SaroPeriod issolar eclipseandlunar eclipseThe cycle of refers toMoonThe time required to run on its orbital disk for one week (so that the lunar intersection can circle along the orbit) - 223 new moons, that is, 223 × 29.53059 days=6585.32157 days, that is, 18 years and 11.32 days (18 years and 10.32 days if there are 5 leap years).This isBabylonianyessolar eclipseIts periodicity found after observation“Saro”It means repetition.This time is close to 242Node month(242 × 27.21222 days=6585.35724 days).becauseSaroThe cycle has a "fraction" of 0.32 days, so you must wait for 3 Saro cycles before you canearthSee similar places onsolar eclipseIt happens again.
Around the worldSaroOne third of the continuous eclipses in the cycle occur in this waySaroAfter the cycle, i.e. 54 years and 33 days,solar eclipseAlmost in the same geographical location.12 different mainSaro solar eclipse(Grand Saros eclipse) It is happening now. One of the eclipses occurred in 1937, 1955, 1973, 1991 and 2009 respectively, and the duration of each eclipse is within 7.5 minutes.
Lunar eclipses near the descending node
Occurring near the intersection pointlunar eclipse, belonging to odd columnsSaroSequence.The first of this sequencelunar eclipseWhen it happens,MoonThrough the southern edge of the shadowSaroIt gradually moves north in the cycle.
“Saro”In Latin, the word means repetition. Each Saro cycle has an average of 71 sexual intercourse, includingsolar eclipse43 times,lunar eclipse28 times.becauseearthAroundsunlightAnd the moon's revolution around the earth have certain laws, sosolar eclipseandlunar eclipseThe occurrence of also has its cyclical nature.YesSaroPeriod, we can predictlunar eclipseHas.For example, on July 11, 1991lunar eclipse, the shelter belt goes throughLatin AmericaandPacific region。People pushed forward 18 years and 11 days. It must have happened on June 30, 1973solar eclipse, the eclipse cover of the total solar eclipse crossedAfrican continent。If you push one backSaroThe time of the cycle, people can calculate that it will also happen on July 22, 2009solar eclipseThis is what happenedChinaYangtze river basinThe total solar eclipse of.
Historical discovery
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Schematic diagram of total solar eclipse on July 22, 2009
SaroPeriod isChaldeansIt was discovered several centuries before the Western Yuan Dynasty, and later spread toHipachas、Pliny andPtolemy , but they are all presented with different names.staySu Mei/The word "SAR" in Babylon is a unit of measurement, with a value of about 3600.It was in 1691 that "Saro" wasedmond halley It is used to describe the cycle of food, and it is converted from the 11th century Byzantine Suda dictionary.Although in 1756 Guillaume Le Gentil pointed out thatHarleyThe name is wrong, but the noun is still in use.
ancientBabylonPeople may be the first people to see this rule, and they have found it early“SaroPeriod ".The so-called "Saro",LatinThe original meaning of "repetition" in "is that the Saro cycle is about 6585.32 days long, which is equivalent to 18 years and 10.3 or 11.3 days (depending on whether there are 5 or 4 leap years in the 18 years).That is to say, they are in aSaroAfter the cycle, the celestial phenomena of the year will reappear - however, there will always be some differences in the type of food, whether it is total or partial, and where the food can be seen.For example, February 16, 1980（Spring Festival）, onChinaA total solar eclipse occurred in the southwest;It must have happened on February 5, 1962 6585 days agosolar eclipse——A total solar eclipse in Indonesia;And there must be 6585 days after that, namely February 27, 1998Somewhere——South America——One day (partial) eclipse, the rest can be analogized.
ancientBabylonOf course, people get this rule from long-term practical observation and experience.In fact, this is two cycles - the new moon and“Node month”OfCommon multipleQuestion.The former is 29.530588 days long;The latter isMoonThrough its orbit andEclipticThe period of the intersection (this is the date of occurrencelunar eclipseNecessary conditions), about 27.212220 days.After some conversion, 242Node monthCoincidentally, the length of 223 new moons is 6585 days.That is:
27.212220 × 242 = 6585.35724
29.530588 × 223 = 6585.32157
The difference is less than 0.036 days or 50 minutes.Obviously, this is very remarkable.In ancient China, there was also something to be proud oflunar eclipselaw.As in the Han Dynasty《Primordial calendar》There is a "three system calendar period", which is 135 new moons, i.e. 3986.62965 days, which is the same as 146.5Node month(3986.59023).
