A Catalogue of Eclipse Cycles

Contents

This web page is organized as follows:

• Introduction
• List of Eclipse Cycles
• Comments on the Listed Cycles
• Eclipse Cycle Calculator
• Solar & Lunar Eclipse Catalogues
• References

Introduction

From ancient times, lunar and solar eclipses have been regarded both as signs of awe and fear or of beauty and amazement. It is therefore understandable that astronomers have continuously searched for methods of predicting their occurrence and circumstances.

Long before the theories of the relative motions of the Sun and the Moon had reached the stage of development that the circumstances of a lunar or a solar eclipse could be solved from first principles, astronomers noted that eclipses occurred at semi-regular intervals. The earliest of such periods to be employed would have been the Semester (5 or 6 lunar months) and the lunar year, after which would probably come the Hexon (35 lunar months), the Hepton (41 lunar months) and the Octon (47 lunar months).

Though numerous eclipse cycles of varying lengths can be constructed by combining basic cycles such as the Saros and the Inex in different ways (see below), there is no evidence that ancient astronomers were aware of any eclipse cycles longer than the Saros (18.0 years), the Metonic Cycle (19.0 years), the Exeligmos (54.1 years) and the Babylonian Period (441.3 years). New World (Maya) astronomers appear to have been familiar with the Hepton, the Octon, the Tritos (10.9 years), the Thix (25.6 years) and the Triple Tritos (32.7 years). The Tritos and the Triple Tritos were also employed by ancient Chinese astronomers for predicting eclipses.

Many of the longer eclipse cycles listed below were first studied in the early 1950’s by George van den Bergh (1890-1961), a Dutch amateur astronomer and professor of law at the University of Amsterdam. With these cycles he devised simple recipes, to be used together with Von Oppolzer’s eclipse tables, to predict the circumstances of lunar and solar eclipses occurring before or after the period spanned by Von Oppolzer’s tables. As the character of a lunar or a solar eclipse also strongly depends on the solar anomaly, many of Van den Bergh’s cycles were chosen to approximate a whole number of solar years in length.

Van den Bergh also discovered that the lunar and solar eclipses calculated by Von Oppolzer (1887) could be grouped in a large Saros-Inex Panorama from which numerous interrelations between eclipse families can be derived.

List of Eclipse Cycles

The following table gives an overview of the various eclipse cycles mentioned in the astronomical literature.

Entries in red denote eclipse cycles in which eclipses repeat at the same lunar node (i.e. ascending/ascending or descending/descending) while entries in purple denote cycles in which eclipses repeat at alternating lunar nodes (i.e. ascending/descending etc.).

The average life expectancy (T ) and number of members ( M ) in an eclipse cycle (with repeat period P) can be roughly estimated from the shift in the Moon’s orbital position with respect to the lunar node after each eclipse. As long as this shift is smaller than a certain limit (here taken to be 17.4º distant on either side of the lunar node), a new eclipse will occur. If the eclipse cycle is of the form a I + b S (with a and b integer), then:

M=Int(34.8/abs(0.04002*a-0.47787*b)+1)

and

T=(M-1)*P

As will be shown later the shift of the Moon’s orbital position with respect to the lunar node is affected by secular variations and the above relation is only valid for the epoch 2000.

The above diagram indicates how the repeat period P of an eclipse period and its expected number of members M depend on its Inex/Saros factors.

Comments on the Listed Cycles

Fortnight

Shortest possible interval separating a lunar and a solar eclipse. The occurrence of a lunar and solar eclipse within two weeks was already noted by Pliny the Elder (Naturalis Historia II.10 [57]) in the year AD 71 (lunar eclipse on 4 March, solar eclipse on 20 March).

Synodic month (Lunation, Nova)

Shortest interval separating two successive lunar or solar eclipses.

Two consecutive New Moons can each produce a solar eclipse though in nearly all cases both will be partial only (one for the North Pole region, the other for the South Pole region). Very rarely, one of both will be total somewhere near the poles: the last occurrence was in 1928 (total on 19 May, partial on 17 June), the next such pair will be not until in 2195 (partial on 7 June, total on 5 August).

The name Nova was suggested by George van den Bergh (1951, 1954).

Short Semester (Pentalunex)

The name Pentalunex was suggested by Felix Verbelen (2001).

Semester

The semester can be used for predicting short series of lunar eclipses with 5 or 6 members (penumbral eclipses excluded). The series start with one or two partial eclipses, a few total eclipses and is terminated by one or two partial eclipses.

Short series of solar eclipses can also be predicted with the semester and contain about 7 or 8 members which alternate in visibility from the northern and the southern hemisphere. A semester series of solar eclipses can commence with a total eclipse.

The name Semester was suggested by George van den Bergh (1951, 1954).

Long Semester

Very rarely, two lunar or solar eclipses can be separated by seven months. Mentioned by Pliny the Elder?

Lunar year

Lunar and solar eclipses can reoccur after 12 lunar months or one lunar year. One lunar year is about ?? days longer than an ‘eclipse year’ of 346.37 days, the mean interval between two successive solar returns to the same lunar node.  

It is possible to have three total lunar eclipses within one (Western) calendar year. Since the begin of the Christian era, this occurred in 307, 372, 437, 828, 893, 958, 1414, 1479, 1544, 1917 and 1982. The next trio of total lunar eclipses will not occur until 2485.

