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Orbital Sidereal & Synodic Periods

Relate two distinct positive sidereal periods to their synodic recurrence time for motion in the same direction.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Periods of 1 year and 0.5 years produce a synodic period of 1 year. Periods of 1 year and 2 years instead produce a synodic period of 2 years.

1 / synodic period = |1 / first sidereal period − 1 / second sidereal period|

Enter these known values and leave the other values blank.

Both sidereal periods are positive and different. Equal periods give zero relative mean angular rate and no finite recurrence period in this model.
This describes mean angular motion in the same direction about a common center. Opposite directions require adding the positive frequencies. Orbital eccentricity makes individual event intervals vary.
Planet presets are rounded illustrative orbital periods, not an ephemeris. Choose Custom for the periods you need; a year means 365.25 days and a month one twelfth of that year.
The inverse is not unique: this retained inverse chooses the missing sidereal period shorter than the known one. A longer-period branch may also exist, but must be evaluated separately.

Nearly equal mean angular rates take a long time to gain one full cycle on each other.

No. The absolute frequency difference can correspond to a faster or slower orbit. The supplied inverse chooses the faster, shorter-period branch.

Bookify rejects equal sidereal periods because this model has no finite synodic period when the relative angular rate is zero.