Saros cycle

The Saros cycle is an eclipse cycle with a period of 223 synodic months (approximately 6585.3213 days, or nearly 18 years 11 1/3 days), that can be used to predict eclipses of the Sun and Moon. One cycle after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur.

A series of eclipses that are separated by one Saros cycle is called a Saros series.

Contents

History

The earliest discovered historical record of the Saros cycle is by the Chaldeans (ancient Babylonian astronomers) in the last several centuries BC [1][2][3], and was later known to Hipparchus, Pliny[4] and Ptolemy,[5] 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.[6] 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. Although Halley's naming error was pointed out by Guillaume Le Gentil in 1756, the name continues to be used.

Description

The Saros cycle of 18 years 11 days and 1/3 of a day is very useful for predicting the times at which nearly identical eclipses will occur, and is intimately related to 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 the Moon passes close to the ecliptic plane 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 at a new or full moon around 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 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.

The origin of the Saros cycle comes from the recognition that 223 synodic months is approximately equal to 242 draconic months, which is approximately equal to 239 anomalistic months (this approximation is good to within about 2 hours). What this means is that after one Saros cycle, 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. If one knew the date of an eclipse, then one Saros later, a nearly identical eclipse should occur. Mind that during that 18 year cycle, about 40 other solar and lunar eclipses take place, but with a somewhat different geometry. Note also that the Saros cycle (18.031 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 cycle 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 cycle, 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 Saros cycles, the local time of day of an eclipse will be nearly the same. This period of three Saros cycles (54 years 1 month, or almost 19756 full days), is known as a Triple Saros or exeligmos (Greek: "turn of the wheel").

Saros Series

Lunar eclipses occurring near the Moon's descending node are given odd Saros series numbers. The first eclipse in such series passes through the southern edge of the Earth's shadow, and the Moon's path is shifted northward each successive Saros cycle.

As described above, the Saros cycle is based on the recognition that 223 synodic months is to a good approximation 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 cycle 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 cycle, 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, and each successive Saros cycle 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. 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 articles references.[7][8] See also external links to interactive maps. 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 to 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). Lunar eclipse series are not as long-lived. 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.[9][10] 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 reversed. 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

Saros 131 lunar eclipse dates
May 10, 1427
(Julian calendar)		 First penumbral
(southern edge of shadow)
...6 intervening penumbral eclipses omitted...
July 25, 1553
(Julian calendar)		 First partial
...19 intervening partial eclipses omitted...
March 22, 1932
Final partial		 12:32 UT Lunar eclipse chart close-1932Mar22.png
April 2, 1950
First total		 20:44 UT Lunar eclipse chart close-1950Apr02.png
April 13, 1968 04:47 UT Lunar eclipse chart close-1968Apr13.png
April 24, 1986 12:43 UT Lunar eclipse chart close-1986Apr24.png
May 4, 2004 20:30 UT Lunar eclipse chart close-04may04.png
May 16, 2022
First central		 04:11 UT Lunar eclipse chart close-2022may16.png
May 26, 2040 11:45 UT Lunar eclipse chart close-2040May26.png
June 6, 2058 19:14 UT Lunar eclipse chart close-2058Jun06.png
June 17, 2076
Central		 02:37 UT Lunar eclipse chart close-2076Jun17.png
June 28, 2094 09:59 UT Lunar eclipse chart close-2094Jun28.png
July 8, 2112 17:16 UT
July 21, 2130 00:34 UT
July 31, 2148 07:51 UT
August 11, 2166 15:11 UT
August 21, 2184 22:32 UT
September 3, 2202
Last total		 05:59 UT
September 13, 2220
First partial
...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 cycle, 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 cycle, the visibility of each eclipse will differ for an observer at a given fixed 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.

See also

References

Cited references

  1. ↑ 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
  2. ↑ 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.
  3. ↑ P.J. Huber & S de Meis (2004): Babylonian Eclipse Observations from 750 BC to 1 BC, par. 1.1. IsIAO/Mimesis, Milano
  4. ↑ Naturalis Historia II.10[56]
  5. ↑ Almagest IV.2
  6. ↑ Microsoft Encarta College Dictionary, 2001
  7. ↑ Meeus, Jean (2004). Ch. 18 "About Saros and Inex series" in: Mathematical Astronomy Morsels III. Willmann-Bell, Richmond VA, USA. 
  8. ↑ Espenak, Fred; Jean Meeus (October 2006). "Five Millennium Canon of Solar Eclipses, Section 4 (NASA TP-2006-214141" (PDF). NASA STI Program Office. http://sunearth.gsfc.nasa.gov/eclipse/5MCSE/5MCSE-Text.pdf. Retrieved 2007-01-24. 
  9. ↑ G. van den Bergh (1955). Periodicity and Variation of Solar (and Lunar) Eclipses (2 vols.). H.D. Tjeenk Willink & Zoon N.V., Haarlem. 
  10. ↑ Bao-Lin Liu and Alan D. Fiala (1992). Canon of Lunar Eclipses, 1500 B.C. to A.D. 3000. Willmann-Bell, Richmond VA. 

General references

External links