When partial and penumbral eclipses are included it is possible to have four or even five lunar eclipses within one (Western) calendar year. Since the introduction of the Gregorian Calendar quartets occurred in 1582, 1593, 1600, 1611, 1615, 1629, 1633, 1637, 1640, 1651, 1658, 1669, 1680, 1684, 1687, 1698, 1702, 1705, 1709, 1712, 1716, 1720, 1723, 1727, 1734, 1738, 1741, 1745, 1752, 1756, 1763, 1767, 1774, 1781, 1785, 1792, 1803, 1806, 1810, 1814, 1821, 1828, 1832, 1839, 1843, 1846, 1850, 1857, 1861, 1864, 1868, 1886, 1890, 1897, 1908, 1915, 1926, 1933, 1944, 1951, 1973 and 1991. The next quartets will be in 2009, 2020, 2038, 2056, 2085 and 2096.

Quintets are of course much rarer and since the introduction of the Gregorian calendar they have only occurred in 1676, 1694, 1749 and 1879. The next quintet will not occur until 2132.

For eclipses of any kind (but excluding penumbral lunar eclipses) it is even possible to have seven in one (Western) calendar year. Since the introduction of the Gregorian Calendar this occurred in 1591, 1656, 1787, 1805, 1917, 1935 and 1982. The next septet will be in 2094.

N.B. This list is based on Von Oppolzer’s tables and does not include penumbral lunar eclipses.

Hexon

Third convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. As its length of duration lasts six eclipse seasons, the name Hexon would seem to be appropriate.

Hepton

The hepton can be used for predicting series of solar eclipses with some 13 or 14 members which alternate in visibility from the northern and the southern hemisphere. The name was introduced by George van den Bergh (1951) and reflects its length of duration (i.e. seven eclipse seasons).

Octon

The name was introduced by George van den Bergh (1951) and reflects its length of duration (i.e. eight eclipse seasons). Fourth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Tzolkinex

First studied by George van den Bergh (1951). The name Tzolkinex was suggested by Felix Verbelen (2001) as its length is nearly 10 Tzolkins (260-day periods).

Hibbardina

Nearly half of the Saros period. First identified by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses. The name Hibbardina was suggested by George van den Bergh (1957).

Sar (Half Saros)

Half of the Saros period, equal to 111.5 synodic, 121 draconic and 119.5 anomalistic months. Solar and lunar eclipses of the same character repeat after this cycle; i.e. a solar eclipse visible in the northern (southern) hemisphere is followed by a lunar eclipse at which the Moon passes through the northern (southern) part of the Earth’s umbral cone. A long solar eclipse (when the Moon is near the perigee of its orbit) is followed by a deep lunar eclipse (when the Moon is near the apogee of its orbit). According to Jean Meeus (1965) this cycle was first discussed by Paul Ahnert in his Kalender für Sternfreunde 1965. The name Sar was suggested by Jean Meeus (1965).

Tritos

This eclipse cycle was known to Chinese astronomers as the shuo wang shi hui or the jiao shi zhou and appears to have been developed in the first century B.C. (Needham, 1959). The name Tritos was introduced by George van den Bergh (1951, 1954).

The Tritos can be used for predicting series of solar eclipses with more than 60 members which alternate in visibility from the northern and the southern hemisphere. At the begin and the end of a solar Tritos series it is possible to have a few “missing” eclipses.

Saros (Chaldean)

The Saros cycle is a successful eclipse series as its period of 223 synodic months not only closely approximates 242 draconic months but also because the number of anomalistic returns of the Sun (18.029) and the Moon (238.992) are nearly whole numbers. Successive eclipses in a Saros series are therefore very similar in character. The main drawback of the cycles lies in the fact that after each eclipse the time of maximum obscuration is shifted by nearly 8 hours so that successive eclipses are about 120º apart in longitude and thus often not visible from a fixed position on Earth.

The Saros series number SNS of a solar eclipse (introduced by George van den Bergh in the 1950’s) can be derived from the lunation number LN with the following algorithm first given by Charles Kluepfel (1985):

ND=LN+105
NS=136+38*ND
NX=-61*ND
NC=FLOOR(NX/358+0.5-ND/(12*358*358))
SNS=MODULO(NS+NC*223-1,223)+1

with:

LN = Lunation number (0 on 6 January 2000)
N.B.: LN = Brown Lunation Number - 953
         = Islamic Lunation Number - 17038
         = Goldstine Lunation Number - 37105

Solar eclipses in an odd-numbered Saros series occur near the ascending node of the lunar orbit: they start with a small partial eclipse in the northern polar regions and slowly progress southwards, ending with a small partial eclipse in the southern polar regions. Solar eclipses in an even-numbered Saros series occur near the descending node of the lunar orbit: they start with a small partial eclipse in the southern polar regions and slowly progress northwards, ending with a small partial eclipse in the northern polar regions.

Solar Saros series can be as short as 1226 years (with 69 members) and as long as 1532 years (with 86 members). An average solar Saros series lasts about 1370 years and contains about 77 members of which some 48 are central. At the moment 39 solar Saros series are active (nrs. 117 to 155). A new series (nr. 156) will commence on 1 July 2011 after which 40 solar Saros series will be active until 3 August 2054 with the demise of series nr. 117.

For lunar eclipses the Saros series number SNL is defined by Bao-Lin Liu & Fiala (1992) as:

SNL=MODULO(LN+60,223)+1

For a different method of obtaining the Saros series number of a solar or a lunar eclipse, cf. Verbelen (2001).

