Saros (astronomy)

The saros (i/ˈsɛərɒs/) is a period of approximately 223 synodic months (approximately 6585.3211 days, or 18 years, 11 days, 8 hours), that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros.[1]

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

History

The earliest discovered historical record of what we call the saros is by the Chaldeans (ancient Babylonian astronomers) in the last several centuries BC.[2][3][4] It was later known to Hipparchus, Pliny[5] and Ptolemy.[6]

The name "saros" (Greek: σάρος) was applied to the eclipse cycle by Edmond Halley in 1691, who took it from the Suda, a Byzantine lexicon of the 11th century. The Suda says, "[The saros is] a measure and a number among Chaldeans. For 120 saroi make 2222 years according to the Chaldeans' reckoning, if indeed the saros makes 222 lunar months, which are 18 years and 6 months."[7] The information in the Suda in turn was derived directly or otherwise from the Chronicle of Eusebius of Caesarea, which quoted Berossus. (Guillaume Le Gentil claimed that Halley's usage was incorrect in 1756, but the name continues to be used.) The Greek word apparently comes from the Babylonian word "sāru" meaning the number 3600.[8]

Mechanical calculation of the cycle is built into the Antikythera mechanism.

Description

Lunar eclipses occurring near the Moon's ascending 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.

The saros, a period of 6585.3211 days (14 common years + 4 leap years + 11.321 days, or 13 common years + 5 leap years + 10.321 days), is useful for predicting the times at which nearly identical eclipses will occur. Three periodicities related to lunar orbit, the synodic month, the draconic month, and the anomalistic month coincide almost perfectly each saros cycle. 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 result from solar and lunar orbits producing the Moon's synodic period of 29.53059 days. During most full and new moons, however, the shadow of the Earth or Moon falls to the north or south of the other body. Eclipses occur when the three bodies form a nearly straight line. Because the plane of the lunar orbit is inclined to that of the earth, this condition occurs only when a full or new Moon is near or in the ecliptic plane, that is when the moon is at one of the two nodes (the ascending or descending node). The period of time for two successive lunar passes through the ecliptic plane (returning to the same node) is termed the draconic month, a 27.21222 day period. The three-dimensional geometry of an eclipse, when the new or full moon is near one of the nodes, occurs every 5 or 6 months when the Sun is in conjunction or opposition to the Moon and coincidentally also near a node of the Moon's orbit at that time, or twice per eclipse year. Two Saros eclipses have the same appearance and duration due to the distance between the Earth and Moon being nearly the same for each event because the Saros eclipse cycle is also an integer of the anomalistic month, the period of the eccentricity of lunar orbit, 27.5545 days.

Visualization of a period of one Saros cycle in 3D.

After one saros, the Moon will have completed roughly an integer number of lunar orbit cycles and synodic, draconic, and anomalistic periods (241, 223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase and be at the same node and 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).[9] Given the date of an eclipse, one saros later a nearly identical eclipse can be predicted. During this 18-year period, about 40 other solar and lunar eclipses take place, but with a somewhat different geometry. One saros equaling 18.03 years is not equal to a perfect integer number of lunar orbits (earth revolutions with respect to the fixed stars of 27.32166 days sidereal month), 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 slightly different position with respect to the stars for each eclipse in a Saros series. The axis of rotation of the Earth-Moon system exhibits a precession period of 18.59992 years).

The saros is not an integer number of days, but contains the fraction of   1⁄3 of a day. Thus each successive eclipse in a saros series occurs 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 about 120°, or about 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. Given three saros eclipse intervals, the local time of day of an eclipse will be nearly the same. This three saros interval (19,755.96 days) is known as a triple saros or exeligmos (Greek: "turn of the wheel") cycle.

Saros series

Solar eclipses occurring near the Moon's descending node are given even saros series numbers. The first eclipse of each series starts at the southern limb of the Earth and the eclipse's path is shifted northward with each successive saros.

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) due to the fact that the saros is not an exact integer of draconic months (about one hour short). 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.[10][11] 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.[12][13] 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, the 40 series numbered between 117 and 156 are active, whereas for lunar eclipses, there are now 41 active saros series.

Example

Saros 138 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
April 2, 1950
First total 		20:44 UT
April 13, 1968 04:47 UT
April 24, 1986 12:43 UT
May 4, 2004 20:30 UT
May 16, 2022
First central		 04:11 UT
May 26, 2040 11:45 UT
June 6, 2058 19:14 UT
June 17, 2076
Central 		02:37 UT
...6 intervening total eclipses omitted...
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, this table gives the dates of some of the 72 lunar eclipses for saros series 138. 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. In 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 in 2078. The first partial eclipse after this will occur in the year 2220, and the final partial eclipse of the series will occur in 2707. The total lifetime of lunar saros series 138 is 1280 years.

Because of the   1⁄3 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 138, 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 about 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 about 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 start to the end 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.[14]

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

References

  1. ↑ van Gent, Robert Harry (8 September 2003). "A Catalogue of Eclipse Cycles".
  2. ↑ 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
  3. ↑ 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
  4. ↑ P.J. Huber & S de Meis (2004): Babylonian Eclipse Observations from 750 BC to 1 BC, par. 1.1. IsIAO/Mimesis, Milano
  5. ↑ Naturalis Historia II.10[56]
  6. ↑ Almagest IV.2
  7. ↑ The Suda entry is online here.
  8. ↑ "saros". Encarta Dictionary. Microsoft. Archived from the original on Jun 8, 2009.
  9. ↑ Littmann, Mark; Fred Espenak; Ken Willcox (2008). Totality: Eclipses of the Sun. Oxford University Press. ISBN 0-19-953209-5.
  10. ↑ Meeus, Jean (2004). Ch. 18 "About Saros and Inex series" in: Mathematical Astronomy Morsels III. Willmann-Bell, Richmond VA, USA.
  11. ↑ 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.
  12. ↑ G. van den Bergh (1955). Periodicity and Variation of Solar (and Lunar) Eclipses (2 vols.). H.D. Tjeenk Willink & Zoon N.V., Haarlem.
  13. ↑ Bao-Lin Liu; Alan D. Fiala (1992). Canon of Lunar Eclipses, 1500 B.C. to A.D. 3000. Willmann-Bell, Richmond VA.
  14. ↑ Mathematical Astronomy Morsels, Jean Meeus, p.110, Chapter 18, The half-saros
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