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This was likely discovered by the ancients, somewhat forgotten in the middle ages and rediscovered during the Scientific Revolution.

Essentially since Ancient times man has been curious about the apparent movement of the Sun, Moon, and various stars across the sky, as well as the progression of the seasons.

With the idea that the earth was spherical (an idea that had been discovered by the Greeks, Romans and Mayans), one explanation was that the earth was fixed in the center of the universe and the earth, moon, and stars revolved around the earth.

The closest planets appear in the night sky as stars. But, their movement is different than the stars, and the ancients were able to identify all of the closest planets to earth, even without the help of telescopes.

By observing the movement of Mercury, Venus, Mars, Jupiter, and Saturn in the night sky, they were able to determine that their positions were best described by orbits around the sun rather than orbits around the earth. This coupled with the observations of the angle of the sun in the sky and progression of the seasons would also lead one to conclude that the earth also orbited around the sun at the rate of one revolution per year.

Once one concludes that the earth and all the planets in our solar system orbits around the sun, and the earth's orbital period is once a year, then one can conclude that the earth must rotate for the days to exist.

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