In contrast with the solar Saros numbers, the parity (the even- or oddness) of SNL does not correlate with eclipses at either the ascending or the descending node of the lunar orbit. Of the current Lunar Saros series, numbers 2, 14, 26, 38, 49, 61, 73, 85, 96, 108, 120, 132, 143, 155, 167, 178, 179, 190, 202 and 214 take place at the ascending node of the lunar orbit: they start with a penumbral eclipse at the southern limb of the lunar disk and slowly progress northwards, ending with a penumbral eclipse at the northern limb of the lunar disk.

Of the current Lunar Saros series, numbers 8, 20, 32, 43, 44, 55, 67, 79, 90, 91, 102, 114, 126, 137, 149, 161, 173, 184, 196, 208 and 220 take place at the descending node of the lunar orbit: they start with a penumbral eclipse at the northern limb of the lunar disk and slowly progress southwards, ending with a penumbral eclipse at the southern limb of the lunar disk.

Of the complete lunar Saros series contained in the catalogue of Bao-Lin Liu & Fiala (1992) the shortest lasted 1262 years (with 71 members) while the longest lasted nearly 1551 years (with 87 members). However, the length distribution of lunar Saros series is strongly skewed to short values resulting in a most likely lunar Saros length of about 1280 years with 72 members of which the number of total eclipses ranges from 40 to 58. At the moment 41 lunar Saros series are active. A new series (nr. 3) will commence on 25 May 2013 after which 42 lunar Saros series will be active until 18 August 2016 with the demise of series nr. 43.

Strictly speaking, the name Saros for this eclipse cycle is a misnomer as the ancient Babylonians actually used this term to indicate a period of 3600 years. As demonstrated by W.T. Lynn (1889) and again by Otto Neugebauer (1937, 1938), the name was first coined in 1691 by the English astronomer Edmund Halley, who extracted it from the lexicon of the 11th-century Byzantine scholar Suidas who in turn erroneously linked it to the (unnamed) 223-month Babylonian eclipse period mentioned by Pliny the Elder (Naturalis Historia II.10 [56]). Some have therefore argued that it would be better to name this cycle the Chaldean but the name Saros has now become so familiar that it will be difficult to supplant it.

Fifth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Metonic Cycle

As the Octon (a fifth part of the Metonic Cycle), the Metonic Cycle can be used for predicting short series of lunar or solar eclipses with only 4 or 5 members which nearly fall on the same calendar day. Cuneiform sources indicate that this cycle was used by Babylonian astronomers (perhaps as early as the 6th century B.C.) for predicting lunar eclipses (Koch, 2001). The cycle was also briefly mentioned as an eclipse cycle by Stockwell (1895).

Semanex

First studied by Colton & Martin (1967). Felix Verbelen (2001), who suggested the name, discovered that eclipses repeat on the same day of the week.

Thix

The name Thix was suggested by Charles H. Smiley (1973) as its length is equal to thirty-six Tzolkins.

Inex

Although the cycle was already known at the begin of the 20th century (first mentioned by Stockwell in 1901), the name Inex (sometimes erroneously given as Index) was first introduced by George van den Bergh in 1951.

According to Van den Bergh an average solar Inex series lasts about 22 600 years and contains about 780 members. At the moment some 70 solar Inex series are active.

At the begin and the end of an Inex series there are several long gaps during which no eclipses take place.

Triple Tritos (Fox, Mayan Eclipse Cycle)

The Mayan Eclipse Cycle (often abbreviated as MEC or Mec). Van den Bergh (1951) calls this cycle the Maya. The name Fox was suggested by Charles H. Smiley (1973) as its length is equal to forty-six Tzolkins.

According to Colton & Martin (1967) this cycle was employed by ancient Chinese astronomers to predict eclipses.

Double Saros

???

Unnamed (40)

Mentioned in Colton & Martin (1967).

Unnamed (47)

Mentioned in Colton & Martin (1967).

Unnamed (51)

Mentioned in Colton & Martin (1967).

Exeligmos (Triple Saros)

Similar eclipses follow approximately the same paths on the Earth’s surface.

According to Geminus (Elementa Astronomiae XVIII.1-19) and Claudius Ptolemy (Almagest IV.2), who named this cycle the Exeligmos (the “Revolution [of the celestial bodies]”), this cycle was already known to the “most ancient astronomers” (i.e. the Babylonians).

Double Inex

This cycle was intensively studied by Torroja Menéndez (1941). Sixth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Unnamed (61)

Mentioned in Colton & Martin (1967).

Unidos

Mentioned in Colton & Martin (1967). The name was suggested by Karl Palmen (2001, unpublished).

Unnamed (69)

Mentioned in Colton & Martin (1967).

Short Calippic Cycle

Mentioned in Colton & Martin (1967).

Triad (Triple Inex)

Quarter Palmen Cycle

???

Mercury Cycle

The length of this cycle is very nearly equal to 353 synodic periods of the planet Mercury. The cycle and its name was suggested by Peter Nockolds (2001, unpublished).

Tritrix

Briefly mentioned by George van den Bergh (19??).

Unnamed (176)

Briefly mentioned by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses.

Unnamed (176.5)

Karl Palmen (2001, unpublished) has suggested to name this cycle the Half Tropicana.

Trihex

Briefly mentioned by George van den Bergh (19??).

