Humans have been predicting eclipses for thousands of years, but it’s harder than you might think

The coastal town of Exmouth in Western Australia is due to experience one of the most spectacular astronomical phenomena on April 20 2023 – a total solar eclipse.

Eclipses have entranced us for millennia. But it turns out calculating exactly when and where we can watch an eclipse in its full glory can be surprisingly hard.

Watching the Sun and the Moon

Being so dominant in the sky, the Sun and the Moon were the most captivating celestial bodies for ancient cultures to observe. Naturally, they also tried to anticipate and predict their motions.

While the Sun’s movement is quite simple, the Moon moves across the sky with much more complexity. For one thing, it has phases; it also grows and shrinks in apparent size as it travels on an elliptical orbit around Earth.

On top of this, the Moon appears to rock and wobble quite haphazardly on its journey across the sky, making it extremely challenging to accurately describe its orbit. In fact, explaining the Moon’s motion was the only problem that made Isaac Newton’s head hurt.

Since eclipses are so startling to witness, many ancient peoples both noted their occurrence in writing and art, and discovered the repeating characteristics of such events.

During a lunar eclipse, where Earth blocks sunlight that would otherwise illuminate a full moon, the dimmed Moon takes on a bloody hue. Many cultures attached foreboding to such events (like the partial lunar eclipse seen during the Fall of Constantinople in 1453) and quite reasonably wondered when the next such event might occur.

The not-so-mythical Saros cycle

Various cultures around the world have independently discovered eclipses seem to occur on an 18-year cycle. It was mentioned in written records by the Babylonians and Assyrians (of ancient Mesopotamia and modern Iraq), and oral tradition suggests the cycle was used for ceremonial purposes by Torres Strait Islanders in what is now Australia.

This 18-year cycle, which can persist as a sequence for over a thousand years, is now known as a Saros cycle. The word “Saros” was referenced in the 10th-century Byzantine Suda encyclopedia, and possibly has a Greek origin (“saro” meaning “sweep”, perhaps relating to how eclipses sweep across the sky).

The Saros cycle represents how long it takes for the Sun-Earth-Moon system to return to almost exactly the same triangular configuration. So, if you see a lunar eclipse, you can expect another one 18 years later, visible from most places on Earth.

If you were an ancient culture that happened to observe a total solar eclipse, you would have been very lucky indeed (they occur roughly every 375 years at a given region on Earth). But would you have seen a similar event 18 years later? Alas, no. While there probably was another total solar eclipse 18 years later, it would have been over a completely different part of the planet.

After 54 years – three Saros cycles – the eclipse region should have returned to roughly the same position on Earth. But only very roughly, as it could be thousands of kilometres away from the previous observation spot.

Worldwide, there is a total solar eclipse visible somewhere roughly every 18 months during one of two possible “eclipse seasons” per year. This is much more frequent than an 18-year Saros cycle, and is possible because multiple repeating Saros sequences overlap at once (roughly a dozen), each offset by at least six months. For example, the 2028 total solar eclipse that will be visible in Sydney is part of an entirely different Saros sequence than this year’s eclipse.

After about a thousand years, when one long-term Saros sequence ends, another will begin with slightly different timing.

From antiquity to modern day

So could our ancient ancestors actually predict eclipses? Yes, if we are talking about lunar eclipses, and perhaps even partial solar eclipses.

A famous predictive example is the Eclipse of Thales in 585 BCE, although the fact that a total solar eclipse happened over Greece was almost certainly more luck than science. That is, they wouldn’t have predicted that 18 years later (567 BCE) a total solar eclipse was visible in what is now the United States.

It is likely the famed Greek Antikythera Mechanism, an astoundingly complicated 2,000-year-old mechanical device that was used to predict the night sky, could calculate the 18-year Saros accurately. But significantly, it could not predict total solar eclipses at a precise place on Earth – just their timing.

The Saros period (marked with a red rectangle) is visible on a fragment of the ‘user manual’ of the Antikythera mechanism. Xmoussas/Wikimedia Commons, CC BY-SA

In summary, it is clear ancient people could predict timings for lunar eclipses and partial solar eclipses, but there is no convincing evidence of people predicting the times and locations of total solar eclipses.

The path of the eclipse as described by Halley in 1715. University of Cambridge, Institute of Astronomy Library

Entering the modern era of science, the first true prediction of a total solar eclipse (both in time and location) occurred in 1715. Edmond Halley (of comet fame) correctly predicted, to within four minutes and 20 miles, a total solar eclipse that rather conveniently passed over his own house in London. He did this by making full use of Isaac Newton’s new theories of gravity and orbital mechanics: the Principia.

