Saros cycle

A Saros cycle is a relatively long series of solar or lunar eclipses , which is characterized by the fact that two of its directly following eclipses are very similar, but also that its period - the Saros period (also Chaldean period or Halley period ) - with around 18 .03 years is relatively long.

The Saros cycle is the most important and longest known cycle of eclipses . Like every cycle of eclipses, it has a limited duration. Each individual cycle consists of about 71 eclipses and is about 1270 years long. There are about 40 Saros cycles at the same time, which are numbered for differentiation. The solar eclipse of August 11, 1999, for example, was part of Saros cycle number 145.

Since the cycle formation in solar and lunar eclipses is basically the same, the solar Saros cycle consisting of solar eclipses is mainly dealt with in the following sections . Special features of the lunar Saros cycle follow at the end.

history

The English astronomer Edmund Halley chose the name Saros in 1691. He mistakenly used the Babylonian - Sumerian term SAR , because it was based on an inadequate writing by the Roman historian Pliny . SAR means either the number 3600 or something like "in space".

The Saros cycle was already known in ancient times . The oldest from 748 BC. Cuneiform tablets (Saros Cycle Texts) that have been preserved in the 3rd century BC come from the Babylonians . A few centuries later, the Saros cycle is also called by the Greek and Roman scholars Herodotus , Hipparchus , Pliny and Ptolemy . Thales , who could have found out about his existence on a trip to the Orient , is said to have used it for his prediction of the solar eclipse in 585 BC. Chr. Have used. According to the traditions of Herodotus , Thales only predicted the year.

The Babylonian term 17,46,40 (meaning the break

${\displaystyle (0;17,46,40)_{60}:=0\cdot 60^{0}+17\cdot 60^{-1}+46\cdot 60^{-2}+40\cdot 60^{-3}={\frac {8}{27}}\approx 0{,}296}$

in the sexagesimal system ) does not mean the length of the Saros cycle of approx. 18 years, but indicates the change in the value in the column in the Astronomical Cuneiform Text , measured in uš. A uš is a unit of time that corresponds to a rotation of the earth by 1 angular degree, i.e. 4 minutes. ${\displaystyle \Phi }$

Formation and meaning of the Saros cycle

→ Main article : Eclipse cycles

In a canon of eclipses, (oldest canon of eclipses by Theodor von Oppolzer ) all eclipses that follow one another are listed. They can already be grouped into short cycles, the semester cycles . The first figure below shows the superimposed images of all solar eclipses of such a cycle in the sky. The reference point are the two lunar nodes drawn on top of each other . The cycle is on both sides by the darkness limit limited to nine darkness. These differ from one another by a relatively large change in the node distance , a sign that they take place far from one another in a north-south direction on the earth's surface.

Semester cycle of nine solar eclipses (−4 to +4)

Eclipses can be read out from the Canon, which form an ever larger cycle, the more events in the basic sequence are skipped. The selection condition is that the eclipse period contains a whole number of half synodic months (lunations) as well as a whole number of half draconian months . The change in node distance becomes smaller and smaller, until the period, the cycle duration and the number of eclipses per cycle assume "astronomical dimensions" and a practical benefit is more and more lost. In addition, in rare cases, the period is approximately a whole multiple of a half anomalous month , making a significant cycle. In addition to the much shorter heptone, such is the Saros cycle in particular.

223 synodic months	242 draconian months	239 anomalous months
6585.32 days	6585.36 days	6585.54 days

For the Saros cycle, the table shows, in addition to the good agreement between whole numbers from synodic and draconian months, the good agreement with a whole number from anomalistic months. These multiples of the three different lunar periods are identical at around 18.03 years. This is the Saros period given in years.

In the Saros cycle, which consists of 71 solar eclipses (see second figure), the change in node distance is relatively small (only the sky image of every second eclipse could be recorded). Many neighboring eclipses are of the same type of eclipse. The shift of the observation location between two eclipses in north-south direction is relatively small. The shift relative to the node is westwards, since the change in node distance is negative.

Saros cycle of 71 solar eclipses (−35 to +35); only every second eclipse is marked

Eclipses of the same kind in the Saros cycle

After a whole number of anomalous months, the moon is back in the same place in its elliptical orbit around the earth. Its distance from the earth is the same again. Because the Saros period is only about 11 days longer than 18 full years, the earth is again almost at the same place of the slightly elliptical earth's orbit. For both reasons, the moon casts almost the same shadow ( core and penumbra ) on the earth. From the central eclipses, eclipses of the same kind follow one another: either total or annular .

Triple Saros (Exeligmos cycle)

The excess of the period with 6585.32 days (from 223 synodic months) to a number of whole days is about a third day. Three Saros periods ( Triple Saros or Exeligmos cycle ) result in approximately a whole number of days. Therefore, the third solar eclipse in the Saros cycle takes place at approximately the same geographical longitude on Earth. It can be observed from the same place on earth, but not again as a central darkness. Even ancient scientists had 54 years of working life, during which they made astronomical observations. On the other hand, observations over this period could be passed down orally, for example from the Orient at Thales (see above: History ).