Half Babylonian Period

Plutarch of Chaeronea (De facie in orbe lunae 20 [933E]) states that 465 eclipse seasons are made up of 404 six-month eclipse seasons while the remainder (61) are five-month eclipse seasons. As its period is half of that of the Babylonian Period, I suggest to name it the Half Babylonian Period.

Unnamed (246)

Briefly mentioned by Torroja Menéndez (1941) and George van den Bergh (1951).

Unnamed (298)

Briefly mentioned by George van den Bergh (1951).

Macdonald Cycle

Briefly mentioned by A.C.D. Crommelin (1905), Torroja Menéndez (1941) and George van den Bergh (1951). Macdonald (2000) noted that solar eclipses of long duration visible from the British Isles between +1 and +3000 tend to occur in pairs separated by this period.

Utting Cycle

Seventh convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. First discussed by ?. Utting (1829).

Unnamed (327)

Briefly mentioned by George van den Bergh (1951, 1954).

Unnamed (336)

Briefly mentioned by George van den Bergh (1951, 1954).

Hipparchus Cycle

According to Hipparchus of Nicaea (Ptolemy, Almagest, IV.2), the Moon makes 4573 complete returns in lunar anomaly within this period. Briefly mentioned by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses. The name Hipparchus Cycle was suggested by Tom Peters (2003, unpublished).

Unnamed (353)

Karl Palmen (2001, unpublished) has suggested to name this cycle the Tropicana.

Square Year (Jubilee Period)

Introduced by George van den Bergh (1951), who initially called it Jubilee Period but later changed the name to Square Year as its length in years was nearly equal to the number of days in a year. Eighth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. This cycle has an exceptionally long life expectancy.

Gregoriana

Briefly mentioned by Stockwell (1901) and by Torroja Menéndez (1941). The name Gregoriana was suggested by George van den Bergh (1954). Combined with the Accuratissima this cycle also gives good predictions for the latitudinal position of the central line of a solar eclipse on the Earth’s surface; for details, cf. Van den Bergh (1954). The greatest accuracy is achieved for eclipse pairs centred on –600.

Hexdodeka

Introduced by George van den Bergh (1954). Combined with the Palaea-Horologia, this cycle can be employed for giving accurate predictions of the time of luni-solar syzygies.

Grattan Guinness Cycle

Shortest cycle that predicts lunar or solar eclipses with the same date (more or less) in both the Gregorian calendar as in a 12-month lunar calendar. Discovered by Henry Grattan Guinness (18??) from a speculative reading of Revelation 9:15.

Babylonian Period (Hipparchian Period)

According to Hipparchus of Nicaea (Ptolemy, Almagest IV.2) the Moon makes 5923 complete returns in latitude within this period. The name was introduced by George van den Bergh (1951, 1954), who called it the Long Babylonian Period and the Old Babylonian Period, although there is no evidence that this cycle was known to ancient Babylonian astronomers. In the earlier literature, this cycle is also known as the Hipparchian Period.

Unnamed (520.5)

Briefly mentioned by George van den Bergh (19??).

Basic Period (Pingré Cycle, Hyper Saros)

Achieves a nearly integer number of calendar years (521 years + 4 days) and anomalistic years (521 years – 5 days). According to Lalande (Astronomie, 3rd ed., vol. II, 195) this cycle was first discovered by A.G. Pingré. It was rediscovered by Monck (1902) and named Hyper Saros by Alexander Pogo (1935). Also mentioned by Torroja Menéndez (1941) and in Barlow et al. (1944). Van den Bergh lists it as the Basic Period.

Chalepe (Great Chaldean Cycle)

Introduced by George van den Bergh (19??). Also known in the earlier literature as the Great Chaldean Cycle though there is no evidence that this cycle was known to Babylonian astronomers.

Tetradia

Rules the regularity of lunar eclipse tetrads (four successive lunar eclipses that are all total and occur at intervals of six lunations) and solar eclipse duos (two solar eclipses at an interval of one lunation). The change in lunar anomaly is too large for the cycle to be useful in predicting the character of solar eclipses.

Unnamed (595)

Briefly mentioned by George van den Bergh (19??).

Unnamed (600)

Briefly mentioned by A.C.D. Crommelin (1905) and George van den Bergh (1951).

Unnamed (702)

Briefly mentioned by George van den Bergh (19??).

Unnamed (725)

Briefly mentioned by George van den Bergh (19??).

Hyper Exeligmos

Equals twelve Short Calippic Periods. First mentioned by Alexander Pogo (1935).

Double Basic Period

Briefly mentioned by George van den Bergh (19??).

Unnamed (1154)

Briefly mentioned by George van den Bergh (19??).

Unnamed (1172)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1404)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1418)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1490)

Briefly mentioned by George van den Bergh (1951).

Cartouche

Introduced by George van den Bergh (19??).

Triple Basic Period

???

Unnamed (1610)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1628)

Briefly mentioned by George van den Bergh (1951).

Palaea-Horologia

Introduced by George van den Bergh (19??). Combined with the Hexdodeka, this cycle can be employed for giving accurate predictions of the time of luni-solar syzygies; for details, cf. Van den Bergh (1954).

Hybridia

Introduced by George van den Bergh (19??).

Selenid I

Introduced by George van den Bergh (19??). Gives good predictions for the magnitudes of lunar eclipses in the third millennium A.D.