In the Tang Dynasty, there was an astronomer and mathematicianLi Chunfeng, he told Japanlunar eclipseIt is said that he had calculated in advance that there would be a total solar eclipse in Xinweishuo (June 1, 634 AD) in May of the eighth year of Zhenguan, and reported it to the imperial court in time according to regulationsTang TaizongFor the 32 year old“Taishiling”Not enough trust, so he asked: "If the sun doesn't eclipse (eat), how will you deal with it?" Li Chunfeng calmly replied: "If you don't eclipse (eat), please die." If you are not very sure, who dares to use his own life as a guarantee?Of course, the final result is a comedy, butLi ChunfengSince then, he has gained great fame and obtainedTang TaizongFull trust.
Description of nature
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18 years, 11 days and 8 hoursSaroThe cycle is very useful for predicting the recurrence of the same food, because it andMoonThe three periods of the orbit are related to:Node month、Perigee monthAnd the new moon.When eating occurs, it's notMoonbe locatedearthandsunlightBetween（solar eclipse）, isearthBetween the sun and the moon（lunar eclipse）This phenomenon only occurs in the new moon or full moon, so it determines the change of the moon phaseOutlookThe cycle is 29.53 days.However, not every full moon or new moon, Earth orMoonAll the shadows of the three celestial bodies can fall on the opposite celestial bodies, so in order for an eclipse to occur, the three celestial bodies must also be close to the same line, which only occurs when the moon crossesEcliptic surfaceOne of the two intersections (ascending or descending) on the, the moon crossesEcliptic surfaceThe period of the last same intersection is determined to be 27.21 days.Finally, if the food should have the same phenomenon and duration, thenearthandMoonThere should be the same distance, and the period for the same distance isPerigee month，time intervalIt is 27.55 days.
Sarrow algorithm
SaroThe origin of the cycle is 223 new moons, about 242 in lengthNode monthSimilar to 239Perigee monthClose (about less than 2 hours).This means that after aSaroPeriod,MoonThe new moonNode monthandPerigee monthAlmost all are integers,earth、sunlightThe geometric relationship between the moon and the moon is almost the same: the moon has the same phase and the same distance from the earth at the same intersection.If you know that an eclipse has occurred on a certain daySaroAt the turn of the cycle, almost the same eclipse will occur again.However,SaroCycle (18.031 years) andMoonOfPrecessionThe cycle (18.60 years) is not the same, so even ifearth、sunlightandMoonThe geometric relationship of the three is almost the same, but the positions of the moon with stars as the background are still different.
SaroThe number of days in the cycle includes a fraction of 1/3 days, which is not an integer, making the problem more complicated.becauseearthThe rotation ofSaroThe eclipses that occur on the day of the cycle will be delayed by about 8 hours.staysolar eclipseThis means that the area where the eclipse can be seen will move 120 ° to the west, or one third of the sphere, so only one of them can be seen every three times at the same place.staylunar eclipseThe next eclipse will be seen at the same placeMoonThe time on the horizon may be the same, but if you wait three timesSaroThe lunar eclipse after the cycle (54 years and one month, about 19756) will occur at almost the same time of the day, which is called the 3-saro cycle or exerigmos（Greek: "Runner").
Saros series
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The monthly cycle is called "Saro"
As mentioned earlier,SaroThe cycle is based on 223 new moons and 239 new moonsPerigee monthAnd 242Node monthHowever, because the relationship between them is not perfect, two eclipses separated by a Saro cyclegeometryThere is still a little difference in the relationship.actually,sunlightandMoonAt the closing positionSaroThe intersection point of the cycle still differs by about 0.5 °, which involves a series of eclipses. Every time you see the situation, there is a slight change, called the Saro sequence.eachSaroThe sequence starts from partial eclipse, and every time it goes through a Saro cycle,MoonThe path ofDescending pointOr moving southward (passing through the ascending node).At a certain point, food can no longer occur, and the sequence ends.From 2000 BC to 3000 AD, each sequence lasted from 1226 to 1550 years, and there were 69 to 87 timessolar eclipseMost of them are 71 or 72 times.39 to 59 times per sequenceCentral eclipse(Most of them are 43 times, including total eclipse, annular eclipse and total annular eclipse).lunar eclipseThe sequence ofSaroThe sequence is in progress.
whetherMoonAt the descending or ascending node (solar eclipse orlunar eclipse)，SaroThe sequences are numbered with numbers.The odd number indicates thatsolar eclipse, the even number indicates the solar eclipse near the falling node;But inlunar eclipseThe collocation of these numbers is opposite.Saros series The numbers of are arranged by the time when the maximum eclipse occurs, that is, the closest to the intersection.In 2008, for example, there were 39 (117 to 155)solar eclipseOfSaroThe sequence is in progress, andlunar eclipseThere are 41 (109 to 149) sequences in progress.
