In almost all ancient cultures and societies without writing, a prodigious phenomenon such as an eclipse of the Moon, and more of the Sun, has been reported to a supernatural cause, the intervention of a god, a demon or an evil genius threatens to turn off both lights. A fatal event we usually attempt to stave forcefully with magic formulas to prevent the Moon or the Sun to be eaten forever. In Asia, a celestial dragon was supposezd to be responsible for eclipses (the oldest Chinese word for eclipse, shih, means "eat"). In India, it was Rahu and Ketu, the two parts of a Demon beheaded by Vishnu corresponding ,respectively to the ascending and descending nodes of the Moon when the eclipses occur, seeking to devour the Moon and the Sun. Long in the Western countries, astronomers designate these two nodes that make a complete revolution of the zodiac in 18 years and 6 months under the name Caput Cauda Draconis (Head and Tail of the Dragon). In America, from Canada to Peru through Mexico, and even in Africa, it was such mythical animal or that demon who threatened to eat either the Moon or the Sun. About ancient Greece, it was no exception to the rule. According to Democritus (460-370 before J.C.), eclipses of the Moon and of the Sun were among the terrifying celestial events making men believing that the gods were the perpetrators .
According to a legend firmly established, Thales of Milet (VIth century before J.-C.) would be released very early from the belief in the divine causality of eclipses. In fact, according to the Greek historian Herodotus (about 484-425 BC), Thales had predicted to the Ionians an obscuration of the the Sun "for the year in which it occurred" (Survey I 74). Few authors, both ancient and modern, have questioned that which was held for one of the seven sages, has been able to predict a solar eclipse. According to Pseudo Plutarch (Opinion of philosophers, II 24), Thales understood the nature of the phenomenon ("the solar eclipse occurs when the Moon, whose nature is terrestrial, is placed just under him".) But this would obviously be not enough to move to the infinitely more complex step of the prediction of an eclipse occurring on a specific date and visible in a specified region of the globe. Some historians determined as sure that May 28, 585 BC was the date of the solar eclipse announced by Thales and the American historian O. Neugebauer said that there is no cycle to predict a solar eclipse in a given place, and that around 600 BC, and that the ephemerides compiled by the Babylonians and used by Thales did not contain any theory for predicting eclipses of the Sun. This legend of Thales is as unreliable as the one of Anaxagoras (500-428 BC) who "thanks to his knowledge of astronomical science" (Pliny the Elder, Natural History, II, 149), would have predicted a meteorite fall!
If solar eclipses are about as numerous as lunar eclipses when one considers the Earth in its entirety, we approximately have twice chance to observe, in a given place, a lunar eclipse. But there are some periods which are more favorable than others to observe solar eclipses in the same region. The Greek historian Thucydides (460- to 395 BC) lived in such a period. He noted that during the Peloponnesian War, the "solar eclipses were more numerous than at any another historical era" (The Peloponnesian War, I 23). This assertion is confirmed by F. Richard Stephenson (see the bibliography), which dates the two solar eclipses mentioned by Thucydides (op. cit. II 28 and IV 52), respectively, on 3 August 431 and 21 March 424 BC. The first eclipse (annular visible from Athens) is described in these terms by the Greek author, which could state to a personal observation: "A New Moon day (this is the only time it seems that this phenomenon can occur) there was in the early afternoon a solar eclipse. The Sun took the form of a crescent and some stars became visible. Then resumed the Sun resumes its normal form".
According to Aristotle (384-322 B.C.), the Pythagoreans, who thought that
lunar eclipses were more numerous in absolute that the
solar eclipses, tried to explain this by supposing
that it was not only the Earth, but
another Earth , named anti-Earth facing away
ours and that we do not see, which is also interposed between the
Moon and its illumination source (Treaty of heaven, II 13).
For free as this hypothesis, it assumes that the Pythagoreans,
including Philolaos (about 470-390 BC) understood the generam mechanism
of eclipses which postulates that the celestial bodies
have a spherical shape, that some are opaque
and other bright, and that their position relative
the Earth, at the surface of which the observer is located,
determines the time for a partial or total obscuration of
the Moon or the Sun. Concerning Aristotle, it is apparently the first
to have mentioned among the "sensitive" evidences of roundness of the
Earth that the figure projected on the Moon when eclipsed "during eclipses, the Moon has always as limit a curved line: therefore, as the eclipse is due to the interposition of the
Earth, it is the shape of the surface of the Earth that is due to
the shape of the line" (Treaty of heaven, II 14).
The different types of solar eclipses.
