The saros () is a period of exactly 223

synodic month In lunar calendars, a lunar month is the time between two successive Syzygy (astronomy), syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month. Variations In Shona people, S ...

s, 18 years 11 days and 8 hours, that can be used to predict

eclipse An eclipse is an astronomical event which occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ...

s of the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

and

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

. One saros period after an eclipse, the Sun,

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

, 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 Eclipses may occur repeatedly, separated by certain intervals of time: these intervals are called eclipse cycles. The series of eclipses separated by a repeat of one of these intervals is called an eclipse series. Eclipse conditions Eclipses ...

. Every eclipse has an associated saros series and all succeeding or preceding eclipses have a different saros series associated with them - as the eclipse of the same series occurs or occurred with a gap of one saros only. Solar and lunar eclipses have different saros series. A series of eclipses that are separated by one saros is called a ''saros series''. It corresponds to: *6,585.321347

solar day A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. The synodic day is distinguished from the sidereal day, which is ...

s *18.029

year A year is a unit of time based on how long it takes the Earth to orbit the Sun. In scientific use, the tropical year (approximately 365 Synodic day, solar days, 5 hours, 48 minutes, 45 seconds) and the sidereal year (about 20 minutes longer) ...

s *223

s *241.999 draconic months *18.999 eclipse years (38

eclipse season An eclipse season is a period, roughly every six months, when eclipses occur. Eclipse seasons are the result of the axial parallelism of the Orbit of the Moon, Moon's orbital plane (orbital inclination, tilted five degrees to the ecliptic, Earth ...

s of 173.31 days) *238.992 anomalistic months *241.029 sidereal months The 19 eclipse years means that if there is a

solar eclipse A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of Earth, totally or partially. Such an alignment occurs approximately every six months, during the eclipse season i ...

(or

lunar eclipse A lunar eclipse is an astronomical event that occurs when the Moon moves into the Earth's shadow, causing the Moon to be darkened. Such an alignment occurs during an eclipse season, approximately every six months, during the full moon phase, ...

), then after one saros a new moon will take place at the same

node In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics * Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines ...

of the

orbit of the Moon The Moon orbits Earth in the retrograde and prograde motion, prograde direction and completes one orbital period, revolution relative to the March Equinox, Vernal Equinox and the fixed stars in about 27.3 days (a tropical month and sidereal mont ...

, and under these circumstances another solar eclipse can occur.

History

The earliest discovered historical record of what is known as the saros is by Chaldean (neo-Babylonian) astronomers in the last several centuries BCE. It was later known to

Hipparchus Hipparchus (; , ; BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...

, Pliny and

Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...

. The name "saros" () was applied to the eclipse cycle by

Edmond Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, Hal ...

in 1686, who took it from the ''

Suda The ''Suda'' or ''Souda'' (; ; ) is a large 10th-century Byzantine Empire, Byzantine encyclopedia of the History of the Mediterranean region, ancient Mediterranean world, formerly attributed to an author called Soudas () or Souidas (). It is an ...

'', a

Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...

lexicon of the 11th century. The Suda says, " he saros isa measure and a number among

Chaldea Chaldea () refers to a region probably located in the marshy land of southern Mesopotamia. It is mentioned, with varying meaning, in Neo-Assyrian cuneiform, the Hebrew Bible, and in classical Greek texts. The Hebrew Bible uses the term (''Ka� ...

ns. For 120 saroi make 2220 years (years of 12 lunar months) according to the Chaldeans' reckoning, if indeed the saros makes 222 lunar months, which are 18 years and 6 months (i.e. years of 12 lunar months)." The information in the ''Suda'' in turn was derived directly or otherwise from the ''Chronicle'' of

Eusebius of Caesarea Eusebius of Caesarea (30 May AD 339), also known as Eusebius Pamphilius, was a historian of Christianity, exegete, and Christian polemicist from the Roman province of Syria Palaestina. In about AD 314 he became the bishop of Caesarea Maritima. ...

, 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 either comes from the Babylonian word ''sāru'' meaning the number 3600 or the Greek verb ''saro'' (σαρῶ) that means "sweep (the sky with the series of eclipses)". Manual2021-X MOUSSAS SAROS

The Saros period of 223 lunar months (in

Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordi ...

, ΣΚΓ′) is in the

Antikythera Mechanism The Antikythera mechanism ( , ) is an Ancient Greece, Ancient Greek hand-powered orrery (model of the Solar System). It is the oldest known example of an Analog computer, analogue computer. It could be used to predict astronomy, astronomical ...

user manual on this instrument, made around 150 to 100 BCE in Greece, as seen in the picture. This number is one of a few inscriptions of the mechanism that are visible with the unaided eye. Above it, the period of the

Metonic cycle The Metonic cycle or enneadecaeteris (from , from ἐννεακαίδεκα, "nineteen") is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise obser ...

and the Callippic cycle are also visible.

