Synodic Period Calculator Formula

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

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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

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