Editing Eclipse cycle (section)

==Saros series and inex series==
[[File:Solar eclipses 1995-2035.svg|thumb|400px|Solar eclipses around the present time. Series of semesters, heptons, and octons are easily visible. Note that the hepton series tend to remain total or annular, because the interval is near a whole number of anomalistic months, whereas in the octon series the type of eclipse changes over a cycle of 3, since the anomaly changes by around 130° each time.]]
[[File:Solar eclipses 1600-2400.png|thumb|700px|Eclipses between AD 1600 and 2400. One can fairly easily see six of the eclipse cycles mentioned in this article. During some periods there are (non-consecutive) eclipses seven lunar months apart (a change of 69 in inex index). The two eclipses are seen both near the Arctic Circle or both near the Antarctic Circle. The next such period begins in 2098.]]
Any eclipse can be assigned to a given [[saros series]] and [[inex]] series. The year of a solar eclipse (in the [[Gregorian calendar]]) is then given approximately by:<ref>Based on [https://web.archive.org/web/20070630062339/http://user.online.be/felixverbelen/cycles.htm Saros, Inex and Eclipse cycles].</ref>

:year = 28.945 × number of the saros series + 18.030 × number of the inex series − 2882.55

When this is greater than 1, the integer part gives the year AD, but when it is negative the year BC is obtained by taking the integer part and adding 2. For instance, the eclipse in saros series 0 and inex series 0 was in the middle of 2884 BC.

A "panorama" of solar eclipses arranged by saros and inex has been produced by Luca Quaglia and John Tilley showing 61775 [[solar eclipse]]s from 11001 BC to AD 15000 (see below).<ref>[http://www.geoastro.de/saros/panorama.html Saros-Inex Panorama]. Data in [https://web.archive.org/web/20120418221009/http://eclipse.gsfc.nasa.gov/SEsaros/SEpanorama.xls Solar eclipse panaorama.xls].</ref>
Each column of the graph is a complete [[Saros cycle|Saros series]] which progresses smoothly from partial eclipses into total or annular eclipses and back into partials. Each graph row represents an inex series. Since a saros, of 223 synodic months, is slightly less than a whole number of draconic months, the early eclipses in a saros series (in the upper part of the diagram) occur after the Moon goes through its node (the beginning and end of a draconic month), while the later eclipses (in the lower part) occur before the Moon goes through its node. Every 18 years, the eclipse occurs on average about half a degree further west with respect to the node, but the progression is not uniform.

[[File:Saros-Inex panorama.png|800px|thumb|Solar eclipses from –11000 to +15000.]]

[[File:Calculated saros and inex numbers.png|thumb|800px|Saros and inex values for solar eclipses calculated from approximate date]]

Saros and inex number can be calculated for an eclipse near a given date. One can also find the approximate date of solar eclipses at distant dates by first determining one in an inex series such as series 50. This can be done by adding or subtracting some multiple of 28.9450 Gregorian years from the solar eclipse of 10 May, 2013, or 28.9444 Julian years from the Julian date of 27 April, 2013. Once such an eclipse has been found, others around the same time can be found using the short cycles. For lunar eclipses, the anchor dates May 4, 2004 or Julian April 21 may be used.

Saros and inex numbers are also defined for lunar eclipses. A solar eclipse of given saros and inex series will be preceded a fortnight earlier by a lunar eclipse whose saros number is 26 lower and whose inex number is 18 higher, or it will be followed a fortnight later by a lunar eclipse whose saros number is 12 higher and whose inex number is 43 lower. As with solar eclipses, the Gregorian year of a lunar eclipse can be calculated as:

:year = 28.945 × number of the saros series + 18.030 × number of the inex series − 2454.564

Lunar eclipses can also be plotted in a similar diagram, this diagram covering 1000 AD to 2500 AD. The yellow diagonal band represents all the eclipses from 1900 to 2100. This graph immediately illuminates that this 1900–2100 period contains an above average number of total lunar eclipses compared to other adjacent centuries.

[[File:Inex saros lunar series 1000-2500.png|640px|thumb]]

This is related to the fact that [[Tetrad (astronomy)|tetrads]] (see above) are more common at present than at other periods. Tetrads occur when four lunar eclipses occur at four lunar inex numbers, decreasing by 8 (that is, a semester apart), which are in the range giving fairly central eclipses (small [[Gamma (eclipse)|gamma]]), and furthermore the eclipses take place around halfway between the Earth's perihelion and aphelion. For example, in the tetrad of 2014-2015 (the so-called [[Four Blood Moons]]), the inex numbers were 52, 44, 36, and 28, and the eclipses occurred in April and late September-early October. Normally the absolute value of gamma decreases and then increases, but because in April the Sun is further east than its [[mean longitude]], and in September/October further west than its mean longitude, the absolute values of gamma in the first and fourth eclipse are decreased, while the absolute values in the second and third are increased. The result is that all four gamma values are small enough to lead to total lunar eclipses. The phenomenon of the Moon "catching up" with the Sun (or the point opposite the Sun), which is usually not at its mean longitude, has been called a "stern chase".<ref>{{cite journal |last1=John H. Duke |title=Do periodic consolidations of Pacific countercurrents trigger global cooling by equatorially symmetric La Niña |journal=Climate of the Past Discussions |date=May 20, 2010 |volume=6 |issue=3 |page=905 |doi=10.5194/cpd-6-905-2010 |bibcode=2010CliPD...6..905D |url=https://cp.copernicus.org/preprints/6/905/2010/cpd-6-905-2010-print.pdf |doi-access=free }} See also {{cite book |last1=Fergus Wood |title=The Strategic Role of Perigean Spring Tides in Nautical History and North American Coastal Flooding, 1635-1976 |date=1976 |url=https://books.google.com/books?id=k02T9PU19ioC&q=%22stern+chase%22&pg=PA269}}</ref>

Inex series move slowly through the year, each eclipse occurring about 20 days earlier in the year, 29 years later. This means that over a period of 18.2 inex cycles (526 years) the date moves around the whole year. But because the perihelion of Earth's orbit is slowly moving as well, the inex series that are now producing tetrads will again be halfway between Earth's perihelion and aphelion in about 586 years.<ref name=Duke>{{cite journal |last1=John H. Duke |title=Do periodic consolidations of Pacific countercurrents trigger global cooling by equatorially symmetric La Niña |journal=Climate of the Past Discussions |date=May 20, 2010 |volume=6 |issue=3 |doi=10.5194/cpd-6-905-2010 |url=https://cp.copernicus.org/preprints/6/905/2010/cpd-6-905-2010-print.pdf|pages=928–929 |bibcode=2010CliPD...6..905D |doi-access=free }} See especially Figures 10 and 13.</ref>

[[File:Solar eclipse time of year.png|thumb|550px|Time of year for solar eclipses between saros 90 and saros 210]]
One can skew the graph of inex versus saros for solar or lunar eclipses so that the x axis shows the time of year. (An eclipse which is two saros series and one inex series later than another will be only 1.8 days later in the year in the Gregorian calendar.) This shows the 586-year oscillations as oscillations that go up around perihelion and down around aphelion (see graph).