planet
S = the synodic period of the other planet (wrt 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 to the same position relative to the sun.

and using algebra we obtain

For a superior planet one derives likewise:

Table of synodic periods in the Solar System, relative to Earth:

  Sid. P. (yr)   Syn. P. (yr)   Syn. P. (day)
Mercury           0.241   0.317   115.9
Venus       0.615   1.596   582.9
Earth       1     —     —
Mars       1.881   2.135   779.9
Ceres       4.603   1.278   466.6
Jupiter     11.87   1.092   398.9
Saturn     29.47   1.035   378.1
Uranus     84.00   1.012   369.7
Neptune   164.9   1.006   367.5
Pluto   247.7   1.004   366.7

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