Synodic Period Calculator

The synodic period is the time it takes for a planet (or other celestial body) to return to the same position relative to both Earth and the Sun — for example, the time between two successive oppositions or conjunctions. Because Earth is also orbiting the Sun, this period differs from the sidereal period, which is measured relative to distant background stars.

For an inferior planet (inside Earth's orbit, like Venus or Mercury), use: 1/P_sid = 1/P₀ + 1/P_syn, which rearranges to P_syn = (P₀ × P_sid) / (P₀ − P_sid). For a superior planet (outside Earth's orbit, like Mars or Jupiter), use: 1/P_sid = 1/P₀ − 1/P_syn, giving P_syn = (P₀ × P_sid) / (P_sid − P₀). Here P₀ is Earth's sidereal period (365.25 days) and P_sid is the planet's sidereal period.

The sidereal period is the true orbital period of a planet — the time it takes to complete one full orbit around the Sun as measured against distant background stars. The synodic period is the apparent period observed from Earth, measuring how long until the planet returns to the same position in the sky relative to the Sun. The synodic period is always affected by Earth's own orbital motion.

Yes! The synodic period formula works for any reference body. Simply replace Earth's sidereal period (365.25 days) with the sidereal period of whichever planet you're observing from. This calculator lets you change the reference body's sidereal period to compute synodic periods as seen from Mars, Jupiter, or any other vantage point.

No — they are different. The Moon's sidereal period (the time to complete one orbit relative to the stars) is about 27.32 days. Its synodic period (the time between identical lunar phases, e.g. full moon to full moon) is about 29.53 days. The difference arises because Earth moves along its own orbit around the Sun while the Moon orbits Earth.

Venus has a sidereal period of about 224.7 days but a synodic period of about 583.9 days. Because Venus orbits the Sun faster than Earth, the two planets must 'lap' each other for Venus to return to the same position relative to Earth and the Sun. This extra catch-up time makes the synodic period considerably longer than the sidereal period.

Yes. Besides the sidereal period (relative to stars) and synodic period (relative to Earth and Sun), there are anomalistic periods (measured from perihelion to perihelion), draconitic or nodal periods (time between crossings of the orbital node), and tropical periods. For the Moon especially, each of these differs slightly due to gravitational perturbations.

If you know the synodic period and Earth's sidereal period, you can calculate the planet's sidereal period. For a superior planet: P_sid = (P₀ × P_syn) / (P_syn + P₀). For an inferior planet: P_sid = (P₀ × P_syn) / (P_syn − P₀). Select 'Reverse Mode' in this calculator and enter the known synodic period to get the sidereal period automatically.