HOW DID THE ANCIENTS PREDICT ECLIPSES? THE SAROS CYCLE

 From -  Sky & Telescope

 By - Fred Espenak

 Edited by - Amal Udawatta

This clay cuneiform tablet records lunar eclipses between 609 and 447 BC. The Babylonians also recorded solar eclipses.
© The Trustees of the British Museum

Before the advent of computers or even a working theory of the solar system, the ancients predicted solar eclipses. How did they do it?

Today's astronomers use electronic computers and mathematical models to calculate the motions of the Sun and the Moon. This information can then be used to predict when solar (and lunar) eclipses take place. But the ability to predict eclipses goes back more than 25 centuries ago. This is long before the advent of computers or even Copernicus's heliocentric theory needed to understand the motions of the Sun and the Moon.

So how could ancient civilizations foresee the occurrence of eclipses? They used a clever idea called the Saros cycle.

In a previous post “How Rare is a Total Solar Eclipse?”, I described the two conditions required for a solar eclipse:

1) The Moon must be in its new phase.

2) The Moon must be near one of its two orbital nodes (the points where the Moon’s orbit crosses Earth’s orbit around the Sun).

These conditions are related to two ways of measuring the lunar month. The synodic month (which follows the cycle of the Moon through its phases) has an average length of 29.53 days. The draconic month (which follows the cycle of the Moon through its two nodes) has an average length of 27.21 days. (For a detailed explanation of how these periods vary, see “Eclipses and the Moon's Orbit.”

After one solar eclipse takes place, the next one will occur in some combination of synodic and 1/2 draconic months (because a solar eclipse can occur at either node). A check of a solar eclipse catalog reveals that the interval between any two solar eclipses is either 1, 5, or 6 synodic months.

But none of these intervals repeats on a regular basis to permit the prediction of future eclipses. For instance, the number of synodic months between the most recent solar eclipse on October 14, 2023, to one six years down the line, on December 5, 2029, is: 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5, 1, 5. No repeatable pattern is present over this interval.

Solar eclipses from 2022–2041 are plotted to show the intervals between each eclipse. The general grouping of eclipses approximately every six months reveals eclipse seasons. This pattern is repeated after one saros cycle (18 years 11 days 8 hours).
Courtesy of "Totality: the Great North American eclipse of 2024," by Mark Littmann and Fred Espenak, Oxford University Press, October 2023

However, if we expand our search to longer intervals, we will eventually make an astonishing discovery: It turns out that 223 synodic months (6,585 days, 7 hours, and 43 minutes) is very nearly equal to 242 draconic months (6,585 days, 8 hours, and 35 minutes). The difference between these two intervals is just 52 minutes over a period of 18 years, 11 days, and 8 hours! This is known as the saros cycle.

If we take the eclipse date of Oct. 14, 2023, and add one saros cycle to it, we get Oct. 25, 2041. A check of the eclipse catalog above confirms there is indeed a solar eclipse on that date. Add another saros to this date to get Nov. 5, 2059, and again there is an eclipse on this date. The biggest difference between these three eclipses is the extra 8 hours (beyond a whole number of days) in each saros cycle. Also note that because Earth rotates an additional 120 degrees between each eclipse, the eclipses are visible from different geographic regions.

There is another important lunar cycle to consider regarding eclipses. The Moon's orbit around Earth is elliptical. The average time it takes the Moon to travel from perigee, where it’s nearest to Earth, to apogee, farthest from Earth, and then back to perigee again is 27.55 days. This is known as the anomalistic month. It’s important because the Moon’s distance from Earth determines whether a central eclipse is annular (such as the one that just occurred on October 14th) or total (such as the one coming up on April 8, 2024).

By a remarkable coincidence, 239 anomalistic months is nearly equal to 223 synodic months, the length of the saros — it differs by just 5 hours and 11 minutes. This means that two eclipses separated by one saros will occur with the Moon at very nearly the same distance. If the first eclipse is total, the next one, one saros later, will (in most cases) also be total. The same holds true of annular eclipses.

During the next saros cycle (that is, the 18 years, 11 days, and 8 hours between October 2023 to October 2041), there will be 40 solar eclipses. Each one belongs to its own “family,” in which each member is separated from the next by one saros cycle. Each family is identified by a series number. For instance, the total eclipse of April 8, 2024, is a member of Saros 139.

There are some subtleties to all of this. First, while the durations of the three lunar months that occur in one saros cycle are very close, they are not equal. The small differences add up when going hundreds of years into the future or the past. A consequence of the 52-minute difference between the synodic and the draconic periods in the saros is that the Moon shifts about 0.5 degrees west with respect to the Moon's orbital node with each successive saros cycle.

Also, the 5-hour, 11-minute difference between the draconic and anomalistic months in the saros means the Moon's distance will gradually change between each member within a saros series — at some point the series could change from total to annular or vice versa.

A saros series typically lasts 12 or 13 centuries and contains 70 or more eclipses. Each series begins with about 10 partial eclipses at high latitudes. It slowly evolves to produce to 40 to 50 central eclipses (total, annular, or hybrid). The series eventually ends with about another 10 partial eclipses.

A world map shows the path of nine solar eclipses from 1901 to 2045. They are all members of Saros 136, so the interval between each eclipse is 18 years 11 days 8 hours. The 8 hours in the Saros cycle shifts the path of each succeeding eclipse by about 120 degrees in longitude. The shift in latitude of each eclipse is due to the change in the Moon's distance from its orbital node.
Diagram courtesy of the “Five Millennium Canon of Solar Eclipses”

THE SAROS AND THE ANCIENTS

Babylonian astronomers discovered the saros cycle around the 7th or 8th century B.C. They were keen observers and kept meticulous records of astronomical events for hundreds of years on clay tablets. This allowed them to recognize the saros pattern in both solar and lunar eclipses. They used the saros to predict future eclipses, which they also recorded on clay tablets.

The Babylonian prediction of eclipses was much more than an academic pursuit. A common Mesopotamian belief was that the gods used eclipses as omens to foretell future events. Lunar eclipses, in particular, were thought to portend the imminent death of a king. But the consequences of such celestial signs were avoidable, especially if the eclipse was predicted in advance. The king would abdicate his throne briefly, while one of his subjects was substituted in his place. After the danger of the eclipse has passed, the unfortunate substitute was killed, and the king could then safely resume his royal position.

Modern astronomers no longer rely on the saros to predict eclipses. They use sophisticated mathematical models, known as astronomical ephemerides, to predict the positions of the Sun and the Moon and thereby can predict eclipses thousands of years into the past and future. Nevertheless, the saros remains a simple and useful tool to understand the repetition of solar and lunar eclipses.