This quotation from the gospel of Luke (quoted from the New English Bible) describes one of the most momentous celestial events in history, for it reportedly occurred at the time of Jesus Christ’s death. Whether or not this is an accurate account, or a literary embellishment, it well illustrates the deep significance that all ancient cultures have attached to solar eclipses.

When the Moon passed across the face of the Sun on August 11, 1999, the event was watched avidly by tens of millions of people all over Europe and the Middle East. Some saw it as a millennial sign, others expected miracles, while the majority simply enjoyed this natural spectacle. It happens that eclipses repeat on a regular cycle, with gaps of 18 years plus 10 or 11 days. The next one in that particular sequence, occurring on August 21, 2017, will sweep its path of totality across more than a dozen of the United States, the first total solar eclipse to visit North America for 38 years (although Hawaii got one in 1991). If you can’t wait that long, there are several opportunities elsewhere-such as in southern Africa and Australia at the end of 2002—but you would

need to travel in order to experience the unique feeling such an event evinces.

Total solar eclipses always generate huge interest from the general public. Partly this reflects a deep-seated mystical appeal that attaches to these astronomical phenomena, partly it is because of their sheer aesthetic beauty. The glaring solar disk that is so familiar to us swamps the weak light from the tenuous gas that envelops the Sun. Only during an eclipse is the delicate tracery of this material revealed, in the form of the solar corona. For a few precious minutes the sky is suffused with the eerie coronal glow, a sight that must have struck awe and terror into the hearts of our ancestors.

In astronomical terms, however, an eclipse is a perfectly straightforward affair. By a strange coincidence, the angular sizes of the Sun and Moon as viewed from Earth are almost exactly the same. The Sun is, of course, a much bigger body, but located a lot farther away. If the Moon’s orbit around the Earth were in the same plane as the Earth’s orbit around the Sun, eclipses would occur every month, but because the orbital planes are tilted obliquely relative to one another, only rarely do the Earth, Moon, and Sun stand in alignment. Even when that happens, the Moon’s shadow projected onto the Earth’s surface is so small that, at any given spot, total eclipses can be hundreds of years apart. For example, before 1999 the last one to occur anywhere in mainland Britain was in 1927; preceding that, one has to go back to 1715 and 1724. Now there’s not another one due to visit those islands until 2090. This rarity factor adds considerably to the sense of excitement.

There is no simple formula to predict the dates of eclipses, and it took heroic effort on behalf of priests and astrologers to

figure out when they were likely to occur. It is a testimony to the enormous supernatural significance bestowed upon eclipses by early cultures that the complex mathematical rules were worked out independently so many times. From the Mayas to the Sumerians, from the Egyptians to the Chinese, algorithms were devised to foretell the next time the Sun would be gobbled up and the sky would go dark in daytime.

These early attempts to predict eclipses amounted to no more than fitting cycle times to observations using trial and error. No physical understanding lay behind them. By the seventeenth century, however, Isaac Newton had formulated his laws of motion and gravitation, and the prediction of eclipses became a classic application of Newtonian physics. At last human beings could comprehend why solar and lunar eclipses happened when they did. Today, with computer models of planetary motion, the dates for future eclipses can readily be worked out for millennia ahead. Conversely, astronomers can “retrodict,” and find out when eclipses occurred in history. In turn, this can be checked against ancient records, allowing history and astronomy to confirm each other.

Historically, solar eclipses have provided ideal opportunities for scientists to study a range of phenomena besides the spectacular corona. For example, by timing the exact moment of transit, the Moon’s position can be measured to very high precision. Although the Moon orbits the Earth in a roughly elliptical path, there are small variations, such as a very gradual drift away from Earth. It is important for astronomers and geophysicists to understand these corrections. Today, better measurements can be made using laser ranging.