If these three cycles completely repeat every 6585.322 days, the solar eclipse will also completely repeat everySaroAfter the cycle.However, these cycles differ slightly from each other, which causesSaroThe change of the geometric position of the solar eclipse after the cycle.Notably, 19ConsulThe year minus 223 new moons is about 11 hours.This gap of 11 hours isSaroThe reason why the cycle is delayed along time.
If the current solar eclipse is recorded asSolar eclipseA，Put aSaroThe corresponding solar eclipse after the cycle is recorded as solar eclipse B, at any positionsunlightandMoonIt must be aligned to form a full moon.However,sunlightAt B, it will not return to the same distance from the intersection of the moon (the position of the sun at eclipse A).It is 11 hours away before it finishes the 19th consul year.sunlightDuring these 11 hours, it moved at the speed of one arc (about one degree) in an average of 27 minutes. Therefore, the location of eclipse B drifted 0.5 degrees westward (note that the conditions for the occurrence of solar eclipse must be within 18 degrees near the intersection of the sun and the moon).Because of this half degree drift,SaroThe cycle also has a beginning and an end. It will completely coincide with the previous cycle after 70 to 80 consecutive solar eclipses.So, the wholeSaroThe cycle takes 12 to 14 centuries.Suppose that the solar eclipse we see is about 18 degrees east of the northern intersection of the moonMoonAlso inEcliptic1.5 degrees north of.
moonThe shadow ofsunlightTo the north, onlyearthSuperficialArcticScratch the edgearcticA solar eclipse is formed nearby.The next solar eclipse in 18 years will be more close to the northern node of the moon by about half a degree, so thatMoonThe shadow of moves south.The solar eclipse will be "deeper" (moresunlightIs covered by shadows), longer durationearthThe surface coverage is also greater.besides,MoonShadow directionearthThe equator moves.Finally, after 10 to 11 solar eclipses, the moon'sUmbra deliver toearth, causing a total solar eclipse (or annular eclipse).The next solar eclipse will be a total eclipse (or annular eclipse).
stayequatorThere will be a wholeSaroThe solar eclipse with the longest duration in the family (after about 35 to 40 solar eclipses, the eclipse occurred just after the northern intersection of the moon. The whole eclipse will repeat the first half of the process in reverse order. After several total eclipses,SaroThe family ended near the South Pole with 10 to 11 solar eclipses.Finally, the new moon is too far away from the north intersection of the moon, so that the moon's shadow cannot be castearthSurface, this timeSaroThe cycle ends.If the solar eclipse occurs at the south intersection of the moon, the period will be the same, unless the solar eclipse occurs atantarcticOccurs and starts moving toward the North Pole.An eclipse of the moonSaroThe process of circulation is similar.
As mentioned above, solar eclipses only occur insunlightWithin 18 days before and after the north-south intersection of the moon.This month long period is called "solar eclipse season";One to three solar eclipses may occur during this period.The solar eclipse in the sky is very frequent, so in fact, each solar eclipse season is differentSaroThe cycle and the lunar eclipse sarro cycle are similar.In addition, along withOld Saro cycleThe new cycle begins to replace him and continues to overlap.Therefore, multipleSaroCirculate an eclipse season.
In general, there will be 38 to 42sunlightSaroCycles work at the same time, so does the moon Saro cycle, each in its own stage.Therefore, the wholeSaroThe structure of the cycle is extremely complex.
Numeration
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becauseSaroIt is very important to distinguish each Saro cycle because of the chaos of the cycle.This requires us to name or number these cycles to identify them.Astronomers have a set ofSaroThe astrologer also has an independent counting method.AstronomicSaroThe periodic counting method is published in van den Bergh《a 1955 paper》However, some crucial details were ignored.He put theSaroThe cycles are numbered.IfsunlightNear the north intersection of the moon,SaroIt is numbered odd. If it is near the south intersection,SaroIt is numbered even.Saro cycle of the sun andMoonThe Saro cycle is numbered separately (strictly according to the sun and moon).
