Synodic Period Calculator Formula

Understand the math behind the synodic period calculator. Each variable explained with a worked example.

Formulas Used

Synodic Period

synodic_period = abs(1 / (1 / period1 - 1 / period2))

Synodic Period (years)

synodic_years = abs(1 / (1 / period1 - 1 / period2)) / 365.25

Variables

VariableDescriptionDefault
period1Inner Body Period(days)365.25
period2Outer Body Period(days)687

How It Works

Synodic Period

The synodic period is the time between identical relative configurations of two orbiting bodies.

Formula

1/P_syn = 1/P1 - 1/P2

where P1 and P2 are the sidereal orbital periods.

Worked Example

Find the synodic period of Mars as seen from Earth.

period1 = 365.25period2 = 687
  1. 011/P_syn = |1/365.25 - 1/687|
  2. 02= |0.002738 - 0.001456| = 0.001282
  3. 03P_syn = 1/0.001282 ≈ 780 days ≈ 2.14 years

Frequently Asked Questions

What does synodic period mean practically?

It tells you how often a planet returns to the same position relative to Earth and the Sun, like how often Mars is at opposition.

Why is it different from the sidereal period?

The sidereal period is measured against fixed stars. The synodic period accounts for the observer also moving in orbit.

Does this work for moons?

Yes, for any two bodies orbiting the same central body.

Ready to run the numbers?

Open Synodic Period Calculator