Saturn doesn't really have months like we do on Earth. Our month is based on the amount of time it takes the moon to orbit. Saturn has over 60 moons, so they don't really have any one reference to base a month on.
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The "month" is purely a human invention. The "day" and the "year" are both marked
by natural processes ... the "day" is linked to light and dark, and the "year" is linked
to the cycle of the seasons. In ancient times, the month was intended to be linked to
the cycle of the moon's phases, but it got disconnected from the moon, and we don't
worry about that at all anymore. The month is just something we keep on the calendar
and is no longer connected to any natural occurrence. Our months don't even have the
same lengths.
Since Saturn rotates on its axis and orbits the sun, you might say that it has a
natural day and a natural year. But there's no reason to expect that it has a
month. Even if you wanted to use moon phases to define months, that would
be a real problem, since in Saturn's case, we have already discovered more than
sixty moons, all with different periods.
A month on Saturn is equal to about 29.5 Earth years, so it doesn't have a fixed number of days like we do on Earth.
The sun does not orbit Saturn. Saturn orbits the sun.
It takes Saturn 29.45 years to orbit the sun or 10,759 days. Saturn is similar to Earth in that its axis is at a tilt and goes through four seasons.
On average, a month has about 2,592,000 seconds (30 days x 24 hours x 60 minutes x 60 seconds).
One Saturn day is approximately 10.7 Earth hours, so about 0.45 Earth days.
Uranus which has an orbital period of 84.016846 years which is 30,687.153 days.