One of the most famous scientific uses of a solar eclipse occurred on May 29, 1919. Four years before, Albert Einstein had

published his general theory of relativity, which explains gravitation in terms of a warping or curvature of space-time. Among the various manifestations of these geometrical distortions is a minute “spacewarp” around the Sun. In effect, the Sun’s gravitational field acts like a lens, slightly bending light beams that pass close to the solar surface. Einstein computed that a star beam might be deflected in this way by up to 1.75 seconds of arc, thus displacing the apparent position of the star in the sky when it is located close to the Sun along our line of sight. This is actually a very tiny shift, though measurable with a good telescope. Unfortunately, the Sun’s glare prevents us from observing stars in the daytime, but during a total solar eclipse, the stars become visible. The British astronomer Sir Arthur Eddington went on an expedition to the island of Principe off Spanish Guinea in Africa, with the express purpose of testing Einstein’s prediction. The results brilliantly vindicated the general theory of relativity, and more than anything else served to propel Einstein to international fame. For some decades, this “bending of light” measurement constituted one of only three firm tests for the theory, which is regarded by many as the intellectual triumph of the twentieth century.

Today, solar eclipses have somewhat less scientific value than in the past, but they still attract an enormous amount of attention, not just from keen astronomers, but also from the public at large. Some people are so inspired by observing a total eclipse that they will travel thousands of miles to see another. Although this unique astronomical phenomenon is a consequence of the normal cycles and rhythms of the Solar System, and need no longer be feared as a bizarre supernatural sign, the splendor and spectacle of the event ensures that the popularity of solar eclipses will never wane.

Paul Davies

Total solar eclipses are so infrequent one might say they happen “once in a blue moon.” That phrase is used colloquially to imply something seldom occurring, but here the allusion is a mixed metaphor: eclipses, of course, involve the Moon, and it looks pretty black when obscuring the Sun during such an event.

How often does a blue moon occur? That’s an impossible question to answer, because there are several distinct—even contradictory—meanings for the phrase. This is something we’ll discuss in detail later, but for the present let us assume the modern definition of two full moons within a single calendar month. Full moons occur about 29 and a half days apart, so you could get two within a 30-day month, but this is much more likely in a 31-day month. It is quite straightforward to show that a blue moon, according to that definition, happens about once every 32 or 33 months, on average.

Now, how does that compare with the frequency of eclipses? In fact there are at least two eclipses every year, and there may be up to seven, but that includes lunar as well as solar eclipses, the majority being partial events (incomplete shadowing). Total solar eclipses occur somewhere on Earth on average once per 18 months, but very often they happen over the oceans or the poles. Half of the eclipse tracks might cross some populated land, so that the

frequency of potential visibility is typically once per 36 months (unless you are keen enough to take a trip to the Antarctic to catch one).

Even that is less than the blue moon frequency, but more pertinent is how often a total solar eclipse track traverses a particular location on our planet. How long do you need to wait until one of these visits your city and state? The answer is that a random location on the Earth is graced by such an event once every four centuries, once every five or six human lifetimes. Blue moons happen all the time, compared to that.

Blue moons can tell us something else about eclipses and their frequency. The year 1999 was unusual for several astronomical reasons, such as an eclipse over Europe (discussed below), a transit of Mercury across the face of the Sun, and the recurrence of the great Leonid meteor shower. It was also a double blue moon year. Because February had only 28 days, it happened to have no full moon in 1999, whereas the adjacent January and March had two each.

Now step forward a few decades. Calculations show that in both 2018 and 2037 we may anticipate double blue moons, again in January and March. One immediately notices that there are 19-year gaps. Full moons are spaced by lunar months. Counting up those months, there are 235 in each interval.

Looking backwards, 1961 was a double blue moon year. With this information in hand you might bet that 1980 was also a double blue moon year, but it was not: only March contained two full moons. A clue as to why that was the case comes from the fact that 1980 is divisible by four: it was a leap year. Our sequence of 19-year gaps between double blue moon occurrences was upset by the way we choose to correct for the length of the solar year not

being an exact number of days long. That is, a period of 19 solar years is close to 235 lunar months long, but any particular 19 calendar years will vary by a day because there can be either four or five leap years contained therein. In 1980 a full moon slipped out of January into the lengthened February.

