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While studying Spherical Astronomy, I came to know the two terms: 'Synodic Period' & 'Sidereal Period'. Both were referring to the returning of a particular celestial body on the sky or the celestial sphere but I couldn't spot the difference between the two definitions. What is the actual difference between the two periods and what is their importance?

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A planet is in opposition when it is on the opposite side of the sky from the sun, so it will be due south at midnight.

The synodic period is the (average) time between oppositions. Or, more generally, it is the time for a planet to reach a given position relative to the Earth. This latter definition can also be applied to the synodic period of Venus and Mercury.

The sidereal period is the time it takes (on average) for the planet to return to the same position relative to the stars. Because the stars are fixed, this is the same as the actual period of time for the planet to orbit the sun.

The periods are related by the formula $$1/P = 1/E \pm 1/S$$ Where S= synodic period, P= sidereal period and E=356.25 days=orbital period of the Earth, and you add for Venus and Mercury, but subtract for Mars and the outer planets.

James K
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  • So does this mean that the Earth doesn't have a synodic period? – Michael Sep 25 '22 at 22:35
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    No, the synodic period is always relative to observations made on Earth. So the Earth can't have a synodic period. You could ask for the synodic period of Earth as viewed from Mars, The synodic period of Earth from Mars is the same as the synodic period of Mars from Earth. – James K Sep 25 '22 at 22:37
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    "Synodic" does not, by definition, mean "as observed from Earth". An observer on the moon could easily define a synodic period for the Earth, likewise an observer on Mars could define synodic periods for its moons. – Greg Miller Sep 26 '22 at 13:14
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    Yes @greg you're right but that would make the answer needlessly less clear. In particular, you couldn't talk about the synodic period of Earth (or mars or any other ssb), you would always need to mention the observer. Michael asks about the synodic period of Earth. That isn't defined. So "Earth doesn't have a synodic period". But "Earth has a synodic period when observed from Mars, and a synodic period from Pluto and from Mercury. but there is no one number. Similarly when we say "the synodic period of mars" we imply "from earth" – James K Sep 26 '22 at 19:34
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If you think of the Sun, Earth, Moon system. The Earth orbits the Sun, and the Moon orbits the Earth. At a full moon, the bodies are essentially lined up, the synodic period is the average time to the next full moon, when they're lined up again (in the same order).

Now, if you ignore the Sun, and just think of the moon's movement relative to the Earth and stars. E.g. imagine every time the Earth, Moon, and Gemini are nearly lined up. This is the sidereal period.

Put another way, the sidereal period is measuring a period relative to the distant stars. And the synodic period is measuring the period relative to some other object.

Greg Miller
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