Space · Orbits
Synodic period calculator.
See how long it takes for two orbiting bodies to line up with each other again.
Inputs
Synodic period
Choose two bodies.
How the synodic period is worked out
The sidereal period is how long a body takes to orbit relative to the stars. The synodic period is how long it takes to return to the same alignment with another body, such as opposition or conjunction as seen from Earth. For two periods P1 and P2 the relation is 1/S = |1/P1 − 1/P2|. The closer two periods are, the longer the wait.
Worked example. Mars (687.0 days) and Earth (365.2 days): 1/S = 1/365.2 − 1/687.0 = 0.001283 per day, so S = 779.7 days, about 2.13 years or 25.6 months. Wikipedia lists Jupiter at 398.8 days from Earth, which this tool matches (398.8). Periods come from the NASA planetary fact sheet and are rounded, so results can differ by a day or so from published values.
Choose Custom periods to compare any two bodies: for the Moon, 27.32 days and 365.256 days give 29.53 days, the length of the lunar phase cycle.
Frequently asked questions
How often is Mars at opposition?
About every 780 days, roughly 26 months, which is also the spacing of the best launch windows to Mars.
What is the difference between sidereal and synodic periods?
Sidereal is measured against the distant stars; synodic is measured between repeating alignments of two bodies, so it also depends on Earth’s own motion.
How long is the synodic period of Venus?
About 584 days (1.6 years) from Earth. Wikipedia gives 1.6 years.
Why is the Moon’s synodic month longer than its orbit?
The Moon orbits Earth in 27.3 days, but Earth moves along its own orbit meanwhile, so the Moon needs about two more days to return to the same phase: 29.53 days on average.
Can the formula be used for any two orbiting bodies?
Yes, for circular or near-circular orbits in one plane, with both periods measured in the same units.
Sources
Checked
- Wikipedia: Orbital period (synodic period)
- NASA NSSDCA: Planetary Fact Sheet (metric)
- NASA NSSDCA: Moon Fact Sheet
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Scope
Mean values for ideal circular orbits. Real alignment dates vary a little because orbits are elliptical.