Geminus (near 50), in his Introduction to the phenomena, X 1-6, appears to offer the first synthetic presentation of the cause and the different types of solar eclipse. It specifies that the transit of the Moon in front of the Sun (that is to say when the Moon is in "synod" or in conjunction with it) causes an interception of sunlight, so it should be better and his remark is correct, to speak in this case of interposition and not of eclipse of the Sun: "in fact never the smallest part of the Sun is eclipsed: it becomes only invisible to us by interposition of the Moon". Geminus adds that consequently, the eclipses are not the same everywhere, and there are large differences in the magnitude of eclipses for different places: at the same time, the Sun is eclipsed completely that is to say for locations in the alignment of the interposition and elsewhere in places located slightly outside line interposition is eclipsed partially; still elsewhere, no eclipse is visible.
The prediction: knowledge of cycles and geometric models
This is truly with the Almagest, the greatest astronomical work of antiquity due to the astronomer Claudius Ptolemy (II th century AD), that the calculation of eclipses of the Sun becomes possible, but not yet that of their global zone visibility. It had long been recognized that eclipses of the Sun require two conditions: that the Moon is new and it is close, as the Sun, to one of its nodes. Predicting a solar eclipse presupposes that one has a theory of the motion of the Moon and a theory of the motion of the Sun. If the theory of this motion was not a problem, it was not so in the case of the Moon. Our satellite has a complex motion in longitude, affected by many inequalities. The observation had revealed in ancient times the two most important, the equation of the center (already known by Hipparchus) and the evection precisely discovered by Ptolemy. The author of the Almagest knew also that the lunar parallax, which can exceed one degree affects significantly the geocentric latitude of the Moon, that is to say its angular distance to the ecliptic. Finally, Ptolemy knew the apparent diameters of the Sun and the Moon in relation to their distance from Earth. It is this last point that makes the superiority of the Greek astronomy on the Babylonian one. Even at its peak, that is to say, from 300 BC until the beginning of our era, the Babylonian astronomy was not able to predict the possibility or the impossibility of a solar eclipse. The Babylonian ephemerides, which are not based on a geometric pattern, but only on arithmetic functions, are nevertheless able to predict, as well as Ptolemy's the coordinates of the Sun and the Moon. But the lack of data on the relative dimensions of these two bodies prevents the prediction of the visibility of the eclipse. p>
Calculating a solar eclipse occurs in the Almagest in three steps. At first, Ptolemy calculates the angular distance from the Moon to one of its nodes. These are also not fixed: it was recognized early enough that they moved on the ecliptic, and the observation identified their average period of revolution. All calculations were facilitated by tables, so that it was quite easy to predict from one year to the other, dates where eclipse was possible. They knew that the eclipses occurred every six months, when the Sun crosses a node of the lunar orbit (draconitic year). p>
Secondly, Ptolemy determined near the date where the eclipse is possible, the time of the conjunction Moon-Sun, ie the time of the New Moon. He has for that a good value of the synodic month (mean interval between two New Moons) which gives him the moment of the average conjunction, and after correction of some inequalities, the time of the true conjunction. At this step of the calculation, it is already possible to say whether or not the eclipse will be visible: a conjunction taking place at night for example is obviously invisible. p>
From antiquity to the XVII th century, astronomers searched the conditions of eclipse where is the observer and not for the Earth in general, as it is done today in modern astronomy. It is thus calculated, for a certain area in latitude, the conditions of occurrence of the eclipse. This problem, one of the more complex developed in the Almagest is processed using the parallax effects on the ecliptic coordinates of the Moon. Not only the Almagest shows whether the eclipse is partial or total in a some place (the magnitude is expressed in fingers), but also makes it possible to calculate its duration and the moment the first and the last contact. p>
Just note that Ptolemy never used the period of 223 lunations - improperly named Saros by Edmond Halley - to predict a solar eclipse. A clarification is needed here regarding this period allegedly used by the Babylonians for the prediction ofsolar eclipses. Halley published in 1692 in the Philosophical Transactions a memory in which he proposed to correct a passage of Pliny the Elder (23-79 AD), which concerned a period after which eclipses recur in the same order. Some manuscripts of the Natural History circulating at the time contained variants, and in the one of Halley, it was written: "There is no doubt that eclipses recur in the same order after 222 months [Defectus CCXXII mensibus redire in suos orbs], and that the Sun is eclipsed only when Moon ends or begins its course, that is to say at the moment of the conjunction" (Natural History, II 56). Halley corrected 222 to 223 (CCXXIII). But by looking at the Souda, Byzantine encyclopedia written during the Xt century by a group of scholars (which was took a long time for a scientist named Suidas), he found mention of the word in the following terms: " the Saros, measurement and number for the Chaldeans. A lunar saros contains 222 lunar months which make 18 years and six months. 120 saros correspond to 2222 (sic for 2220) years". Mistakenly believing that Souda depended here on Pliny (which does not use the term Saros), Halley concluded that the Babylonians meant thus a period of 223 lunations making the eclipses coming back. But the Souda expressly says that 222 months = 18.5 years, i.e. just a year of 12 months exactly (222/18.5 = 12). But the Babylonian calendar is lunar, and the duration of the months is variable. p>