Today, we don’t rely on calculating the orbits of the whole Solar System to predict eclipses. For example, NASA uses a highly advanced form of an ancient technique – pattern recognition. Using some 38,000 repeating mathematical terms, NASA can predict both solar and lunar eclipses for 1,000 years into the future. Beyond that, the Moon’s wobble and Earth’s changing rotation make eclipse prediction less accurate.

So for those of you lucky enough to witness a total solar eclipse this month, take a moment to think about what this shared experience has meant to humans around the world for thousands of years.

Trying to predict and explain this phenomenon has directly driven advancements in mathematics and orbital mechanics, and with its beauty we have been forced to embrace the limits of our scientific knowledge.

Authors: Aaron Robotham

Research Associate Professor & UWA Research Fellow, The University of Western Australia

Sabine Bellstedt 

Research Fellow in Astronomy, The University of Western Australia

This article is republished from THE CONVERSATION under a creative common licence. You can find the original article here: humans-have-been-predicting-eclipses-for-thousands-of-years-but-its...

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QS based on this:

Q: Who first predicted eclipses?

K: The eclipse of Thales was a solar eclipse that was, according to ancient Greek historian Herodotus, accurately predicted by the Greek philosopher Thales of Miletus. If Herodotus' account is accurate, this eclipse is the earliest recorded as being known in advance of its occurrence. Many historians believe that the predicted eclipse was the solar eclipse of 28 May 585 BC. How exactly Thales predicted the eclipse remains uncertain; some scholars assert the eclipse was never predicted at all. Others have argued for different dates, but only the eclipse of May 585 BC matches the conditions of visibility necessary to explain the historical event. (1)

While doubt has been cast on the truth of the story, there are other accounts of it besides that of Herodotus. Diogenes Laërtius says that Xenophanes, who lived in the same century as Thales, was impressed with the prediction, and he also gives additional testimonies from the pre-Socratics Democritus and Heraclitus. Cicero mentions that Thales was the first man to successfully predict a solar eclipse during the reign of Astyages, the last king of the Median empire.Pliny the Elder mentions as well that Thales had predicted a solar eclipse during the reign of Alyattes of Lydia. At the time of Thales' purported prediction it was not yet known that eclipses were caused by the Moon coming between the Earth and the Sun, a fact that would not be discovered until over a century later by either Anaxagoras or Empedocles. If the account is true, it has been suggested that Thales would have had to calculate the timing of any eclipse by recognizing patterns in the periodicities of eclipses.  It has been postulated that Thales may have used the Saros cycle in his determination, or that he may have had some knowledge of Babylonian astronomy. However, Babylonians were far from being able to predict the local conditions of solar eclipses at that point, which makes this hypothesis highly unlikely. In fact, there is no known cycle that can be reliably used to predict an eclipse for a given location and, therefore, any accurate prediction would have been down to luck during ancient times.

The TIFR paper on eclipses in ancient India (2) says: 

The earliest description of a solar eclipse can be found in the Rig Veda, the oldest document from
India dated to between 1700 and 1400 BC (Subbarayappa 2008; Sarma and Subbarayappa, 1985).
In later literature, dated to between 900 and 600 BC, a more detailed description of the phases of
an eclipse can also be found. However, these details are not accompanied by calendrical details
and hence it is not possible to date them. The eclipses are explained through the existence of a
body-less head of Rahu who tried to eat up the Sun and the Moon due to an enmity to them
(Damle, 2011). In 499 AD, Aryabhata gave a formal theory of eclipses based on the transit of Moon
between Earth and Sun and in the shadow of the earth. In India, eclipses are considered occasions
when the gods are in trouble because the Sun or the Moon is eaten up by Rahu and hence large
donations are common at the time of eclipses. These donations are often recorded on stone or
copper plate inscriptions along with the date and place of donation. A fraction of these are
catalogued in various records of the Archaeological Survey of India. We have scanned them and
found record of more than a thousand records dated to between 400 AD and 1800 AD. They make
a useful database for systematic studies of ΔT (Soma and Tanikawa, this volume) as well as other
possible causes of perturbations in earth’s rotation (2).

The paper uses the word  'descriptions' but not 'predictions' like many people claim.

In determining and predicting eclipses, it is important to determine the true instantaneous motion of the planets or stars at any given moment. Tat-kalika-gati or instantaneous calculation of motion , was probably first mentioned and used by Aryabhatta, Brahmagupta, and Manjula around 1200CE, Bhaskara (1114 to 1185CE)  figured out formulas involving differentials, using Chakravala method, which is defined as a cyclic method used to solve indeterminate quadratic equations. 

Footnotes:

1. https://en.wikipedia.org/wiki/Eclipse_of_Thales#:~:text=Thales'%20prediction,-While%20doubt%20has&text=Cicero%20mentions%20that%20Thales%20was,reign%20of%20Alyattes%20of%20Lydia.

2. https://www.tifr.res.in/~archaeo/papers/Others/Eclipses%20in%20Anci...