Unnamed (1700)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1751)

Briefly mentioned by George van den Bergh (1951).

Proxima

Introduced by George van den Bergh (1951).

Heliotrope

Introduced by George van den Bergh (19??). Gives good predictions for the longitudinal position of the central line of a solar eclipse on the Earth’s surface. The greatest accuracy is achieved for eclipse pairs encompassing the period +500 to +1100.

Megalosaros

Eclipse cycle first studied by Julius Oppert in 18??. The name was suggested by A.C.D. Crommelin (1901). Gives accurate predictions of the time of syzygies in the third millennium A.D.; for details, cf. Van den Bergh (1954).

Immobilis

Introduced by George van den Bergh (19??).

Accuratissima

Gives good predictions for the magnitudes of lunar eclipses and the character of solar eclipses. According to George van den Bergh (1954), the errors in the predicted magnitudes of lunar eclipses are less than 10% during the third millennium  B.C.

Combined with the Gregoriana this period also gives good predictions for the latitudinal position of the central line of a solar eclipse on the Earth’s surface; for details, cf. Van den Bergh (1954). The greatest accuracy is achieved for eclipse pairs centered on –600.

Unnamed (2471)

Briefly mentioned by George van den Bergh (19??).

Selenid II

Introduced by George van den Bergh (1951). Gives good predictions for the magnitudes of lunar eclipses in the third millennium A.D.

Horologia

Introduced by George van den Bergh (1951). Gives accurate predictions for the time of ecliptic conjunctions (solar eclipses) and oppositions (lunar eclipses).

Eclipse Cycle Calculator

With the following JavaScript calculator a nearly infinite number of eclipse cycles can be generated. The lengths of each period is given in days (mean solar), Gregorian-, Julian-, and Egyptian years, 12-month (Islamic) lunar years, 235-month Metonic cycles, weeks, 60-day cycles and 260-day Tzolkin cycles.

Eclipse Cycle Calculator           Inex   Saros   Epoch                           Number of lunations   Number of eclipse seasons   Node               Length of the eclipse cycle expressed in   Days (mean solar)   Gregorian years   Julian years       Egyptian years   Lunar years   Metonic cycles       Weeks   60-day cycles   Tzolkins       Mean angular displacement in   Distance from lunar node   Lunar anomaly   Solar anomaly       Eclipse cycle statistics (approximate)   Number of members   Life expectancy (years)     © R.H. van Gent 2002

Also listed are the mean angular shift (in degrees) of the Moon’s position with respect to the lunar node and the mean angular shifts (modulo 360º) in the lunar and the solar anomaly. Ideally, all three shifts should be as small as possible as one would then obtain long eclipse cycles in which eclipses repeat under nearly similar circumstances.

The eclipse cycle calculator allows you to account for secular changes in the luni-solar orbital elements (adopted from Meeus (1998), chapter 49) by changing the epoch. Although the lengths of the repeat periods of the eclipse cycles themselves hardly change, the life expectancies of some of them can change dramatically: so the life expectancy of the Saros cycle slowly decreases as time passes by but that of the Inex cycle steadily increases and becomes infinitely long around AD 6035. The optimum inex/saros ratio for long-lasting eclipse cycles also changes with time: around 2000 BC it was close to 6, at the begin of the Christian era it had risen to 8, at present it is about 12 and it still continues to rise with ever increasing speed until it will become infinitely large around AD 6035.

Solar & Lunar Eclipse Catalogues

The basic characteristics of solar and lunar eclipses from –1999 to +4000 have been calculated by Fred Espenak (NASA/Goddard Space Flight Center) and can be accessed from his Eclipse Home Page:

• Six Millennium Catalog of Solar Eclipses (–1999 to +4000)
• Five Millennium Catalog of Lunar Eclipses (–1999 to +3000)

Fred Espenak’s website also provides global maps of solar eclipse paths from 1000 BC to AD 3000 in 20-year periods:

• World Atlas of Solar Eclipse Paths

Similar eclipse catalogues have been prepared by Felix Verbelen (Mira Public Observatory, Grimbergen, Belgium) and can be accessed from his Ancient Astronomy Home Page:

• Saros, Inex and Eclipse Cycles
• Solar Eclipses on Earth, 1001 BC to AD 2500
• Lunar Eclipses on Earth, 1001 BC to AD 2500
• Solar Eclipses in Mesoamerica, AD 1 to AD 1600
• Lunar Eclipses in Mesoamerica, AD 1 to AD 1600

The following printed works provide tables of solar and lunar eclipses with maps of solar eclipse paths covering extended regions and periods:

Shinobu Takesako’s freeware program EmapWin provides very accurate calculations for the circumstances of solar eclipses from 3000 B.C. to A.D. 3000.