In conclusion, the period named Saros by the Babylonians
has nothing to do with eclipses. The error made by Halley
was denounced by the French astronomer
Guillaume Le Gentil in Galaisière (1725-1792) in two articles
very critical published in 1756 but it will
and not heard since, despite the correction made by many
historians of science, the word Saros continues to designate a
period of 223 lunar months, or 18 years and 11 days, or 6,585 days,
after which eclipses of the Sun and the Moon
recur in the same order. p>
The method outlined in the Almagest will suffer almost no change until the seventeenth century. Nevertheless, the famous Arab astronomer Al- Battani (middle of the IXth -929) concludes to the variation of the apparent diameter of the Sun, and therefore to the possibility of annular eclipse of the Sun. Copernicus (1473-1543), in his De revolutionibus orbium Coelestium published in 1543, will take almost point by point the method of Ptolemy, without improvements made. A comprehensive study showed that this method was able to detect virtually all solar eclipses, only the eclipses of faint magnitude affecting polar regions, escaped the investigation of the Ancients. p>
From the XVIth century, there has been an increase in the publications of ephemerides in Europe, all providing very properly solar eclipses and their visibility. There are also, since the Middle Ages, special tables that predict eclipses very long in advance. The work of Tycho Brahe (1546-1601), and of Kepler (1571-1630), will only increase the accuracy of the theories of the Sun and the Moon; this quest for precision will only grow after Newton and the birth of celestial mechanics.
The idea of representing on a map the visibility zone of a solar eclipse appears during the seventeenth century thanks to Jean -Dominique Cassini (1625-1712). This is an important and difficult problem that requires predicting the general eclipse, otherwise said, it is to determine the set of points on the Earth's surface which can actually see one of the phase of given magnitude of the eclipse (partial, annular or total). Edmond Halley had three essential elements in order to achieve such a prediction, namely a good theory of the motions of the Sun and the Moon, an accurate estimate of the distance of the Moon and finally precise geographic coordinates. He left us a remarkable map for the eclipse of the Sun on May 3, 1715 (at right) showing the zone of visibility of the eclipse for the south of England as calculated in advance. Five months later, he ploted the path of totality as it was actually observed on the basis of reports received from various correspondents that Halley had alerted. The difference is of some 20 miles compared to the prediction of Halley.
During the XIXth century, the German astronomer Friedrich Bessel (1784-1846) will develop a method still in use, to facilitate the calculation of local circumstances and conditions of visibility of a solar eclipse. All these developments were mainly possible due to ever-improving knowledge of the distance Earth-Moon and Earth-Sun since the XVIIth century. But even in the early twentieth century the precise plot of the entire strip of totality included uncertainties of a few kilometers due to the imperfection of the theory of the Moon to which should be added, as discussed below, the irregularities of the own rotation of the Earth.
We conclude with some examples that demonstrate that the knowledge of solar eclipses in the past is useful not only for historians of astronomy, but also historians and astronomers. p>
We will discuss first how was treated by astronomical science of the Middle Ages the case of an eclipse of a very special kind. From the De Sphaera of Jean Sacrobosco (XIIIth century) a treaty which will be read and commented until the XVIIth century, ending on the following question, arrising from the reading a passage of the Gospels: " When it was the sixth hour, there was darkness over the whole land until the ninth hour" (Gospel of Mark, 15, 33). The question was to know whether the solar eclipse that took place during the Lord's Passion was natural or miraculous. Matter that the Ptolemaic theory of eclipses perfectly assimilated by medieval astronomers allowed to make a response free of ambiguity: it could not be a natural phenomenon since eclipse necessarily occurs when the Moon is new: Christ was crucified during Passover when the Moon was full; commentators of Sacrobosco added in the same idea the unusual length of the eclipse. It was, therefore, a miracle through which the omnipotence of God manifested itself. A legend (which confuses several characters named Denys) states that learning from the Apostle Paul the true nature of the darkening of the sky he had observed in Athens, Dionysius Areopagite converted himself to Christianity, moved to France, where he would have converted the inhabitants and became bishop of Paris where he would have ended martyr.
The mention of an exceptional or spectacular celestial phenomenon, accompanying a religious, political or military event, and intended to highlight its importance were also frequently associated to comets for this purpose: it is not uncommon in the ancient chronicles. But the precise knowledge of solar eclipses which occurred in the past allows historians to verify and possibly invalidate the stories of some authors. This is for example the case for the eclipse mentioned by the Byzantine historian Zosimus (end of the Vth - early VIth century) in his new History (IV, 58). About the battle which took place on September 5, 394 in the Julian Alps between Eugene, Arbogast and Theodosius, Zosimus wrote: "when Eugene marched against them with all his troops and when the armies came to blows with each other, it occurred at the same time of the battle a solar eclipse so complete that it seemed rather night than day for considerable a period of time". The indication by Zozimus of an eclipse lasted a considerable time is suspect, and for good reason: there was no eclipse on September 5, 394 !
