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Synodic Period of Two Planets Calculator

Enter the two orbital periods to find their synodic period.

How it is calculated

The tool takes two orbital (sidereal) periods in days and applies S = 1 / |1/P₁ − 1/P₂|. The order of the two periods does not matter, because the absolute value is used, and the output also lists which period is the faster (shorter) and which is the slower. The synodic period is shown in days with two decimals and converted to years by dividing by 365.25, shown with three decimals. Both periods must be above zero, and they must differ: if they are equal, the bodies never change their relative position, there is no finite synodic period, and the tool returns no result. Periods that are very close give huge values (365.25 and 365.26 days give about 36,526 years). The formula assumes circular, coplanar orbits.

Worked example

Take Earth (365.25 days) and a planet with a 224.7-day orbit. The inverse periods are 1/224.7 = 0.0044504 and 1/365.25 = 0.0027379 per day. Their difference is 0.0017125, and the reciprocal gives the synodic period: 583.93 days. Dividing by 365.25 gives 1.599 years, so the two bodies line up in the same way roughly every 19 months.

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Common mistakes

  • Entering periods in years for one planet and days for the other. Both must be in days, otherwise the result is meaningless; Earth is 365.25, not 1.
  • Expecting the synodic period to lie between the two orbital periods. It can be longer than both: for 365.25 and 224.7 days it is 583.93 days.
  • Entering the same period twice, for example comparing Earth with itself. Equal periods have no synodic period and return no result.
  • Using the synodic period as a planet's orbital period. It describes how often the two bodies realign as seen from the Sun, not how long either takes to go around.
  • Applying the number to exact alignment dates. The formula assumes circular, coplanar orbits, so real oppositions and conjunctions can differ by days from a multiple of the result.

About this calculator

The synodic period of two planets is the time it takes for them to return to the same relative configuration as seen from the Sun — for instance, the time between successive oppositions or conjunctions — and it's different from each planet's own orbital (sidereal) period because both bodies are moving. It's calculated from 1/S = |1/P1 − 1/P2|, where P1 and P2 are the two orbital periods in the same time unit (this calculator takes them in days); applying it to Earth (365.25 days) and Mars (about 687 days) gives S ≈ 779.9 days, or about 2.135 years, matching the roughly 26-month gap between Mars oppositions.

Because the inner planet always “laps” the outer one, the synodic period is always longer than the shorter of the two orbital periods — Mercury and Venus complete many orbits between each conjunction with Earth. Amateur astronomers planning observation windows, planetarium educators, and mission planners use synodic periods to predict when a planet will next be at opposition (best viewing) or to time interplanetary launch windows, since spacecraft trajectories to another planet are timed around its synodic alignment with Earth.

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  • Editorial team

    The result also explains why outer planets drift through the calendar. Enter Earth at 365.25 days and Jupiter at about 4333 days and you get roughly 398.87 days, so Jupiter reaches opposition about a month later each year. Mars, at 779.88 days, takes more than two years to come around again. Because orbits are not perfect circles, treat any date you add from this as approximate. Which planet are you planning to observe?

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