Synodic Period Calculator

Calculate the synodic period or sidereal period of any planet or celestial body. Enter the sidereal period of the planet and the sidereal period of Earth (or your reference body) to get the synodic period in days. Works in reverse too — enter the synodic period to find the sidereal period. Choose from preset planets like Mercury, Venus, Mars, or enter custom values for any object.

Select a planet to auto-fill its sidereal period, or choose Custom to enter your own values.

days

The time the planet takes to complete one orbit around the Sun relative to the stars.

days

Earth's sidereal period is 365.25 days. Change this if calculating from another reference body.

days

Enter the known synodic period to calculate the planet's sidereal period (reverse mode).

Results

Synodic Period

--

Synodic Period (Years)

--

Planet Type

--

Calculated Sidereal Period (Reverse Mode)

--

Planet's Angular Speed

--

Earth's Angular Speed

--

Orbital Period Comparison (Days)

Results Table

Frequently Asked Questions

What is a synodic period?

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.

How to calculate the synodic period?

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.

What is the difference between a sidereal period and a synodic 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.

Can the synodic period be measured from a planet other than Earth?

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.

Is the sidereal period of the Moon the same as its synodic period?

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.

Why is Venus's synodic period longer than its sidereal period?

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.

Are there other types of orbital periods for planets?

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.

How do I use the synodic period formula in reverse to find the sidereal period?

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.

More Physics Tools