Synodic Period Calculator
How often two orbiting bodies return to the same alignment — the synodic period — from their orbital periods, with the time to the next window from the last one and the windows in a decade.
Earth laps Mars every 780 days: that is the synodic period, the time for the faster body to gain a full lap on the slower one.
How the synodic period calculator works
Earth laps Mars every 780 days: that is the synodic period, the time for the faster body to gain a full lap on the slower one. It is one over the difference of the two orbital frequencies, and it is the interval between launch windows for any transfer that needs the planets in a fixed relative position.
The closer the two periods, the longer the wait — Earth and Venus align every 584 days, Earth and Jupiter every 399, because Jupiter barely moves.
Formula: 1 / S = |1 / P₁ − 1 / P₂|
Worked examples
| Inputs | Synodic period (days) | Note |
|---|---|---|
| Earth and Mars | 779.907 | 780 days — the Mars launch window |
| Earth and Venus | 583.939 | 584 days |
| Earth and Jupiter | 398.876 | 399 days |
FAQFrequently asked questions
What is a synodic period?
The time between successive identical alignments of two orbiting bodies as seen from one of them — for Earth and Mars, the interval between oppositions, about 26 months.
Why is it longer than either orbit?
Because both bodies are moving the same way. The faster one has to gain a whole lap on the slower one, which takes longer than a single orbit.
Why does it set launch windows?
A transfer orbit needs the target to be at a particular angle ahead when you leave. That geometry recurs once per synodic period, so Mars missions launch every 26 months or wait.
Why are Venus windows further apart than Jupiter's?
Venus's period is close to Earth's, so Earth gains on it slowly. Jupiter barely moves in a year, so Earth laps it almost every year.
Does the alignment repeat exactly?
Not quite — orbits are elliptical and inclined, so each opposition differs in distance. The synodic period gives the timing; the quality of each window varies.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- CSIRO Space and Astronomy — Australia's national science agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).