Synodic Period Calculator

A body's orbital (sidereal) period is how long it takes to complete one full lap around whatever it orbits. The synodic period is a different question: how long until two bodies orbiting the same center return to the same position relative to EACH OTHER, as seen from one of them — the time between one 'alignment' (like a planet being at opposition, or two gears' marked teeth meeting again) and the next.

Each body completes 1/T of a lap per day, so the faster one gains on the slower one at a rate of |1/T₁ − 1/T₂| laps per day. It catches up by exactly one full lap — restoring the same relative alignment — once that gap reaches 1, which gives the synodic period Tsyn = 1 / |1/T₁ − 1/T₂|.

The default inputs (365.25 and 686.98 days) are Earth's and Mars's well-known sidereal orbital periods, which work out to a synodic period of roughly 780 days — close to the real-world ~26-month gap between Mars oppositions, the periodic events when Mars, Earth, and the Sun roughly line up and Mars is closest and brightest in Earth's sky.