AstrologerSaroThe numbers are relatively more complex.First, I have only seen two books of discussionSaroThe cycle of the book, and these two books only explain the solar eclipse Saro cycle, the lunar eclipse Saro cycle is ignored.They arbitrarily numbered the eclipse season "1 North" consecutively（sunlight1 degree at the north intersection of the moon), "1 South" (1 degree at the south intersection of the sun).In addition, if two eclipses occur in the same eclipse season (29 days apart), the previous oneSaroThe cycle is called "old" and the latter family is called "new".This makes it possible for aSaro cycleIt has a longer name, "9 South Old", and the Sarro cycle started in 1917 AD is called "9 South New".When the old cycle ends, the new cycle starts again, and the previous "new" is replaced by "old".With the cycle running, "new" is constantly replaced,AstrologyThe numbering method of is more complicated and confusing.
application
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Shaluo period and flood qualitative prediction
The reappearance of similar solar and lunar eclipses means that when the eclipses of the sun and the moon occur at the same kind, at the same time, and in the same area (the last month on the ground, the shadow coverage), the same weather conditions may occur, and the resulting rainstorm and flood are generally the same or similar, that is, the effects are similar.For example, the solar and lunar eclipses in 1662 and 1756 had the same kind of eclipse, similar time, and basically the same passing area. In these two years, the Yellow River had major floods, and the flood area, magnitude, and disaster situation were basically the same.The solar and lunar eclipses in 1853 were very similar to those in 1937, and the weather conditions in the control two years were also basically the same. In the two years, a very similar flood occurred in almost the same area in Henan.
The solar and lunar eclipses in 1864 were generally the same as those in 1958. In 1864, floods occurred in the lower reaches of the Yellow River, Hunan and southern Liaoning, and the middle and lower reaches of the Yangtze River were earlier;In 1958, the middle reaches of the Yellow River, northern Sichuan, southern Liaoning and other places were flooded, and the lower reaches of the Yangtze River dried up early.For another example, the recent 1996 eclipse was similar to the 1931 eclipse, and there were 131 records in 1931: in the middle of August 1931, a catastrophic flood occurred in the Yangtze River basin.According to the statistics of Hubei, Hunan, Jiangxi, Anhui, Jiangsu and other five provinces, 186 counties were affected by floods that year, with 3.333 million hmZ of farmland affected, 28.5 million people affected, 145000 people killed, and 1.35 billion yuan of property lost at that time;In 1996, there were floods in 13 provinces and autonomous regions in China. On July 18, more than 2 million people were urgently transferred, 810000 rooms collapsed and more than 2.8 million were damaged, resulting in a direct economic loss of 40 billion yuan. Among them, catastrophic floods occurred successively in Zishui River Basin, Shushui River Basin and Dongting Lake in Hunan Province.If all the above examples show that the lunar eclipse on the same day is generally the same, the effect is also generally similar[1]。
The rainstorm flood has obvious periodic corresponding relationship with the daily eclipse period.The time, frequency and passing area of the solar and lunar eclipses in 1991 and 1973 are very similar. A large flood occurred in the central part of Jilin Province in 1973, and the situation in 1991 is almost identical with that in 1973.The interval of 18 years is a Saro cycle.The year 1942 of the second Songhua River in Jilin Province was a flood year. After a Saruo cycle, the solar and lunar eclipses in 1960 were the same as those in 1942, and flood also occurred that year.
For another example, 1953 was a flood year in the upstream area of the Songhua River, and the maximum peak discharge of Wudaogou Hydrological Station in the upstream area of the Songhua River in Jilin Province was 7120m3/.,It is the highest flood since 1888. In 1971, 18 years later (a Saro cycle), the flow of the station was 2620 hours/hour, (the average flow of its maximum flood peak for many years was 1235 hours/hour). The solar and lunar eclipses were roughly the same, so the flood also occurred.There is an obvious corresponding relationship between rainstorm flood and the Saro period of solar eclipse, and the large flood in the year without lunar eclipse is more corresponding to the Saro period.In the data of nearly a hundred years (1897-1998), no lunar eclipse occurs alternately every 7, n years.A year without lunar eclipse with an interval of 11 years must have a year without lunar eclipse with an interval of 7 years. Similarly, a year without lunar eclipse with an interval of 7 years must have a year without lunar eclipse with an interval of 11 years. The total interval between the two years is 18 years, which is the same as the Saro cycle of the solar eclipse.
It shows that the lunar eclipse also has a cycle similar to the solar eclipse Saro cycle.In the year without lunar eclipse, the solar eclipse becomes the dominant factor for the flood, so the corresponding relationship between the Saro cycle and the flood is more accurate.Take the Yangtze River as an example. 1951 was a year without lunar eclipse, and the Yangtze River had a flood. The following 18 years, 1969 and 1987, were also a year without lunar eclipse, and there were floods;1% 2 was a year without lunar eclipse, and the Yangtze River was flooded. Eighteen years later, 19801998 was also a year without lunar eclipse, and floods also occurred.
