The saros i// is a period of 223 synodic months (approximately 6585.3213 days, or nearly 18 years 11 days), that can be used to predict eclipses of the Sun and Moon. One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros.
A series of eclipses that are separated by one saros is called a saros series.
The earliest discovered historical record of the saros is by the Chaldeans (ancient Babylonian astronomers) in the last several centuries BC. It was later known to Hipparchus, Pliny and Ptolemy, but under different names. The Sumerian/Babylonian word "šár" was one of the ancient Mesopotamian units of measurement and as a number appears to have had a value of 3600. The name "saros" (Greek: σάρος) was first given to the eclipse cycle by Edmond Halley in 1691, who took it from the Suda, a Byzantine lexicon of the 11th century. The information in the Suda in turn was derived directly or otherwise from the Chronicle of Eusebius of Caesarea, which quoted Berossus. Although Halley's naming error was pointed out by Guillaume Le Gentil in 1756, the name continues to be used.
Mechanical calculation of the cycle is built into the Antikythera mechanism.
The saros, a period of 6585.322 days (14 common years + 4 leap years + 11.322 days, or 13 common years + 5 leap years + 10.322 days), is useful for predicting the times at which nearly identical eclipses will occur, and derives from three periodicities of the lunar orbit: the synodic month, the draconic month, and the anomalistic month. For an eclipse to occur, either the Moon must be located between the Earth and Sun (for a solar eclipse) or the Earth must be located between the Sun and Moon (for a lunar eclipse). This can happen only when the Moon is new or full, respectively, and repeat occurrences of these lunar phases are controlled by the Moon's synodic period, which is about 29.53 days. Most of the times during a full and new moon, however, the shadow of the Earth or Moon falls to the north or south of the other body. Thus, if an eclipse is to occur, the three bodies must also be nearly in a straight line. This condition occurs only when a full or new Moon passes close to the ecliptic plane (during an eclipse season) which is the case around the time when it passes through one of the two nodes of its orbit (the ascending or descending node). The period of time for two successive passes through the ecliptic plane at the same node is given by the draconic month, which is 27.21 days. So the conditions of an eclipse are met when the new or full moon is near one of the nodes, which occurs every 5 or 6 months (the Sun, being in conjunction or opposition to the Moon, is also at a node of the Moon's orbit at that time - this happens twice in an eclipse year). However, if two eclipses are to have the same appearance and duration, then also the distance between the Earth and Moon, as well as the Earth and Sun, must be the same for both events. The time it takes the Moon to orbit the Earth once and return to the same distance is given by the anomalistic month, which has a period of 27.55 days.
After one saros, the Moon will have completed roughly an integer number of synodic, draconic, and anomalistic months, and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase, be at the same node, and have the same distance from the Earth. In addition, because the saros is close to 18 years in length (about 11 days longer), the earth will be nearly the same distance from the sun, and tilted to it in nearly the same orientation (same season). If one knew the date of an eclipse, then one saros later, a nearly identical eclipse should occur. Note that during this 18-year cycle, about 40 other solar and lunar eclipses take place, but with a somewhat different geometry. Note also that the saros (18.03 years) is not equal to an integer number of revolutions of the Moon with respect to the fixed stars (sidereal month of 27.32 days). Therefore, even though the relative geometry of the Earth-Sun-Moon system will be nearly identical after a saros, the Moon will be in a different position with respect to the stars. This is due to the fact that the orbit of the Moon precesses.
A complication with the saros is that its period is not an integer number of days, but contains a multiple of ⅓ of a day. Thus, as a result of the Earth's rotation, for each successive saros, an eclipse will occur about 8 hours later in the day. In the case of an eclipse of the Sun, this means that the region of visibility will shift westward by 120°, or one third of the way around the globe, and the two eclipses will thus not be visible from the same place on Earth. In the case of an eclipse of the Moon, the next eclipse might still be visible from the same location as long as the Moon is above the horizon. However, if one waits three saroses, the local time of day of an eclipse will be nearly the same. This period of three saroses (54 years 1 month, or almost 19756 full days), is known as a triple saros or exeligmos (Greek: "turn of the wheel").
