The Saros

Saros cycle or periodicities of eclipses

Eclipses take place at syzygies, i.e. when there is a quasi alignment between the Sun, Earth and Moon. The eclipse occurs at new moon, the lunar eclipse occurs at full Moon. Cycle of periodicity of eclipses is known as Saros (≈18 ans). A cycle that obeys surprising coincidences and an average Saros eclipse contains 84, 42 solar eclipses and 42 lunar eclipses. Indeed, during this cycle, there are the same number and the same type of eclipses, total, annular, partial every 223 lunations or every 18 years. More precisely, the Saros is a period of 6585.32 days or 18 years 10 or 11 days and 8 hours, depending on the interval contains 4 or 5 leap years. But the irregularities of movement lunar orbit are the type succession of eclipses is not preserved.
Nevertheless, this particular cycle periodicities eclipses is known since antiquity, at least as concerning lunar eclipses because lunar eclipses are visible from much larger land areas than solar eclipses. Saros is the name given to this cycle in 1691 by Edmund Halley (1656-1742). Although Halley interprets this term incorrectly, scientists have kept this term. The Saros (period ≈ 18 years) is dependent on several periods or lunar months, the synodic period, the draconic period and the anomalistic period (see table opposite). The sidereal period of revolution of the Moon is measured relative to the stars. This is the period after which we will find the Moon in the same position as seen from the Earth relative to a star. The sidereal period of revolution is 27.321661 days. The synodic period of revolution, this time measured relative to the Sun, is 29.530589 days. This explains why solar eclipses and lunar eclipses successive 15 days. If the sidereal period of revolution of the Moon is shorter than the synodic period of revolution, because for a month the Earth advanced in its orbit and it will take about 2 days for the Moon to reach the same position to the Sun. The anomalistic period of revolution, or anomalistic lunar month is the time interval between two perigee of the Moon, that is to say, the point of its closest Earth orbit. This period is an average of 27.55455 days.
These three periods are the Saros cycle and allow to find all 18 years, similarity of the properties of eclipses (eclipses of the moon, eclipses of the Sun, phases, total, partial, annular, mixes, apparent diameter), on the order reproduction of these eclipses and even some similarity to the tape visibility on Earth. This is the distance Earth Moon which will determine the duration of the eclipse and determine the nature of the eclipse, annular or total. The orbit of the Moon is not exactly Keplerian, there are other planets in the solar system that influences the orbit, especially the Sun. The gravitational influence of the Sun causes the orbit of the Moon, a precession movement (as a movement of the top of the plane of its orbit) with a period of 18.5996 years. In addition to the movement of precession of the orbit, it causes also a movement of recession of perigee in this plane with a period of 8.8504 years. The line joining the two points, the perigee and apogee (line of apsides) rotates slowly in the same direction as the Moon itself, making a complete revolution in 3232.6054 days, or about 8.85 years earth).
Why Saros cycle is 18 years 10 or 11 days and 8 hours?

Among all the lunar periods or lunar months, there is the sidereal month (relative to the stars) of 27.321661 days, month tropic (relative to the vernal equinox, precession of the equinoxes) of 27.321582 days, the synodic month (relative to the Sun) of 29.530589 days, the draconic month (relative to the ascending node passage) of 27.212221 days and anomalistic months (relative to the passage at perigee) of 27.55455 days.
To explain the Saros cycle must find the lowest common multiple between the synodic month and draconic months. The closest common multiple is 6585.3 which corresponds to 223 synodic months (from the Sun) and 242 draconic months (relative to the ascending node passage) and 239 months anomalistic coincidence (relative to perigee passage). 6585.3 = ≈ 18 years 10 or 11 days and eight hours. So eclipses similar breed a cycle of 18 years and as the distance from the Sun to the node is the same at the time of syzygy, we also observe the same apparent diameter and strips of visibility from the surface of the Earth, similar.
But the three Saros cycle is even more interesting because the eclipses return to the same position in the same geographic area on earth, with the same thickness of the shade, with the same apparent diameter, etc.. A Saros is equal to 18 years 10 or 11 days and 8 hours so 3 Saros is equal to 54 years 34 or 35 days depending on the interval contains 13 or 14 leap years, this cycle is called Exeligmos (≈54 ans). There is therefore a nearly perfect periodicity of eclipses of about 54 years. However, the irregularities of the movement of the lunar orbit due to the gravitational forces of the Sun, changing the succession of the type and the number of eclipses (84) in a Saros, we observe poor Saros of 78 eclipses and rich Saros of 94 eclipses.
The figure against track remarkably eclipses over 23 years, from 1990 to 2012. One can observe a Saros 18 years from June 1993 to June 2011. This Saros contains 81 eclipses, 40 solar eclipses and 41 lunar eclipses, of the 40 solar eclipses, 15 are partial and 25 are central (12 anular, 12 total and 1 mixed). Eclipses occur each year in the same period but with 11 days in advance each year. It highlights the numerous properties of Saros, for example the season of the eclipses that returns every 6 months and also the correlation between eclipses and passages of the Sun at the nodes of the lunar orbit. It also shows that there is a lunar eclipse and a solar eclipse at least every season of eclipses. We notes also short suites of lunar eclipses and Sun (red to the Moon and blue to the Sun). We see that there are at least 4 eclipses per year, and that when there are three eclipses that follow, the central eclipse is maximum and extreme eclipses are minimum. The Saros cycle is remarkable if we observe couples years 1990-2008, 1991-2009, 1992-2010, 1993-2011, 1994-2012. The four eclipses of 1990 are the counterparts of the eclipses of 2008, six eclipses in 1991 are homologous to those of 2009...

Image: Calendar of lunar eclipses and Sun 1990-2012. In this graph we see that there are 15 days between a solar eclipse and a lunar eclipse. Period eclipses last 34.5 days, so there 2 or 3 eclipses during this period. We also see that there is a little less than a year between two eclipses, one year less 11 days. There are also 1, 5 or 6 months between two eclipses of the sun or moon consecutive. There is also short series, successions of total eclipses in 2008, 2009 and 2010. And finally, the Saros cycle, a cycle of 18 years and 10 days. We have the same concatenation of total eclipses, partial, annular every 18 years and 10 days, as in 1990 and 2008, as in 1991 and 2009...

Table: The Tropic month is 7s shorter than the sidereal month, the synodic month is 2d 5h longer than the sidereal month, the draconic month is 2h 38mn shorter than the sidereal month, the anomalistic month is 5h35mn longer than the sidereal month.