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The Saros cycle is an eclipse cycle. It is a period of about 6585⅓ days (approximately 18 years 11 days) which can be used to predict eclipses of the Sun and the Moon. One Saros period after an eclipse, the Sun, Earth, and the Moon return to approximately the same places and therefore almost identical solar and lunar eclipses repeat one Saros apart. For example, there was a total eclipse of the Sun on 11 August 1999 centered over Europe, and there will be a similar eclipse of the Sun on 21 August 2017, when it will be visible in North America.
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Explanation
The Saros was discovered by the Chaldeans (ancient Babylonian astronomers) several centuries BC. It is very useful for predicting possible eclipses since the calculations involve simple counting of cycles with integer numbers. The main problem is that the next eclipse after one Saros cycle occurs about 8 hours later in the day. In the case of an eclipse of the Sun this means the region of visibility shifts west one third of the way around the world, and most places from which the first eclipse was visible do not see any of the second one. 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. Therefore a longer cycle of three Saroses (54 years and a month, almost 19756 full days), known as a Triple Saros or exeligmos (''Greek'': "turn of the wheel"), has been used. After an exeligmos, an eclipse will again be visible at or near the original location.
In astronomical terms the Saros is due to several lunar and solar cycles repeating after about the same period of time:
Therefore the circumstances of an eclipse are also very similar to an eclipse one Saros earlier, and an eclipse (which happens when a conjunction or opposition of the Sun and Moon occurs in one of the nodes, that is, crossing the plane of the orbit) occurs again one Saros later.
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Name
The Saros cycle was known to the Babylonians, and later to Hipparchus, Pliny (Naturalis Historia II.1056) and Ptolemy (Almagest IV.2), but not under this name. The Babylonian "Saros" appears to have been a name for a period of 3600 years. The name "Saros" was first given to the eclipse cycle by Edmund Halley in 1691, who took it from the Suda, a Byzantine lexicon of the 11th century. Halley's naming error was pointed out by Guillaume Le Gentil in 1756, but the name stuck.
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Saros Series
So in principle one Saros after an eclipse, there will be another eclipse: however this does not repeat indefinitely because the match of the underlying periods (223 synodic = 242 draconic = 239 anomalistic months) is not perfect. In practice there is a long series of eclipses separated by one saros, that lasts many centuries but has a definite first and last eclipse.
At any one time theoretically there could be at most 223 possible Saros series of solar eclipses running simultaneously, because there are only 223 New Moons in the time span of a Saros. Similar for lunar eclipses at Full Moons.
For solar eclipses, these Saros series have been numbered by van den Bergh (1955). Currently (2003) the 39 series numbered 117 to 155 are active, i.e. a solar eclipse occurs at a New Moon that belongs to one of these series. Solar Saros series last for 69 to 86 eclipses (1226 to 1532 years), but on average 77 eclipses (1370 yr). They start and end with partial eclipses, but have about 48 central (total or annular) eclipses around the middle of the series.
For lunar eclipses, there are now 41 Saros series active. They last from 71 to 87 eclipses (1262 to 1551 years), but on average are not as long lived as for solar eclipses: 72 eclipses (1280 years), of which 40 to 58 are total.
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Example: Lunar Eclipses of Saros 131
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A single eclipse series can be used as a representative example of the life cycle of every Saros series. Choosing only the lunar eclipses for simplicity because they are more visible, we can consider Saros series 131. It began in the year AD 1427 with a partial southern penumbral lunar eclipse and will end in the year AD 2707 with a partial northern penumbral lunar eclipse. The total cycle period will be 1280 years.
Within this long period, there is a shorter period from 1950 to 2202 when total lunar eclipses will occur. We can consider 1950 as the birthday for the total lunar eclipse series:
The first total lunar eclipse in the series began in 1950 when the moon crossed fully into the southern edge of the earth's shadow.
The darkest and longest (central shadow) total lunar eclipse will occur in 2076 (126 years later)
The final total lunar eclipse in the series ends in 2202 when the moon makes its final pass across the northern edge of the earth's shadow.
This total lunar eclipse cycle lifetime is 252 years.
Sets of three
The Saros cycle repeats approximately every 18 years, 10⅓ days. The one-third day shift means the projected longitude on the Earth's for the maximum eclipse is shifted by about 120 degrees in sequential eclipses and it return again to approximately the same longitude after 3 cycles.
This is demonstrated below for the total eclipses from the perspective of the United States and western hemisphere, the eclipses are labeled as:
rising - seen east after sunset
setting - seen west before sunrise
down - invisible (occurs during the day)
In sequence, the Saros 131 lunar eclipse dates are:
Partial lunar eclipses (Southern edge of shadow)
May 10, 1427 (First partial penumbral south)
July 25, 1553 (First partial umbral south)
March 22, 1932 (Final partial umbral south)
Total lunar eclipses
April 2, 1950 (0 years) – down - First total
Apr 13, 1968 (18 years) – rising
Apr 24, 1986 (36 years) - setting
May 4, 2004 (54 years) – down
May 16, 2022 (72 years) - rising
May 26, 2040 (90 years) - setting
Jun 6, 2058 (108 years) – down
Jun 17, 2076 (126 years) – rising - Central
Jun 28, 2094 (144 years) - setting
Jul 8, 2112 (162 years) – down
Jul 21, 2130 (180 years) - rising
Jul 31, 2148 (198 years) - setting
Aug 11, 2166 (216 years) – down
Aug 21, 2184 (234 years) – rising
Sep 3, 2202 (252 years) – setting – Last total
Partial lunar eclipses (Northern edge of shadow)
Sep 13, 2220 (First new umbral partial north)
Apr 9, 2563 (Last partial umbral north)
Jul 7, 2707 (Last partial penumbral north)
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Saros 131 reference
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Reference
G. van den Bergh, Periodicity and Variation of Solar (and Lunar) Eclipses, 2 vols. H.D. Tjeenk Willink & Zoon N.V., Haarlem, 1955
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