Saros series 
The saros is based on the recognition that 223 synodic months approximately equal to 242 draconic months and 239 anomalistic months. However, as this relationship is not perfect, the geometry of two eclipses separated by one saros will differ slightly. In particular, the place where the Sun and Moon come in conjunction shifts westward by about 0.5° with respect to the Moon's nodes every saros, and this gives rise to a series of eclipses, called a saros series, that slowly change in appearance.
Each saros series starts with a partial eclipse (Sun first enters the end of the node), and each successive saros the path of the Moon is shifted either northward (when near the descending node) or southward (when near the ascending node). At some point, eclipses are no longer possible and the series terminates (Sun leaves the beginning of the node). Arbitrary dates were established by compilers of eclipse statistics. These extreme dates are 2000 BCE and 3000 CE. Saros series, of course, went on before and will continue after these dates. Since the first eclipse of 2000 BCE was not the first in its saros, it is necessary to extend the saros series numbers backwards beyond 0 to negative numbers to accommodate eclipses occurring in the years following 2000 BCE. The saros -13 is the first saros to appear in these data. For solar eclipses the statistics for the complete saros series within the era between 2000 BCE and 3000 CE are given in this article's references. It takes between 1226 and 1550 years for the members of a saros series to traverse the Earth's surface from north to south (or vice-versa). These extremes allow from 69 to 87 eclipses in each series (most series have 71 or 72 eclipses). From 39 to 59 (mostly about 43) eclipses in a given series will be central (that is, total, annular, or hybrid annular-total). At any given time, approximately 40 different saros series will be in progress.
Saros series are numbered according to the type of eclipse (solar or lunar) and whether they occur at the Moon's ascending or descending node. Odd numbers are used for solar eclipses occurring near the ascending node, whereas even numbers are given to descending node solar eclipses. For lunar eclipses, this numbering scheme is somewhat random. The ordering of these series is determined by the time at which each series peaks, which corresponds to when an eclipse is closest to one of the lunar nodes. For solar eclipses, (in 2003) the 39 series numbered between 117 and 155 are active, whereas for lunar eclipses, there are now 41 active saros series.
Example: Lunar saros 131 
|May 10, 1427
(southern edge of shadow)
|...6 intervening penumbral eclipses omitted...|
|July 25, 1553
|...19 intervening partial eclipses omitted...|
|March 22, 1932
|April 2, 1950
|April 13, 1968||04:47 UT|
|April 24, 1986||12:43 UT|
|May 4, 2004||20:30 UT|
|May 16, 2022
|May 26, 2040||11:45 UT|
|June 6, 2058||19:14 UT|
|June 17, 2076
|...6 intervening total eclipses omitted...|
|September 3, 2202
|September 13, 2220
|...18 intervening partial eclipses omitted...|
|April 9, 2563||Last partial umbral|
|...7 intervening penumbral eclipses omitted...|
|July 7, 2707||Last penumbral
(northern edge of shadow)
As an example of a single saros series, the accompanying table gives the dates of some of the 72 lunar eclipses for saros series 131. This eclipse series began in AD 1427 with a partial eclipse at the southern edge of the Earth's shadow when the Moon was close to its descending node. Each successive saros, the Moon's orbital path is shifted northward with respect to the Earth's shadow, with the first total eclipse occurring in 1950. For the following 252 years, total eclipses occur, with the central eclipse being predicted to occur in 2078. The first partial eclipse after this is predicted to occur in the year 2220, and the final partial eclipse of the series will occur in 2707. The total lifetime of the lunar saros series 131 is 1280 years.
