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Relating Synodic and Sidereal Periods

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Mathematical formula that relates a planet’s sidereal period to its synodic period.
Synodic and Sidereal Periods

Planet's synodic period – Time required for the planet to complete one complete orbit (Time that elapse between two successive identical configurations as seen from Earth).

Planet's sidereal period – Time between two successive identical configurations (True orbital period of a planet, the time it takes the planet to complete one full orbit of the Sun).

For inferior planets:
Orbit smaller than Earth's orbit (Example – Mercury, Venus)
For inferior planets
where:
P – Inferior planet's sidereal period
E – Earth's sidereal period = 1 year
S – Inferior planet's synodic period

For superior planets:
Orbit larger than Earth's orbit (Examples – Mars, Jupiter, Saturn)
For superior planets
where:
P – Superior planet's sidereal period
E – Earth's sidereal period = 1 year
S – Superior planet's synodic period
 
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