References

• Auric, A., “Sur le cycle des éclipses”, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, 169 (1919), 1026-1027.
• Barlow, C.W.C., Bryan, G.H. & Spencer Jones, H., Elementary Mathematical Astronomy, 5th ed. (University Tutorial Press Ltd., London, 1944), chapter X.
• Beard, Darren, “An Investigation of the Incidence of Solar Eclipses on the Chinese New Year”, Journal of the British Astronomical Association, 109 (1999), 70-72.
• Bell, R.M., “Recurrence of Total Solar Eclipses”, Popular Astronomy, 59 (1951), 22-24.
• Bricker, H.M. & Bricker, V.R., “Classic Maya Prediction of Solar Eclipses”, Current Anthropology, 24 (1983), 1-24 [not seen].
• Closs, M.P., “Cognitive Aspects of Ancient Maya Eclipse Theory”, in: A.F. Aveni (ed.), World Archaeoastronomy: Selected Papers from the 2nd Oxford International Conference on Archaeoastronomy held at Merida, Yucatan, Mexico, 13-17 January, 1986 (Cambridge University Press, Cambridge, 1989), pp. 389-415.
• Cohen, A.P. & Newton, Robert R., “Solar Eclipses Recorded in China During the Tang Dynasty”, Monumenta Serica, 35 (1984), ??-?? [not seen].
• Colton, R. & Martin, R.L., “Eclipse Cycles and Eclipses at Stonehenge”, Nature, 213 (1967), 476-478.
• Couderc, Paul, “Eclipses and their Sequences”, Leaflets of the Astronomical Society of the Pacific, 8 (1961), 263-270 [nr. 384].
• Crommelin, A.C.D., “The 29-Year Eclipse-Cycle”, The Observatory, 24 (1901), 379-382.
• Crommelin, A.C.D., “Cycles of Eclipses”, Knowledge, 26 (1903), 202-206 & 224-227.
• Espenak, Fred, Fifty Year Canon of Solar Eclipses 1986 – 2035 (Sky Publishing Corporation, Cambridge [Mass.], 1987 [= NASA Reference Publication, nr. 1178, revised]).
• Espenak, Fred, Fifty Year Canon of Lunar Eclipses 1986 – 2035 (Sky Publishing Corporation, Cambridge [Mass.], 1989 [= NASA Reference Publication, nr. 1216]).
• Flammarion, Camille, “???”, Bulletin de la Société Astronomique de France, 10 (1896), ???-??? [not seen].
• Ginzel, F.K., “Finsterniss-Canon für das Untersuchungsgebiet der römischen Chronologie”, Sitzungsberichten der Kaiserlichen Akademie der Wissenschaften zu Wien, II Abtheilung, ?? (1887), 1099-1133 [not seen].
• Ginzel, F.K., Spezieller Kanon der Sonnen- und Mondfinsternisse für das Ländergebiet der klassischen Altertumswissenschaften und den Zeitraum von 900 vor Chr. bis 600 n.Chr. (Mayer & Müller, Berlin, 1899).
• Grattan Guinness, H., Creation Centred on Christ (???, ???, 18??).
• Gray, R., “Eclipse Maps”, Journal of African History, 6 (1965), 251-262.
• Halley, Edmond, “Emendationes & Notæ in tria loca vitiose edita in Textu vulgato Naturalis Historiæ C. Plinii”, Philosophical Transactions, Giving some Account of the Present Undertakings, Studies and Labours of the Ingenious, in many Considerable Parts of the World, 17 (1691), 535-540.
• Hibbard, William B., “Similarity in Central Solar Eclipses”, Journal of the Royal Astronomical Society of Canada, 50 (1956), 245-249.
• Johnson, S.J., “Three Lunar Eclipses in a Year”, The Observatory, 22 (1899), 235-236.
• Kluepfel, Charles, “What Saros Number?”, Sky & Telescope, 70 (1985), 366-367.
• Koch, J., “Die Mondeklipsen von BM 41004 rev. 18”, Centaurus, 43 (2001), 176-183.
• Können, G.P. & Meeus, Jean, “Periodicities of Eclipses”, Journal of the Royal Astronomical Society of Canada, 70 (1976), 81-83.
• Kudlek, M. & Mickler, E.H., Solar and Lunar Eclipses of the Ancient Near East from 3000 B.C. to 0 with Maps (Butzon & Bercker/Neukirchener Verlag des Erziehungsvereins, Kevelaer/Neukirchen-Vluyn, 1971 [= Alter Orient und Altes Testament, Sonderreihe, Band 1]).
• Lewis, I.M., “The Maximum Duration of a Total Solar Eclipse”, Publications of the American Astronomical Society, 6 (1931), 265-266.
• Light, Edward S., “Total Solar Eclipses of Great Duration”, Journal of the Royal Astronomical Society of Canada, 66 (1972), 295-302.
• Link, F., Eclipse Phenomena in Astronomy (Springer-Verlag, Berlin/Heidelberg, 1969) [not seen].
• Liu, Bao-Lin, “Die Halbschatten-Mondfinsternisse von den Jahren 1964 bis 2163”, Acta Astronomica Sinica, 12 (1964), 61-67 [in Chinese, summary in German].
• Liu, Bao-Lin, “On the Number of Lunar Eclipses in a Year”, Acta Astronomica Sinica, 21 (1980), 64 [in Chinese; for an English translation cf.: Chinese Astronomy and Astrophysics, 5 (1981), 376].
• Liu, Bao-Lin & Fiala, A.D., Canon of Lunar Eclipses 1500 B.C. – A.D. 3000 (Willmann-Bell, Richmond, 1992).
