Synodic Period Calculator
The synodic period is how often two orbiting bodies line up the same way again, such as the interval between successive close approaches of a planet to Earth. It depends only on the two bodies' sidereal orbital periods through a simple reciprocal relation. This calculator takes the two periods in any consistent time unit and returns the synodic period in that same unit, along with each body's reciprocal rate and their relative rate. Because the formula uses only the difference of reciprocal periods, the result is exact for the idealized circular case.
Synodic period formula
relative rate = absolute value of (1 / period 1 - 1 / period 2)
synodic period = 1 / relative rate
Each body's reciprocal period equals its angular rate. The relative rate is the absolute difference of the two reciprocal periods. The synodic period is the reciprocal of that relative rate: the time for the bodies to accumulate one full revolution of relative angle and return to the same configuration.
Synodic period context
- The synodic period is the time between repeated alignments such as oppositions or conjunctions.
- It differs from the sidereal period, which is one full orbit against the fixed stars.
- If the two periods are equal, the configuration never changes and the synodic period is infinite.
- Enter both periods in the same time unit; the synodic period uses that unit.
- The relation is exact for idealized coplanar circular orbits.
Synodic period: frequently asked questions
What is a synodic period?
The synodic period is the time it takes for two orbiting bodies to return to the same relative configuration, for example the time between successive oppositions of a planet as seen from Earth. It differs from the sidereal period, which is one full orbit against the fixed stars.
How is the synodic period calculated?
The reciprocal of the synodic period equals the absolute difference of the reciprocals of the two sidereal periods: 1 over synodic equals the absolute value of 1 over period one minus 1 over period two. This calculator applies that exact relation from your two orbital periods.
Why use the difference of reciprocals?
Each body's angular rate is 360 degrees divided by its period, so its reciprocal period is proportional to its angular speed. The relative angular speed is the difference of the two rates, and the synodic period is the time to accumulate one full relative revolution at that relative rate.
What if the two periods are equal?
If both bodies have the same orbital period, their relative angular rate is zero, so they never change configuration and the synodic period is infinite. This calculator flags that case rather than dividing by zero.
Can I use any consistent time unit?
Yes. Enter both sidereal periods in the same unit, such as days or years, and the synodic period comes out in that unit. The relation only involves reciprocals, so the result carries the same time unit you used for the inputs.
Official sources
- NASA: Basics of Space Flight, Orbital Periods.
- NASA Jet Propulsion Laboratory: Planetary Orbital Parameters.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.