Synodical Period

The synodical period of a Planet is the time put by this planet to return to the same configuration Ground - planet Sun, i.e. in the same place in the sky compared to the Sun, seen Earth. This duration differs from the Period of sidereal revolution of planet because the Earth itself moves around the Sun. Consequently, it is about the period of apparent revolution, the duration between two conjunctions planet-Sun, as observed since the Earth.

The term indicates in a general way time separating two identical aspects from the object (opposition, conjunction, Quadrature, etc) and thus depends on the three implied bodies. The synodical periods of the moons of Mars, for example, will depend speeds of revolution of Mars around the Sun and on the moons around Mars, as well as period of rotation of Mars on itself.

Synodical period of planets of the solar system

The more distant the planet is, the less she traverses her Orbite during one year and the more its synodical period approaches the sidereal period of the Earth.

Correspondence between sidereal period and synodical period

The relation between the two periods was calculated for the first time by Copernic in the case of circular orbits.

One poses E the sidereal period of the Earth, P the sidereal period of planet and S his synodical period.

In the case of a planet closer to the Sun than the Earth, one finds:

$P = \ frac1 {\ frac1S + \ frac1E}$

$S = \ frac1 {\ frac1P - \ frac1E}$

In the case of a planet further away from the Sun than the Earth:

$P = \ frac1 {\ frac1E - \ frac1S}$

$S = \ frac1 {\ frac1E - \ frac1P}$

See too

Periods

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Synodical Period