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This question already has an answer here:

I would like to know when Europe obtained the ability to predict lunar and solar eclipses.

I remember reading about some story, where Columbus or someone like that used an eclipse chart to convince the native Indians that he was a god. This would imply that Europe had the ability somewhere around the year 1500, which seems pretty early to me. I would've thought It would have to wait until Keplers Laws at least.

However, I want to be more exact than that. When did they start reliably making predictions without any misses? It would be nice to know which European nation did this first, and how fast it spread around Europe and the world.

If some other region did this first, I would love to know about it too.

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marked as duplicate by Alexandre Eremenko, Michael Weiss, HDE 226868 Apr 28 '16 at 22:02

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It did not happen quite the way you imagined. The first accurate theories of solar and lunar motion in Europe are due to the father of astronomy Hipparchus (c. 190 – 120 BC), over millenium and a half before Columbus. They were geocentric and did not require Kepler's laws or any laws of dynamics, only geometry. But Hipparchus got his data from Babylonians, who could make accurate predictions of eclipses for centuries before that without even kinematics. What it required was careful observations and discerning subtle periodic patterns in the movements of the Sun and the Moon. Later Maya managed to do the same independently by a similar approach, see How accurate are Mayan astronomical "ephemerides"?

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This question makes no sense as stated.

a) There is a huge difference between solar and lunar eclipses in this respect. (Lunar eclipses occur everywhere, while Solar eclipses only on a small area on the Earth). For this reason, a solar eclipse is much harder to predict for a given location.

b) The accuracy of prediction improved slowly with the development of astronomy. So "Predict accurately" needs much further specification.

c) Predict how much in advance?

d) Most solar eclipses are incomplete: only a part of the Sun is obscured. This can be a very small part on a given location.

Prediction of Lunar eclipses was possible already with Babylonian astronomy. Reliable prediction of solar eclipses for a given location few years in advance became possible only in the middle of 18th century when Lunar theory was fully developed. But there are reliably recorded cases when a lunar eclipse was predicted using ancient Babylonian methods. These cases happened in 18s and 19s century when predictions were made by Tamil (in India) astronomers using Babylonian methods, and recorded by French and English travelers.

But one cannot predict a solar eclipse reliably (for a given location) with these methods for the reasons I explained above.

By the way, Kepler laws have little to do with the problem. For the Moon, Kepler laws give only a crude approximation, comparable in accuracy to what Ptolemy already knew. The reason is that the system Earth-Moon-Sun is a three body problem, while Kepler's law is a solution of a two body problem. It is good for planets. But gives a very rough approximation for the Moon. Good theory of the Moon motion (sufficient for reliable solar eclipse prediction) was developed only in the middle of 18th century.

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