This table summarizes the characteristics of various eclipse cycles, and can be computed from the numerical results of the preceding paragraphs; cf. Meeus (1997) Ch.9 . More details are given in the comments below, and several notable cycles have their own pages.

Any eclipse cycle, and indeed the interval between any two eclipses, can be expressed as a combination of saros (s) and inex (i) intervals. These are listed in the column "formula".

cycle formulasolar days

synodic months

draconic months

anomalistic months

eclipse years

tropical years

fortnight (38i – 61s)/2 14.77 0.5 0.543 0.536 0.043 0.040

synodic month

38i – 61s 29.53 1 1.085 1.072 0.085 0.081

pentalunex -33i + 53s 147.65 5 5.426 5.359 0.426 0.404

semester 5i – 8s 177.18 6 6.511 6.430 0.511 0.485

lunar year 10i – 16s 354.37 12 13.022 12.861 1.022 0.970

octon 2i – 3s 1387.94 47 51.004 50.371 4.004 3.800

tzolkinex -i + 2s 2598.69 88 95.497 94.311 7.497 7.115

sar (half saros)

(0i + s)/2 3292.66 111.5 120.999 119.496 9.499 9.015

tritos i – s 3986.63 135 146.501 144.681 11.501 10.915

saros (s) 0i + s 6585.32 223 241.999 238.992 18.999 18.030

Metonic cycle

10i – 15s 6939.69 235 255.021 251.853 20.021 19.000

inex (i) i ± 0s 10,571.95 358 388.500 383.674 30.500 28.945

exeligmos 0i + 3s 19,755.96 669 725.996 716.976 56.996 54.090

Callippic cycle

40i – 60s 27,758.75 940 1020.084 1007.411 80.084 76.001

triad 3i ± 0s 31,715.85 1074 1165.500 1151.021 91.500 86.835

cycle formulasolar days

synodic months

draconic months

anomalistic months

eclipse years

tropical years

Hipparchic cycle

25i – 21s 126,007.02 4267 4630.531 4573.002 363.531 344.996

Babylonian 14i + 2s 161,177.95 5458 5922.999 5849.413 464.999 441.291

tetradia (Meeus III)

22i – 4s 206,241.63 6984 7579.008 7484.849 595.008 564.671

tetradia (Meeus [I])

19i + 2s 214,037.70 7248 7865.500 7767.781 617.500 586.016

Notes:

Fortnight

Half a synodic month (29.53 days). When there is an eclipse, there is a fair chance that at the next syzygy there will be another eclipse: the Sun and Moon will have moved about 15° with respect to the nodes (the Moon being opposite to where it was the previous time), but the luminaries may still be within bounds to make an eclipse.For example, partial solar eclipse of June 1, 2011 is followed by the total lunar eclipse of June 16, 2011 and partial solar eclipse of July 1, 2011.

For more information see eclipse season.

Synodic Month

Similarly, two events one synodic month apart have the Sun and Moon at two positions on either side of the node, 29° apart: both may cause a partial eclipse.

Pentalunex

5 synodic months. Successive solar or lunar eclipses may occur 1, 5 or 6 synodic months apart.[6]

Semester

Half a lunar year. Eclipses will repeat exactly one semester apart at alternating nodes in a cycle that lasts for 8 eclipses. Because it is close to a half integer of anomalistic, draconic months, and tropical years, each solar eclipse will alternate between hemispheres each semester, as well as alternate between total and annular. Hence there can be a maximum of one total or annular eclipse each in a given year.

Lunar year

Twelve (synodic) months, a little longer than an eclipse year: the Sun has returned to the node, so eclipses may again occur.

Octon

This is 1/5 of the Metonic cycle, and a fairly decent short eclipse cycle, but poor in anomalistic returns. Each octon in a series is 2 saros apart, always occurring at the same node.

Tzolkinex

Includes a half draconic month, so occurs at alternating nodes and alternates between hemispheres. Each consecutive eclipse is a member of preceding saros series from the one before. Equal to ten tzolk'ins. Every third tzolkinex in a series is near an integer number of anomalistic months and so will have similar properties.

Sar (Half saros)

Includes an odd number of fortnights (223). As a result, eclipses alternate between lunar and solar with each cycle, occurring at the same node and with similar characteristics. A long central total solar eclipse will be followed by a very central total lunar eclipse. A solar eclipse where the moon's penumbra just barely grazes the southern limb of earth will be followed half a saros later by a lunar eclipse where the moon just grazes the southern limb of the earth's penumbra.[7]

Tritos

A mediocre cycle, relates to the saros like the inex. A triple tritos is close to an integer number of anomalistic months and so will have similar properties.

Saros

The best known eclipse cycle, and one of the best for predicting eclipses, in which 223 synodic months equal 242 draconic months with an error of only 51 minutes. It is also close to 239 anomalistic months, which makes the circumstances between two eclipses one saros apart very similar.

Metonic cycle or Enneadecaeteris

This is nearly equal to 19 tropical years, but is also 5 "octon" periods and close to 20 eclipse years: so it yields a short series of eclipses on the same calendar date. It consists of 110 hollow months and 125 full months, so nominally 6940 days, and equals 235 lunations (235 synodic months) with an error of only ~7.5 hours.

Inex

By itself a poor cycle, it is very convenient in the classification of eclipse cycles, because after a saros series dies, a new saros series often begins 1 inex later (hence its name: in-ex). One inex after an eclipse, another eclipse takes place at almost the same longitude, but at the opposite latitude.

Exeligmos

A triple saros, with the advantage that it has nearly an integer number of days, so the next eclipse will be visible at locations near the eclipse that occurred one exeligmos earlier, in contrast to the saros, in which the eclipse occurs about 8 hours later in the day or about 120° to the west of the eclipse that occurred one saros earlier.

Callippic cycle

441 hollow months and 499 full months; thus 4 Metonic Cycles minus one day or precisely 76 years of 365¼ days. It equals 940 lunations with an error of only 5.9 hours.

Triad

A triple inex, with the advantage that it has nearly an integer number of anomalistic months, which makes the circumstances between two eclipses one Triad apart very similar, but at the opposite latitude. Almost exactly 87 calendar years minus 2 months. The triad means that every third saros series will be similar (mostly total central eclipses or annular central eclipses for example). Saros 130, 133, 136, 139, 142 and 145, for example, all produce mainly total central eclipses.

Hipparchic cycle

Not a noteworthy eclipse cycle, but Hipparchus constructed it to closely match an integer number of synodic and anomalistic months, years (345), and days. By comparing his own eclipse observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldeans used.

Babylonian

The ratio 5923 returns to latitude in 5458 months was used by the Chaldeans in their astronomical computations.

Tetradia

Sometimes 4 total lunar eclipses occur in a row with intervals of 6 lunations (semester), and this is called a tetrad. Giovanni Schiaparelli noticed that there are eras when such tetrads occur comparatively frequently, interrupted by eras when they are rare. This variation takes about 6 centuries. Antonie Pannekoek(1951) offered an explanation for this phenomenon and found a period of 591 years. Van den Bergh (1954) from Theodor von Oppolzer's Canon der Finsternisse found a period of 586 years. This happens to be an eclipse cycle; see Meeus [I] (1997). Recently Tudor Hughes explained the variation from secular changes in the eccentricity of the Earth's orbit: the period for occurrence of tetrads is variable and currently is about 565 years; see Meeus III (2004) for a detailed discussion.