This period of 19 solar years or 235 lunar months is called the Metonic cycle. The Christian churches use it to calculate the dates of Easter; Judaic clerics employ it to define the Hebrew calendar; and many other cultures frame their annual rounds with the Metonic cycle as their basis. The cycle gives us a handle on when blue moons may occur, a mere curiosity. More significantly, it allows eclipses to be predicted.

The total solar eclipse in 1999, on August 11, was eagerly awaited. It was the first to cross any part of Britain for 72 years. After touching down in the Atlantic near Newfoundland, the track of totality proceeded eastwards to the southwestern tip of England where I (along with many others) was waiting for it. The Moon’s shadow then swept onwards across France, Germany, several eastern European countries, Turkey, the Middle East, Pakistan, and India, before eventually petering out in the Bay of Bengal. Millions and millions of people experienced its effects, many having traveled around the globe knowing full well what was to happen. Looking up the tables, there were also eclipses on August 11, 1961 and August 10, 1980 (the leap year upset the date again), and another is due on August 11, 2018. Obviously the Metonic cycle produces some eclipse regularity. In this book we will see that there are also several other systematic features of eclipses, allowing their prediction by knowledgeable people. Nowadays that information is easy to find, but step back a few centuries or millennia, when eclipses were viewed variously as augurs of ill or harbingers

of good fortune: the ability to prophesy eclipses would surely have brought great power and influence. Eclipse dates are clearly intertwined with the calendar—to a surprising extent, we will discover.

Herein I describe not only solar and lunar eclipses (and their celestial brethren such as transits and occultations by planets, comets, and asteroids), but also the great influence these events have had upon the advance of civilization. Knowing when eclipses were due enabled more scientific societies to gain an advantage over others, a matter discussed in the opening chapter. To appreciate how these cosmic events could be predicted by the ancients, long before Nicolaus Copernicus described how the planets orbit the Sun, or Sir Isaac Newton expounded his law of gravity, one needs to understand the cycles and systematics of eclipses, matters discussed in detail in the Appendix. Some may find this heavy going (although it involves only simple arithmetic), and that is why it appears at the end. If you really want to comprehend the astronomical cycles involved, read the Appendix first. For most readers, though, the information in the opening chapters will be sufficient. After that we delve into the cultural and scientific importance of eclipses, in the distant and nearer past, and the future.

Now some words about my sources of information. Many of the eclipse computations used, plus the map shown as Figure 2–5, are derived from the excellent Internet site of Fred Espenak, who works at NASA-Goddard Space Flight Center in Greenbelt, Maryland. Anyone who wants to know more is strongly recommended to take a look at Espenak’s pages, making a start at: http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html

In the age of the Internet, I have accessed several hundred web sites in preparing this book. Especially because so many of these are ephemeral, there is no point in listing them. Similarly I

have made use of some dozens of books to obtain information, to greater and lesser extents. Any interested reader will easily find a multitude of popular-level books and magazine articles dealing with various aspects of eclipses. A few are listed among the picture credits near the end of this volume. A core subject here is the cause of eclipses and their cycles, as described in the Appendix but with related considerations being scattered throughout the text. This is not a matter often treated in books suitable for the non-specialist. Therefore I mention here that my description is based largely on the detailed analysis that appears in the book Eclipses of the Sun and Moon by Frank Dyson and Richard Wooley, published by the Clarendon Press, Oxford, England, in 1937.

Many people have kindly answered questions for me, or helped me with photographs and other illustrations. In particular I would like to mention Graeme Waddington, Tony Beresford, John Hisco, Fraser Farrell, David Asher, Bill Napier, Brian Marsden, Daniel McCarthy, Peter Davison, John Kennewell, Alain Maury Philippe Veron, Leslie Morrison, Steven Bell, Jim Klimchuk, and Paul Davies.

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