A Catalogue of Eclipse Cycles


Contents

This web page is organized as follows:


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.

Cycle Saros-Inex
Combination
Lunations
Eclipse Seasons
Period Comments
Fortnight 19 I – 30½ S ½
0
14.765 d
0.0404 y
Shortest possible interval between a lunar and a solar eclipse.
Synodic month (Lunation, Nova) 38 I – 61 S 1
0
29.531 d
0.0809 y
Shortest possible interval between two successive lunar or solar eclipses.
Short Semester (Pentalunex) 53 S – 33 I 5
1
147.65 d
0.404 y
 
Semester
5 I – 8 S
6
1
177.18 d
0.485 y
Two successive lunar or solar eclipses at alternate lunar nodes.
Long Semester
43 I – 69 S
7
1
206.71 d
0.566 y
 
Lunar year
10 I – 16 S
12
2
354.37 d
0.970 y
1 lunar year
Hexon
13 S – 8 I
35
6
1033.57 d
2.830 y
 
Hepton
5 S – 3 I
41
7
1210.75 d
3.315 y
Eclipses repeat on (nearly) the same weekday.
Octon
2 I – 3 S
47
8
1387.94 d
3.800 y
 
Tzolkinex
2 S – I
88
15
2598.69 d
7.115 y
Nearly 10 Tzolkins.
Hibbardina
31 S – 19 I
111
19
3277.90 d
8.975 y
Nearly similar pairs of central solar eclipses
Sar (Half Saros)
½ S
111½
19
3292.66 d
9.015 y
Alternating lunar and solar eclipses of nearly similar character.
Tritos
I – S
135
23
3986.63 d
10.915 y
 
Saros (Chaldean)
S
223
38
6585.32 d
18.030 y
Similar solar eclipses spaced about 120º apart in terrestrial longitude.
Metonic Cycle
10 I – 15 S
235
40
6939.69 d
19.000 y
Same date in the Julian/Gregorian and luni-solar calendars.
Semanex
3 S – I
311
53
9184.01 d
25.145 y
Same weekday.
Thix
4 I – 5 S
317
54
9361.20 d
25.630 y
Approximately 36 Tzolkins.
Inex
I
358
61
10571.95 d
28.945 y
Similar solar eclipses at the same terrestrial longitude but opposite latitudes.
Triple Tritos (Fox, Maya,
Mayan Eclipse Cycle)
3 I – 3 S
405
69
11959.89 d
32.745 y
Nearly 46 Tzolkins.
Double Saros
2 S
446
76
13170.64 d
36.060 y
 
Unnamed (40)
2 I – S
493
84
14558.58 d
39.860 y
 
Unnamed (47)
I + S
581
99
17157.27 d
46.975 y
Same weekday.
Unnamed (51)
3 I – 2 S
628
107
18545.21 d
50.775 y
 
Exeligmos (Triple Saros)
3 S
669
114
19755.96 d
54.090 y
Similar solar eclipses at approximately the same terrestrial longitude.
Double Inex
2 I
716
122
21143.90 d
57.890 y
 
Unnamed (61)
4 I – 3 S
763
130
22531.84 d
61.690 y
 
Unidos
I + 2 S
804
137
23742.59 d
65.005 y
67 lunar years, nearly same date in Julian/Gregorian calendar.
Unnamed (69)
3 I – S
851
145
25130.53 d
68.805 y
 
Short Calippic Cycle
2 I + S
939
160
27729.22 d
75.920 y
4 Metonic Cycles minus one month.
Triad (Triple Inex)
3 I
1074
183
31715.85 d
86.835 y
 
Quarter Palmen Cycle
4 I – S
1209
206
35702.48 d
97.750 y
 
Mercury Cycle
2 I + 3 S
1385
236
40899.87 d
111.98 y
Nearly equals 353 synodic periods of the planet Mercury.
Tritrix
3 I + 3 S
1743
297
51471.82 d
140.93 y
 
Unnamed (176)
21 S – 7 I
2177
371
64288.09 d
176.01 y
Nearly similar pairs of central solar eclipses.
Unnamed (176.5)
13 S – 2 I
2183
372
64465.28 d
176.50 y
 
Trihex
3 I + 6 S
2412
411
71227.78 d
195.02 y
201 lunar years.
Half Babylonian Period
7 I + S
2729
465
80588.98 d
220.65 y
 
Unnamed (246)
6 I + 4 S
3040
518
89772.99 d
245.79 y
 
Unnamed (298)
24 I – 22 S
3686
628
108849.8 d
298.02 y
 
Macdonald Cycle
6 I + 7 S
3709
632
109529.0 d
299.88 y
Nearly similar eclipses on the same day of the week.
Utting Cycle
10 I + S
3803
648
112304.8 d
307.48 y
 
Unnamed (327)
25 I – 22 S
4044
689
119421.7 d
326.97 y
337 lunar years.
Unnamed (336)
11 I + S
4161
709
122876.8 d
336.43 y
 
Hipparchus Cycle
25 I – 21 S
4267
727
126007.0 d
345.00 y
Nearly similar pairs of central solar eclipses.
Unnamed (353)
26 S – 4 I
4366
744
128930.6 d
353.00 y
Same Gregorian calendar date (approximately).
Square Year (Jubilee Period)
12 I + S
4519
770
133448.7 d
365.37 y
 
Gregoriana
6 I + 11 S
4601
784
135870.2 d
372.00 y
Same Gregorian calendar date and weekday (approximately).
Hexdodeka
6 I + 12 S
4824
822
142455.6 d
390.03 y
402 lunar years.
Grattan Guinness Cycle
16 I – 4 S
4836
824
142809.9 d
391.00 y
403 lunar years and same Gregorian calendar date (approximately).
Babylonian Period (Hipparchian Period)
14 I + 2 S
5458
930
161178.0 d
441.29 y
 
