Synodic Period Calculator
Calculate synodic and sidereal periods for planetary motion and orbital mechanics
Calculate Orbital Periods
Select a planet to auto-fill orbital periods, or use custom values
Planet from which the synodic period is observed
Time for one complete orbit relative to stars
Sidereal period of the observing planet
Period Calculation Results
Formula: 1/Psyn = |1/Psid - 1/P₀|
Planet Position: Auto-detect or unknown
Period Analysis
Example Calculation
Mars Synodic Period from Earth
Mars sidereal period: 1.88 years
Earth sidereal period: 1.0 year
Mars is: Superior planet (farther from Sun than Earth)
Calculation
1/Psyn = |1/Psid - 1/P₀|
1/Psyn = |1/1.88 - 1/1.0|
1/Psyn = |0.532 - 1.0| = 0.468
Psyn = 2.14 years (≈ 780 days)
Solar System Periods
Types of Orbital Periods
Sidereal Period
Time for one orbit relative to distant stars
Synodic Period
Time between same relative positions as observed
Lunar Month
Moon's synodic period (29.5 days)
Tropical Year
Earth's solar year (season to season)
Understanding Synodic and Sidereal Periods
What is a Synodic Period?
The synodic period is the time interval between successive identical configurations of two celestial bodies as observed from one of them. For example, it's the time between successive oppositions of Mars as seen from Earth, or the time between consecutive full moons.
Key Differences
- •Sidereal: "True" orbital period relative to distant stars
- •Synodic: Apparent period as observed from a moving reference frame
- •Synodic periods depend on the relative motion of both objects
- •Important for predicting planetary alignments and conjunctions
Mathematical Relationships
1/Psyn = |1/Psid - 1/P₀|
- Psyn: Synodic period
- Psid: Planet's sidereal period
- P₀: Reference planet's sidereal period
For Inferior Planets:
1/Psid = 1/P₀ + 1/Psyn
For Superior Planets:
1/Psid = 1/P₀ - 1/Psyn
Note: Inferior planets (Mercury, Venus) are closer to the Sun than Earth. Superior planets (Mars, Jupiter, etc.) are farther from the Sun than Earth.