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Physics - Formulas - Synodic and Sidereal Periods

One of the many tools used in Astronomy are the formulas used to determine Orbital Motion. There are two basic forms of orbits:
  • Sidereal Period
  • Synodic Period

Sidereal period, as indicated by the accuracy of sidereal time, is an actual measure of a complete orbit relative to the stars (since the stars are unmoving - or at least moving very slowly). A synodic period is a rotation of a planet so that it appears to be in the same place in the night sky.

We have two formulas that will allow us to determine the sidereal rotation period of the other 8 planets in our Solar System by using the synodic period (simply by observation).

For the planets Venus and Mercury, we would use:

For Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto we would use:

P = sidereal period in both equations
S = synodic period in both equations
E = Earth's orbit in both equations.

Because Earth's rotation is 1 year, E = 1 in both equations.

Here is an example, based on the reference text:

To find the sidereal period of Jupiter:

P = sidereal period
E = 1
S = 1.092 years (the observed synodic period)

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