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Synodic Period Calculator

Find how often two planets line up.

How it is calculated

The tool uses 1/S = |1/T₁ − 1/T₂|, so S = 1 / |1/T₁ − 1/T₂|. T₁ and T₂ are the sidereal orbital periods of the two bodies, both entered in years, and S is the synodic period in years. It is also shown in days by multiplying by 365.25.

Each period must be greater than zero. If the two periods are equal the bodies never change their relative position, so there is no result. Order does not matter because of the absolute value. The formula assumes circular, coplanar orbits traveling in the same direction; actual alignments drift a little because real orbits are elliptical.

Worked example

Compare Earth (T₁ = 1 year) with Mars (T₂ = 1.8808 years). 1/1 = 1 and 1/1.8808 ≈ 0.5317. The difference is about 0.4683. Then S = 1 / 0.4683 ≈ 2.1353 years. The tool shows 2.1353 yr, which is 779.93 days: roughly every 26 months Earth catches up with Mars again.

Try this example →

Common mistakes

  • Entering periods in days or months for one body and years for the other. Both must use the same unit, and the tool reads them as years.
  • Using the synodic period of one body as the input. You need the sidereal (true orbital) periods of both bodies.
  • Adding the periods or taking their simple difference. The relationship works with reciprocals (orbital frequencies), not with the periods themselves.
  • Expecting a result for two equal periods. The bodies never separate or realign in that case, so nothing is returned.
  • Treating the answer as an exact calendar date interval. Eccentric orbits make real intervals between oppositions vary around this average.

About this calculator

This calculator finds the synodic period — the time between successive alignments (e.g. conjunctions or oppositions) of two orbiting bodies as seen from a common reference point — using 1/S = |1/T₁ − 1/T₂|, where T₁ and T₂ are the bodies' sidereal (true orbital) periods. The synodic period differs from the sidereal period because both bodies are moving.

Astronomers and astronomy students use it to predict when planets will appear closest in the sky (like Mars oppositions, roughly every 26 months) or to determine phenomena like the lunar month's 29.5-day cycle relative to Earth's motion around the Sun. Enter the two orbital periods to find how often the bodies realign.

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