Because of the ⅓ fraction of days in a saros, the visibility of each eclipse will differ for an observer at a given locale. For the lunar saros series 131, the first total eclipse of 1950 had its best visibility for viewers in Eastern Europe and the Middle East because mid-eclipse was at 20:44 UT. The following eclipse in the series occurred approximately 8 hours later in the day with mid-eclipse at 4:47 UT, and was best seen from North America and South America. The third total eclipse occurred approximately 8 hours later in the day than the second eclipse with mid-eclipse at 12:43 UT, and had its best visibility for viewers in the Western Pacific, East Asia, Australia and New Zealand. This cycle of visibility repeats from the initiation to termination of the series, with minor variations.
For a similar example for solar saros see solar saros 136.
Relationship between lunar and solar saros (sar) 
After a given lunar or solar eclipse, after 9 years and 5.5 days (a half saros) an eclipse will occur that is lunar instead of solar, or vice versa, with similar properties. For example if the moon's penumbra partially covers the southern limb of the earth during a solar eclipse, 9 years and 5.5 days later a lunar eclipse will occur in which the moon is partially covered by the southern limb of the earth's penumbra. Likewise, 9 years and 5.5 days after a total solar eclipse occurs, a total lunar eclipse will also occur. This 9 year period is referred to as a sar. It includes 111.5 synodic months, or 111 synodic months plus one fortnight. The fortnight accounts for the alternation between solar and lunar eclipse. For a visual example see this chart (each row is one sar apart).
See also 
- Tablets 1414, 1415, 1416, 1417, 1419 of: T.G. Pinches, J.N. Strassmaier: Late Babylonian Astronomical and Related Texts. A.J. Sachs (ed.), Brown University Press 1955
- A.J. Sachs & H. Hunger (1987..1996): Astronomical Diaries and Related Texts from Babylonia, Vol.I..III. Österreichischen Akademie der Wissenschaften. ibid. H. Hunger (2001) Vol. V: Lunar and Planetary Texts
- P.J. Huber & S de Meis (2004): Babylonian Eclipse Observations from 750 BC to 1 BC, par. 1.1. IsIAO/Mimesis, Milano
- Naturalis Historia II.10
- Almagest IV.2
- Microsoft Encarta College Dictionary, 2001
- The Suda entry is online here.
- Littmann, Mark; Fred Espenak, Ken Willcox (2008). Totality: Eclipses of the Sun. Oxford University Press. ISBN 0-19-953209-5.
- Meeus, Jean (2004). Ch. 18 "About Saros and Inex series" in: Mathematical Astronomy Morsels III. Willmann-Bell, Richmond VA, USA.
- Espenak, Fred; Jean Meeus (October 2006). "Five Millennium Canon of Solar Eclipses, Section 4 (NASA TP-2006-214141)" (PDF). NASA STI Program Office. Retrieved 2007-01-24.
- G. van den Bergh (1955). Periodicity and Variation of Solar (and Lunar) Eclipses (2 vols.). H.D. Tjeenk Willink & Zoon N.V., Haarlem.
- Bao-Lin Liu and Alan D. Fiala (1992). Canon of Lunar Eclipses, 1500 B.C. to A.D. 3000. Willmann-Bell, Richmond VA.
- Jean Meeus and Hermann Mucke (1983) Canon of Lunar Eclipses. Astronomisches Büro, Vienna
- Theodor von Oppolzer (1887). Canon der Finsternisse. Vienna
- Mathematical Astronomy Morsels, Jean Meeus, Willmann-Bell, Inc., 1997 (Chapter 9, p. 51, Table 9.A Some eclipse Periodicities)
- NASA - Eclipses and the Saros
- NASA - Catalog of Lunar Eclipses in Saros 0
- NASA - Lunar Eclipses of Saros Series 1 to 180
- NASA - Solar Eclipses of Saros Series 0 to 180
- NASA - Summary of Lunar Eclipses in Saros Series -20 to 183
- NASA - Summary of Solar Eclipses in Saros Series -13 to 190
- Search among the 11,898 solar eclipses over five millennium and display interactive maps
- Search among the 12,064 lunar eclipses over five millennium and display interactive maps
- Eclipses and the Saros Cycle
- Eclipse Search – here one can search 5,000 years of eclipse data by type, magnitude, Saros number or simply by year.
- Saros series 131 table