# What is synodic

1. Jul 23, 2014

### Greg Bernhardt

Definition/Summary

Dealing with the apparent rotational or orbital period of an astronomical body with respect to another body or the period between successive oppositions or conjunctions.

Equations

$$\frac{1}{T_{syn}}= \frac{1}{T_1}-\frac{1}{T_2}$$

Extended explanation

An example of a synodic period is the synodic month, or the time it takes the Moon to go from full moon to full moon. When you start at one full moon, the Earth, Moon and Sun are in a straight line, with the Moon directly opposite the Sun. The next full moon will occur when the Moon is again opposite the Sun. In the time it takes the Moon 360° around the Earth once, the Earth itself has moved a few degrees in its orbit, making the Moon have to travel a few degree past 360° to realign with the Sun to produce the next full moon. This is why the synodic month is about 2 days longer than the sidereal month.

Conjunctions occur when two planets line up with the Sun on the same side of the Sun(or two moons line with their planet). The synodic period is the time between successive conjunctions. Again, since the outer planet will have traveled in its own orbit while the inner planet completes one orbit, the inner planet will have more than 1 complete orbit in order to catch up to the outer planet.

The synodic period is found by taking the reciprocal of the difference of the reciprocals of the sidereal periods of the bodies involved.

For example: Earth's sidereal period is 365.26 days and Mars' sidereal period is 686.98 days.

Thus the synodic period of Mars as seen from Earth is

$$\frac{1}{T_{syn}} = \frac{1}{365.26}-\frac{1}{686.98}$$

or 779.95 days.

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