• Lynn, W.T., “The Chaldæan Saros”, The Observatory, 12 (1889), 261-262.
• Macdonald, Peter, “Total Solar Eclipses of Long Duration in the British Isles”, Journal of the British Astronomical Association, 110 (2000), 266-270.
• Mahler, Eduard, Die centralen Sonnenfinsternisse des 20. Jahrhunderts (Kaiserlich-Königlichen Hof- und Staatsdruckerei, Vienna, 1885 [= Denkschriften der Kaiserlichen Akademie der Wissenschaften zu Wien, Mathematisch-Naturwissenschaftlichen Classe, nr. 49, part 2]) [not seen].
• Meeus, Jean, “Quelques periodes de recurrence des éclipses”, Ciel et Terre, 78 (1962), 265-270.
• Meeus, Jean, “Oppolzer’s foutieve voorspellingen van zonsverduisteringen”, Hemel en Dampkring, 60 (1962), 133-137.
• Meeus, Jean, “De halve Saros”, Hemel en Dampkring, 63 (1965), 141-143 – English version in Meeus (1997), chapter 18.
• Meeus, Jean, Elements of Solar Eclipses 1950 – 2200 (Willmann-Bell, Richmond, 1989).
• Meeus, Jean, Mathematical Astronomy Morsels (Willmann-Bell, Richmond, 1997), chapters 8-18 & 22-24.
• Meeus, Jean, Astronomical Algorithms, 2nd ed. (Willmann-Bell, Richmond, 1998).
• Meeus, Jean, More Mathematical Astronomy Morsels (Willmann-Bell, Richmond, 2002), chapters 8-25.
• Meeus, Jean, Grosjean, C.C., & Vanderleen, Willy, Canon of Solar Eclipses (Pergamon Press, Oxford [etc.], 1966).
• Meeus, Jean & Mucke, H., Canon of Lunar Eclipses –2003 to +2526/Canon der Mondfinsternisse –2003 bis +2526, 2nd ed. (Astronomisches Büro, Vienna, 1983).
• Monck, W.H.S., “An Eclipse Cycle”, Popular Astronomy, 10 (1902), 240-242.
• Monck, W.H.S., “Eclipse Cycles”, The Observatory, 34 (1911), 52-53.
• Mucke, H. & Meeus, Jean, Canon of Solar Eclipses –2003 to +2526/Canon der Sonnenfinsternisse –2003 bis +2526, 2nd ed. (Astronomisches Büro, Vienna, 1983).
• Needham, Joseph, Science and Civilisation in China: Vol. 3. Mathematics and the Sciences of the Heavens and the Earth (Cambridge University Press, Cambridge, 1959), pp. 409-423. 
• Neugebauer, Otto, “Untersuchungen zur antiken Astronomie III. Die babylonische Theorie der Breitenbewegung des Mondes”, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, ser. B, 4 (1937), 193-346.
• Neugebauer, Otto, “Untersuchungen zur antiken Astronomie V. Der Halleysche “Saros” und andere Ergänzungen zu UAA III”, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, ser. B, 4 (1938), 407-411.
• Neugebauer, Otto, A History of Ancient Mathematical Astronomy, 3 vols. (Springer Verlag, Berlin/Heidelberg/New York, 1975).
• Neugebauer, Paul Victor & Hiller, R., “Spezieller Kanon der Sonnenfinsternisse für Vorderasien und Ägypten für die Zeit von 900 v.Chr. bis 4200 v.Chr.”, Astronomische Abhandlungen: Ergänzungshefte zu den Astronomischen Nachrichten, 8, nr. 4 (1931).
• Neugebauer, Paul Victor & Hiller, R., “Spezieller Kanon der Mondfinsternisse für Vorderasien und Ägypten von 3450 bis 1 v.Chr.”, Astronomische Abhandlungen: Ergänzungshefte zu den Astronomischen Nachrichten, 9, nr. 2 (1934).
• Newcomb, Simon, “On the Recurrence of Solar Eclipses with Tables of Eclipses from B.C. 700 to A.D. 2300”, Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, 1 (1879), part 1.
• Newton, Robert R., A Canon of Lunar Eclipses from –1500 to –1000 (Johns Hopkins Press, Baltimore, 1977) [not seen].
• O’Connor, F.J., “Solar Eclipses Visible in Ireland between AD 400 and AD 1000”, Proceedings of the Royal Irish Academy, ser. A, 55 (1952), 61-72 [not seen].
• Oppert, J., “???”, ???, ?? (18??), ???-??? [not seen].
• Pannekoek, Anton, “The Origin of the Saros”, Proceedings of the Section of Sciences of the Koninklijke Akademie van Wetenschappen, 20 (1918), 943-955.
• Pannekoek, Anton, “Periodicities in Lunar Eclipses”, Proceedings of the Section of Sciences of the Koninklijke Nederlandse Akademie van Wetenschappen, ser. B, 54 (1951), 30-41 [= Circulars of the Astronomical Institute of the University of Amsterdam, nr. 2].
• Pogo, Alexander, “The Saros Cycle Ending with the Partial Eclipse of January 5, 1935”, Popular Astronomy, 43 (1935), 7-14.
• Pogo, Alexander, “The Eclipse of February 3, 1935: A Partial Solar Eclipse Visible in Central America”, Popular Astronomy, 43 (1935), 95-99.
• Pogo, Alexander, “Lunar Saros Series”, Popular Astronomy, 43 (1935), 207-213.
• Pogo, Alexander, “Solar Saros Series”, Popular Astronomy, 43 (1935), 335-344.
• Pogo, Alexander, “Calendar Years with Five Solar Eclipses”, Popular Astronomy, 43 (1935), 412-423.