Unnamed (520.5)
13 I + 8 S
6438
1097
190117.9 d
520.53 y
 
Basic Period (Pingré Cycle, Hyper Saros)
18 I
6444
1098
190295.1 d
521.01 y
537 lunar years, same Julian calendar date and same weekday.
Chalepe (Great Chaldean Cycle)
18 I + 2 S
6890
1174
203465.8 d
557.07 y
 
Tetradia
19 I + 2 S
7248
1235
214037.7 d
586.02 y
604 lunar years and same Julian calendar date (approximately).
Unnamed (595)
33 S
7359
1254
217315.6 d
594.99 y
 
Unnamed (600)
12 I + 14 S
7418
1264
219057.9 d
599.76 y
Same day of the week.
Unnamed (702)
23 I + 2 S
8680
1479
 256325.5 d
701.80 y
 
Unnamed (725)
37 S + 2 I
8967
1528
264800.8 d
725.00 y
Same Gregorian calendar date (approximately).
Hyper Exeligmos
24 I + 12 S
11268
1920
332750.7 d
911.04 y
939 lunar years.
Double Basic Period
36 I
12888
2196
380590.2 d
1042.0 y
1074 lunar years, same Julian calendar date and same weekday.
Unnamed (1154)
38 I + 3 S
14273
2432
421490.1 d
1154.0 y
Same Gregorian calendar date (approximately).
Unnamed (1172)
38 I + 4 S
14496
2470
428075.4 d
1172.0 y
1208 lunar years and same Julian calendar date (approximately). 
Unnamed (1404)
46 I + 4 S
17360
2958

512651.0 d
1403.6 y
 
Unnamed (1418)
49 I
17542
2989
518025.6 d
1418.3 y
 
Unnamed (1490)
49 I + 4 S
18434
3141
544366.9 d
1490.4 y
 
Cartouche
52 I
18616
3172
549741.4 d
1505.1 y
 
Triple Basic Period
54 I
19332
3294
570885.3 d
1563.0 y
1611 lunar years and same weekday (approximately).
Unnamed (1610)
55 I + S
19913
3393
588042.6 d
1610.0 y
 
Unnamed (1628)
55 I + 2 S
20136
3431
594627.9 d
1628.0 y
1678 lunar years and same Julian calendar date (approximately).
Palaea-Horologia
55 I + 3 S
20359
3469
601213.3 d
1646.1 y
 
Hybridia
55 I + 4 S
20582
3507
607798.6 d
1664.1 y
 
Selenid I
55 I + 5 S
20805
3545
614383.9 d
1682.1 y
 
Unnamed (1700)
55I + 6 S
21028
3583
620969.2 d
1700.2 y
 
Unnamed (1751)
58 I + 4 S
21656
3690
639514.4 d
1750.9 y
 
Proxima
58 I + 5 S
21879
3728
646099.8 d
1769.0 y
Nearly 2485 Tzolkins and same weekday.
Heliotrope
58 I + 6 S
22102
3766
652685.1 d
1787.0 y
 
Megalosaros
58 I + 7 S
22325
3804
659270.4 d
1805.0 y
95 Metonic Cycles.
Immobilis
58 I + 8 S
22548
3842
665855.7 d
1823.1 y
1879 lunar years.
Accuratissima
58 I + 9 S
22771
3880
672441.0 d
1841.1 y
Same weekday.
Unnamed (2471)
81 I + 7 S
30559
5207
 902425.3 d
2470.8 y
 
Selenid II
95 I + 11 S
36463
6213
1076773.9 d
2948.1 y
 
Horologia
110 I + 7 S
40941
6976
1209011.8 d
3310.2 y
Same weekday (approximately).

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:

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

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

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

Whole World Solar eclipses Lunar eclipses
Mahler (1885) +1901 to +2000
Von Oppolzer (1887) –1207 to +2161 –1206 to +2163
Van den Bergh (1954) –1600 to –1207 –1600 to –1207
Meeus et al. (1966) +1898 to +2510
Mucke & Meeus (1983) –2003 to +2526
Meeus & Mucke (1983) –2003 to +2526
Espenak (1987) +1986 to +2035
Espenak (1989) +1986 to +2035
Meeus (1989) +1950 to +2200
Bao-Lin Liu & Fiala (1992) –1499 to +3000
     
Ancient Near East Solar eclipses Lunar eclipses
Neugebauer & Hiller (1931) –4199 to –899
Neugebauer & Hiller (1934) –3449 to 0
Kudlek & Mickler (1971) –2999 to 0 –2999 to 0
Steele & Stephenson (1997/98) –749 to +1 –749 to +1
     
Mediterranean region Solar eclipses Lunar eclipses
Ginzel (189?) –799 to 0 –399 to 0
Ginzel (1899) –899 to +600 –899 to +600
     
Europe Solar eclipses Lunar eclipses
Schroeter (1923) +600 to +1800 +600 to +1800
     
Ireland Solar eclipses Lunar eclipses
O’Connor (1952) +400 to +1000
     
Africa Solar eclipses Lunar eclipses
Gray (1965) +1000 to +2000
     
East Asia Solar eclipses Lunar eclipses
Newton (1977) –1500 to –1000
Stephenson & Houlden (1986) –1499 to +1900
     
Central America Solar eclipses Lunar eclipses
Wilson (1924) +??? to +???? +??? to +????

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


I am grateful to Herbert Prinz for some corrections.


Return to my homepage

[document last updated on 8 September 2003]