Synodic Period Calculator

Frequently Asked Questions

What is a synodic period?

It is the time for two orbiting bodies to return to the same relative arrangement, such as the gap between successive oppositions of a planet seen from Earth.

Why must the two orbital periods differ?

If both bodies orbit at the same rate they never separate or realign, so the synodic period is undefined and the calculator requires different periods.

Why is the synodic period longer than either orbital period for close orbits?

When two bodies have nearly equal periods, the faster one laps the slower one only very slowly, so it takes a long time to return to the same relative position. The closer the two periods, the longer the synodic period grows, approaching infinity as the periods become equal.

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How This Calculator Works

The synodic period is the time it takes for two orbiting bodies to return to the same relative arrangement as seen from one of them. For example, it is the time between successive oppositions of a planet as observed from Earth. The synodic period depends on the difference between the two orbital rates, so it is found from the reciprocal of the difference of the inverse periods: 1/S = |1/P₁ − 1/P₂|.

Worked Example

Find the synodic period of Mars as seen from Earth, with P₁ = 365.25 days (Earth) and P₂ = 686.98 days (Mars), matching the calculator's default inputs. Take the inverse periods: 1/365.25 ≈ 0.0027379 and 1/686.98 ≈ 0.0014556. Their difference is 1/S = 0.0027379 − 0.0014556 ≈ 0.0012822 per day. Invert to get S ≈ 1 ÷ 0.0012822 ≈ 779.9 days, or about 2.14 years. That is why Mars reaches opposition only about every 26 months rather than once per Earth year.

Why It Matters

Synodic periods set the rhythm of observable events: when an inner planet overtakes an outer one, how often two moons align, and how frequently launch windows open between planets. The closer the two periods are, the longer the synodic period becomes, because the faster body only slowly laps the slower one.

Tips

Bodies with nearly equal periods have very long synodic periods.

The synodic period is always longer than the shorter of the two orbital periods.

When one period is far larger than the other, the synodic period approaches the shorter of the two: a distant, slow-moving body barely shifts while the faster one laps it once each of its own orbits.

Use consistent units; this tool expects days for both inputs.

Synodic Periods Of The Planets

These are the synodic periods of the major planets as seen from Earth - the average time between one opposition or conjunction and the next. Enter Earth's 365.25 days as one period and the planet's orbital period as the other to reproduce each figure.

Planet

Orbital period (days)

Synodic period (days)

Mercury

88.0

≈ 116

Venus

224.7

≈ 584

Mars

687.0

≈ 780

Jupiter

4,333

≈ 399

Saturn

10,759

≈ 378

Notice that the outer planets settle near 365 to 400 days: because they crawl along their orbits, Earth laps them almost once per year, so their synodic period is only a little longer than Earth's own year.

Synodic Period Calculator

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