Synodic Period Calculator (Planet Oppositions & Launch Windows)
Calculate the synodic period between two orbiting bodies from their sidereal periods — how often Mars reaches opposition, Venus its inferior conjunction, or two moons line up — plus the next alignment date and a table for every planet relative to Earth.
How it works
1 ÷ S = | 1 ÷ P₁ − 1 ÷ P₂ | · next alignment = last alignment + S
Two bodies circling the same centre at different rates return to the same relative geometry — opposition, conjunction, a moon-pair alignment — not after one orbit of either but after the faster one has gained a full lap on the slower, and setting the difference in their angular speeds equal to one revolution gives the synodic period. It is always longer than the faster body's year and can be much longer than either when the periods are close, which is why Mars oppositions come only every 26 months although Earth orbits in 12. Real orbits are elliptical, so successive alignments wobble by days around the mean value; the dates here are averages.
Worked example
Earth (365.256 days) and Mars (686.98 days): 1/S = 1/365.256 − 1/686.98 = 0.001282 per day, so S = 779.9 days ≈ 2.135 years. Starting from the opposition of 16 January 2025, the next falls around 6 March 2027, then late April 2029.
Frequently asked questions
Why is the Moon's synodic month 29.53 days when its orbit takes 27.32?
Because Earth moves around the Sun meanwhile, the Moon must travel a little more than one orbit to reach the same phase: 1/(1/27.32 − 1/365.26) = 29.53 days.
Do launch windows fall exactly at opposition?
No — a Hohmann transfer to Mars launches roughly 2–3 months before opposition so the spacecraft arrives as Mars reaches the far side of its transfer ellipse. The interval between windows is still the synodic period.
Related calculators
Textbook astrophysics with simplifying assumptions (circular orbits, point masses, low-redshift Hubble law, blackbody equilibrium). Real systems deviate; use published catalogue values and full models for research.