We may also, from a solar eclipse, date an event on which the manuscript sources do not provide chronological indications more or less ambiguous. For a long time, the exact year of the death of the Emperor of the West, Louis I the Pious, son of Charlemagne was ignored. We only had the testimony recorded in a medieval chronicle from which the year when the Emperor Louis died "there was an eclipse of the Sun on Wednesday before Ascension" (eclipsis solis facta is IV feria ante ascensionem domini). However, the calculation shows a total eclipse of the Sun was visible in Europe on May 5, 840, the eve of the Ascension. So, the Emperor is dead in 840.
The astronomers do not use today the eclipses of the Sun to improve the theory of celestial mechanics, but they continue to draw key lessons from ancient eclipses. In 1749, the English astronomer Richard Dunthorne (1711-1775) used eclipses mentioned by Ptolemy. Recalculating these eclipses, Dunthorne brought to light a regular disagreement between the calculated and observed moments: the motion of the Moon seemed to accelerate of 20" per century. It is only during the XIXth century that the problem was solved: it is not the Moon which accelerates, but it is the Earth that rotates more slowly around its axis due to the friction of seas on the ocean floor. Since the rotation of the Earth slows steadily regardless of seasonal irregularities, the subsequent calculation of ancient eclipses must therefore take into account this slowdown, under penalty of large shifts. It is known for example from Babylonian sources that a total solar eclipse took place at Babylon on April 15, 136 BC. If we recalculate with modern theories, the circumstances of the eclipse regardless of the slowdown of the rotation of the Earth, it is found that the entire band of total visibility passed not to Babylon (located in present-day Iraq about 160 km south of Baghdad), but in Morocco as seen on the map below. We see from this example and from many other recently studied masterfully by F. Richard Stephenson that today astronomers benefit greatly observations of ancient eclipses to highlight the changes in the rotation of the Earth. Thus, the Earth slows 1.6 millisecond per century (i.e. the length of the day increases of 1.6 ms per century), which, cumulated, give a difference of about 4 hours for the eclipse of Babylon. It also shows the limits of the current celestial mechanics for any prediction of the path of totality of an eclipse of the Sun. It cannot, across centuries, be absolutely accurate because of irregularities in the rotation of our planet impossible to determine in advance.
On 22 May 1724, a total eclipse visible in Paris occurred. It took place from 17h 42m to 19h 29m Universal Time. It was complete in Paris between 18h 35m 18h 38m 45s and 13s is for a period of 2m 28s. Below the map of the prediction made at that time.
On April 17, 1912, a central annular eclipse, total for some places because of the variation of the Earth-Moon distance, was observed in the Paris region. The totality was visible only on a line passing west of Paris near 12h 20m (Paris civil time). However, on the Belgian part of the path and further north, the eclipse was visible as a annular. Outside this line, the eclipse was seen as partial. Below is the map showing the A-B line of observation.
On February 15, 1961, a total solar eclipse took place in the south of France, at sunrise. Below is the visibility zone maps and schedules.
On August 11, 1999, a total eclipse was visible just north of Paris between 10h 20m and 10h 30m Universal Time. Unfortunately clouds were present during the observation of this phenomenon.
To get the maps of the zones of visibility click here.
The canon of all the eclipses of the Sun from -1999 to the year 3000 on the site of the NASA http://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html
The canon of all the eclipses of the Moon from -1999 to the year 3000 on the site of the NASA http://eclipse.gsfc.nasa.gov/LEcat5/LEcatalog.html
Aristotle, On the heavens ( Περὶ οὐρανοῦ), in greek translated in english
by Stuart Leggatt, (Warminster: Aris & Phillips, 1995). ISBN 0-85668-663-8
Geminos's Introduction to the Phenomena: A Translation and Study of a Hellenistic Survey of Astronomy; translated in english by Evans, J. and Berggren, J.L. (Princeton University Press, 2006.)
Pliny the Elder "The Natural History": John Bostock, Henry Thomas Riley (translators and editors); Gregory R. Crane (Chief editor) (1855). Taylor and Francis; Tufts University: Perseus Digital Library, retrieved 24 May 2009.
Ptolemy : The Almagest, translated in english by G. J. Toomer, Londres, Duckworth, 1984.
Jean de Sacrobosco, De sphaera, latin text translated in english by L. Thorndike, The Sphere of Sacrobosco and its Commentators, Chicago, 1949.
Credit : M. Lerner/D. Savoie/J.E. Arlot/Bureau des longitudes/Observatoire de Paris