Description

The saros, a period of 6585.3211 days (15 common years + 3 leap years + 12.321 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

, 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

) or the Earth must be located between the Sun and Moon (for a

). This can happen only when the Moon is new or full, respectively, and repeat occurrences of these

lunar phase A lunar phase or Moon phase is the apparent shape of the Moon's directly sunlit portion as viewed from the Earth. Because the Moon is tidally locked with the Earth, the same hemisphere is always facing the Earth. In common usage, the four maj ...

s 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 five or six 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 eclipses separated by one saros have very similar appearance and duration due to the distance between the Earth and Moon being nearly the same for each event: this is because the saros is also an integer multiple of the ''anomalistic month'' of 27.5545 days, the period of the moon with respect to the lines of apsides in its orbit. Saros15122015

After one saros, the Moon will have completed roughly an integer number of synodic, draconic, and anomalistic periods (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). 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 Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...

period of 18.59992 years. The saros is not an integer number of days, but contains the fraction of of a day. Thus each successive eclipse in a saros series occurs about eight 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 An exeligmos () is a period of 54 years, 33 days that can be used to predict successive eclipses with similar properties and location. For a solar eclipse, after every exeligmos a solar eclipse of similar characteristics will occur in a location cl ...

'' ( ''Greek'': "turn of the wheel") cycle.

Saros series

Each saros series starts with a partial eclipse (Sun first enters the end of the node), and in 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). An arbitrary solar saros series was designated as solar saros series 1 by compilers of eclipse statistics. This series has finished, but the eclipse of November 16, 1990 BC (

Julian calendar The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year (without exception). The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts ...

) for example is in solar saros series 1. There are different saros series for solar and lunar eclipses. For lunar saros series, the lunar eclipse occurring 58.5 synodic months earlier (February 23, 1994 BC) was assigned the number 1. If there is an eclipse one inex (29 years minus about 20 days) after an eclipse of a particular saros series then it is a member of the next series. For example, the eclipse of October 26, 1961 BC is in solar saros series 2. Saros series, of course, went on before these dates, and it is necessary to extend the saros series numbers backwards to negative numbers even just to accommodate eclipses occurring in the years following 2000 BC (up till the last eclipse with a negative saros number in 1367 BC). For solar eclipses the statistics for the complete saros series within the era between 2000 BC and AD 3000 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, as mentioned, are numbered according to the type of eclipse (lunar or solar). In odd numbered series (for solar eclipses) the Sun is near the ascending node, whereas in even numbered series it is near the descending node (this is reversed for lunar eclipse saros series). Generally, the ordering of these series determines 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 (series 117 will end in 2054), whereas for lunar eclipses, there are now 41 active saros series (these numbers can be derived by counting the number of eclipses listed over an 18-year (saros) period from the eclipse catalog sites).

Example

As an example of a single saros series, this 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. 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 131 is 1280 years. Solar saros 138 interleaves with this lunar saros with an event occurring every 9 years 5 days alternating between each saros series. Because of the 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 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. Solar saros 138 interleaves with this lunar saros with an event occurring every 9 years 5 days alternating between each saros series. 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 days (a half saros, or sar) an eclipse will occur that is lunar instead of solar, or vice versa, with similar properties.Mathematical Astronomy Morsels, Jean Meeus, p.110, Chapter 18, ''The half-saros'' For example, if the Moon's penumbra partially covers the southern limb of the Earth during a solar eclipse, 9 years and 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 days after a total solar eclipse or an annular solar eclipse occurs, a total lunar eclipse will also occur. This 9-year period is referred to as a sar. It includes synodic months, or 111 synodic months plus one

fortnight A fortnight is a unit of time equal to 14 days (two weeks). The word derives from the Old English term , meaning "" (or "fourteen days", since the Anglo-Saxons counted by nights). Astronomy and tides In astronomy, a ''lunar fortnight'' is hal ...

. The fortnight accounts for the alternation between solar and lunar eclipse. For a visual example see '' this chart'' (each row is one sar apart).

Notes

References

Bibliography

* Jean Meeus and Hermann Mucke (1983) ''Canon of Lunar Eclipses''. Astronomisches Büro, Vienna * Theodor von Oppolzer (1887)
''Canon der Finsternisse''
Vienna * Jean Meeus, ''Mathematical Astronomy Morsels'', Willmann-Bell, Inc., 1997 (Chapter 9, p. 51, Table 9. A Some eclipse Periodicities)

External links

List of all active saros cycles
– Interactive eclipse search
Eclipse Search
– Search 5,000 years of eclipse data by various attributes

– Fundamental astronomy of eclipses {{DEFAULTSORT:Saros cycle 1st-millennium BC introductions Eclipses Time in astronomy Technical factors of astrology Neo-Babylonian Empire Chaldea Units of time