• Pogo, Alexander, “Calendar Years with Three Lunar Eclipses”, Popular Astronomy, 43 (1935), 549-557.
• Pogo, Alexander, “The Eclipse of 1935 December 25: An Umbral Eclipse of the Midnight Sun in the Antarctic”, Popular Astronomy, 43 (1935), 617-627.
• Pogo, Alexander, “Additions and Corrections to Oppolzer’s Canon der Mondfinsternisse”, Astronomical Journal, 47 (1938), 45-48.
• Rigge, W.F., “The Lunar Saros”, Popular Astronomy, 26 (1918), 85-95.
• Sadler, D.H., “Prediction of Eclipses”, Nature, 211 (1966), 1119-1121.
• Schiaparelli, G.V., “I primordi dell’astronomia presso i babilonesi”, Scientia: Rivista di Scienza, 3 (1908?), 36-?? [not seen].
• Schroeter, J.Fr., Spezieller Kanon der Zentralen Sonnen- und Mondfinsternisse, welche innerhalb des Zeitraums von 600 bis 1800 n.Chr. in Europa sichtbar waren (Jacob Dybwad, Kristiania, 1923).
• Shove, D.J. & Fletcher, A., Chronology of Eclipses and Comets AD 1 – 1000 (Boydell Press, Woodbridge, 1984).
• Smiley, Charles H., “Solar Eclipse Intervals in the Dresden Codex”, Journal of the Royal Astronomical Society of Canada, 59 (1965), 127-131.
• Smiley, Charles H., “The Thix and the Fox, Mayan Solar Eclipse Intervals”, Journal of the Royal Astronomical Society of Canada, 67 (1973), 175-182.
• Smiley, Charles H., “A Note on the Periodicity of Eclipses”, Journal of the Royal Astronomical Society of Canada, 69 (1975), 133-135.
• Smiley, Charles H. & Quirk, Mary, “Solar Eclipses of Long Duration of Totality”, Journal of the Royal Astronomical Society of Canada, 49 (1955), 69-72.
• Steele, John M. & Stephenson, F. Richard, “Canon of Solar and Lunar Eclipses for Babylon: 750 B.C. – A.D. 1”, Archiv für Orientforschung, 44/45 (1997/98), 195-209 [not seen].
• Stephenson, F. Richard & Houlden, M.A., Atlas of Historical Eclipse Maps: East Asia 1500 BC – AD 1900 (Cambridge University Press., Cambridge [etc.], 1986).
• Stockwell, John N., “On the Law of Recurrence of Eclipses on the Same Day of the Tropical Year”, Astronomical Journal, 15 (1895), 73-75.
• Stockwell, John N., “Eclipse-Cycles”, Astronomical Journal, 21 (1901), 185-191.
• Strömgren, E. & Strömgren, B., Lehrbuch der Astronomie (Julius Springer Verlag, Berlin, 1933), pp. 195-196.
• Torroja Menéndez, José M., “Contribución al estudio general del problema de la repetición de los eclipses”, Memorias del Observatorio del Ebro, nr. 8 (1941).
• Utting, ?., “???”, Memoirs of the Royal Astronomical Society, 3 (1829), 89-?? [not seen].
• van den Bergh, George, “Reeksen totale maansverduisteringen”, Hemel en Dampkring, 49 (1951), 142-146.
• van den Bergh, George, Regelmaat en wisseling bij zonsverduisteringen, met een aanhangsel over maansverduisteringen, 2 vols. (H.D. Tjeenk Willink & Zoon N.V., Haarlem, 1951).
• van den Bergh, George, Aarde en wereld in ruimte en tijd: Een uiteenzetting voor iedereen, 6th ed. (N.V. Em. Querido’s Uitgeversmaatschappij, Amsterdam, 1951), chapter III.
• van den Bergh, George, “Zichtbaarheid van totale maansverduisterings-tetraden”, Hemel en Dampkring, 51 (1953), 8-9.
• van den Bergh, George, “Merkwaardige opeenvolging van zonsverduisteringen”, Hemel en Dampkring, 52 (1954), 232-234.
• van den Bergh, George, Eclipses in the Second Millennium B.C. (–1600 to –1207) and how to Compute them in a Few Minutes (H.D. Tjeenk Willink & Zoon N.V., Haarlem, 1954).
• van den Bergh, George, Periodicity and Variation of Solar (and Lunar) Eclipses, 2 vols. (H.D. Tjeenk Willink & Zoon N.V., Haarlem, 1955).
• van den Bergh, George, “De Hibbardina of “Halve Saros” ”, Hemel en Dampkring, 55 (1957), 101-103.
• von Oppolzer, Theodor Ritter, Canon der Finsternisse (Kaiserlich-Königlichen Hof- und Staatsdruckerei, Vienna, 1887 [= Denkschriften der Kaiserlichen Akademie der Wissenschaften zu Wien, Mathematisch-Naturwissenschaftlichen Classe, nr. 52]) – reprinted as Canon of Eclipses in 1962 by Dover Publications, New York, with a translation by Owen Gingerich and an introduction by Donald H. Menzel & Owen Gingerich.
• Whitmell, C.T., “Lunar Penumbral Eclipses”, Journal of the British Astronomical Association, 25 (1915), 225-228.
• Wilson, Robert W., “Astronomical Notes on the Maya Codices”, Papers of the Peabody Museum of American Archaeology and Ethnology (Harvard University), 6, nr. 3 (1924), 11-?? [not seen].

I am grateful to Herbert Prinz for some corrections.

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[document last updated on 8 September 2003]