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By identifying patterns in the periodic movements of the sun, moon, and Earth, ancient civilizations realized that identical eclipses repeat about once every 6,585 days, known as the saros cycle.

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Additional insights we found via Astronomy Magazine
The Chaldeans—an ancient Mesopotamian civilization—were familiar with the saros cycle by the seventh century BCE and used it to predict lunar and solar eclipses, a method the Greeks also knew by the second century BCE.
Just as there is always a common multiple between several numbers if one counts high enough—such as 12 being a common multiple of 2, 3, and 4—saros cycles exist because every geometric configuration that produces an eclipse is the result of an alignment of various orbits, which repeat over and over and must eventually align once more.
Because eclipses are viewable from different locations on Earth, there exist many saros cycles, one for each ecliptic configuration.
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