Sidereal-to-Synodic Converter Formula

Understand the math behind the sidereal-to-synodic converter. Each variable explained with a worked example.

Use the Sidereal-to-Synodic Converter

Formulas Used

Synodic Period

synodic_period = abs(1 / (1 / sidereal_period - 1 / earth_period))

Synodic Period (years)

synodic_years = abs(1 / (1 / sidereal_period - 1 / earth_period)) / 365.25

Variables

VariableDescriptionDefault
sidereal_periodPlanet Sidereal Period(days)224.7
earth_periodEarth Sidereal Period(days)365.25

How It Works

Sidereal and Synodic Periods

A planet's sidereal period is its true orbital period. Its synodic period is how long between repeated alignments as viewed from Earth.

Formula

1/P_syn = |1/P_planet - 1/P_Earth|

Worked Example

Venus has a sidereal period of 224.7 days.

sidereal_period = 224.7earth_period = 365.25
  1. 011/P_syn = |1/224.7 - 1/365.25|
  2. 02= |0.004451 - 0.002738| = 0.001713
  3. 03P_syn = 1/0.001713 ≈ 583.9 days

Ready to run the numbers?

Open Sidereal-to-Synodic Converter