Each cycle repeats itself for more than 1,000 years, and 5,000 years of data is now readily available on the Nasa website. For example, the next partial lunar eclipse occurs on June 4, 2012, covering a four-hour period around midday British Summer Time. It lies in a sequence starting in Elizabethan times and repeating itself for 1,370 years.
When did the Babylonians discover these remarkable cycles? No one quite knows. One expert thinks it was probably between 750 and 500 BC. Another suggested it might even have been back in the late Bronze Age. We don't know, but are on more certain ground about when the Babylonians came up with their explanation for this "Saros mechanism". As with any scientific discovery, explanations can be a long time coming — just ask Higgs.
Having discovered the Saros cycles, Babylonian astronomers — the Chaldeans of the Bible — continued making very careful observations, and they noticed a curious fact. The speed of the Moon's motion across the heavenly dome changes, and they measured its period from slow to fast to slow again, finding it was just under a month. This periodic anomaly — caused as we now know by the elliptic nature of the Moon's orbit — is called the anomalistic month, and they noticed that their Saros period of 223 lunar months was almost exactly equal to a whole number of anomalistic months. Very odd, but not much help because the speed of the Moon's motion turned out to be unrelated to the timing of eclipses. Science can be a frustrating business. One almost feels like giving up.
But the Babylonians didn't give up. They had been keeping astronomical records for 2,000 years, and what they needed were more measurements. Finally they found them. Although the Sun, Moon and planets all traverse the same path in the heavenly dome, there are slight differences. The Moon occasionally crosses the path of the Sun, and then crosses back again. The points of crossing are called nodes, and the time taken to return to the same node is called the nodical month. It was tough to measure without large equipment, but they eventually found that the Saros period was extremely close to a whole number of nodical months — the difference is less than one hour in over 18 years. And that was the solution to the Saros mechanism.
Lunar eclipses arise not only when the Moon is full, but when it's also at a node. Likewise for solar eclipses and new moons. Eureka! A solar eclipse arises when the Moon and Sun are at almost exactly the same point in the sky, and a lunar eclipse when they are almost exactly opposite. It's not enough for the Moon to be simply on the opposite side of the earth from the Sun. That yields a full moon, but to create an eclipse it needs to be dead opposite the Sun, and hence in the Earth's shadow. Conclusion: the Moon shines by reflected light.