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What are the known relationships between rotation of planets/moons and their distance to Sun? Or any other known attributes? For example, the sidereal year for planets is directly related to their mass and their distance from the sun, but what about sidereal day? What are the known relationships for it?

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The length of the solar day is related to the sidereal day and the speed at which an object orbits the Sun, which in turn is dependent on its orbital radius.

The sidereal year is not related to the mass of the orbiting object. Any object at the same radius in a circle orbit will have the same year. It IS dependent on the mass of the central object, though. Objects orbit faster around a more massive object if orbital radius is held constant.

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