Example: Saros cycle number 145

The following diagrams of four solar eclipses already show the essential properties of a Saros cycle:

• Most of the eclipses are similar, total here.
• Each subsequent eclipse takes place about 113 ° further west than the previous one.
• Each subsequent eclipse takes place a little further south (about 8 °) than the previous one.
• The fourth eclipse takes place at approximately the same geographical longitude (about 21 ° further east) and a little further south (about 23 °) than the first.

Aug 11, 1999	21 Aug 2017
Sep 2 2035	Sep 12 2053

Numbering of the Saros cycles

Every event contained in the Canon of Eclipses belongs to a Saros cycle. The individual cycles are distinguished by an individual number. This is particularly helpful in order to be able to name the cycles that exist at the same time individually.

The numbering was done by George van den Bergh . He arranged the eclipses in what he called the Saros-Inex panorama . In addition to the Saros cycle, he took into account the Inex cycle he had developed . Therefore the next eclipse in the Canon does not simply belong to the Saros cycle with the next higher number, but to the one whose numbers are five digits higher. If there are only five instead of six lunations before the next eclipse (start of a new semester cycle), the number jumps back by 33 digits. If the next eclipse already follows after one lunation, the number increases by 38.

Van den Bergh started with cycle number 10. In Oppolzer's Canon he found events up to number 165, but could only completely fill cycles from number 57 to 119. In modern constellations, the previous and following cycles have been completed and both older and more recent cycles have been added.

The successive events in the Canon of Eclipses take place alternately in proximity to the ascending or descending lunar node. This change carries over to the Saros number. Odd numbered cycles only contain eclipses that occur near the ascending node. It is the other way around for even numbers. Since the eclipses in the Saros cycle move from east to west, they are slowly shifted from the Arctic to the Antarctic in the case of odd cycle numbers. With even cycle numbers it is the other way round: from Antarctica to the Arctic.

Currently active solar Saros cycles

The 87 solar eclipses that took place between 1971 and 2011 belong to the 39 Saros cycles with the numbers 117 to 155. Cycle 116 ended on July 22, 1971, and cycle 156 began on July 1, 2011. By the end of cycle 117 on August 3, 2054, 40 Saros cycles are active in parallel.

Cycle 136 has reached the middle of its lifetime (1360 to 2622) and is also in the middle between 117 and 155. It therefore includes the currently most pronounced solar eclipses. The total solar eclipse of June 20, 1955 was its longest with a duration of 7 min 8 s, the total solar eclipse of July 11, 1991 its central eclipse with the smallest gamma value (in terms of amount) of −0.004.

The 56 central solar eclipses currently belong to 25 cycles, the 15 partial solar eclipses to the remaining 14 cycles. The two types of eclipse are thus distributed over the two cycle groups in the same ratio as they occur according to the eclipse limits (25/39 = 10.6 ° / 16.6 ° = 0.64), although their ratio is currently higher (56 / 81 = 0.79).

The “European total” solar eclipse of August 11, 1999 belonged to cycle 145 (see above, four figures ), which is still relatively young (1639 to 3009) and its central eclipse with the smallest gamma value (namely 0.007) only on March 8 2342 will take place. The longest eclipse (7 min 12 s) of this cycle will be later, on June 25, 2522.

Lunar Saros cycle

→ Main article : Lunar eclipse cycles

Lunar eclipses are easier to observe because, like solar eclipses, they cannot only be seen within a strip on the earth (the eclipse zone, which is only about 250 km wide in a central eclipse), but from the entire night half of the earth's surface. Therefore, it can be assumed that our ancient ancestors first noticed the lunar cycle. It should also soon have been recognized that a solar eclipse is usually accompanied by one (or two, one before and one after) lunar eclipse at intervals of half a synodic month (lunation), so a solar Saros cycle must also exist.

Van den Bergh also numbered the Saros lunar cycles, for which he used his Saros lunar Inex panorama. Since the penumbral eclipses are missing in Oppolzer's Canon , the Saros columns in the panorama are shorter, the panorama is less high than the solar Saros-Inex panorama.

It started with cycle number 12 (tentatively 2 events) and ended with number 150 (tentatively 1 event). In modern constellations the first and last cycles have been completed and both older and more recent cycles have been added. They also contain the penumbral eclipses.

There is no practical connection between the numbers of solar and lunar Saros cycles. For example, lunar cycle 145 began almost 200 years later than solar. It currently only contains penumbral eclipses, while solar cycle 145 has long since included total eclipses , including the solar eclipse of August 11, 1999 .

However, there is a mathematical connection between the solar and lunar Saros numbers. If a lunar eclipse occurs two weeks after a solar eclipse, the lunar Saros number of the lunar eclipse is 12 greater than the solar Saros number of the previous solar eclipse. In the opposite case, the solar Saros number of the solar eclipse is 26 greater than that of the previous lunar eclipse. Because of 12 + 26 = 38 , the lunar Saros number increases after each lunation by 38. After one semester, i.e. after 6 lunations, the lunar Saros number increases by 5 (= 6 × 38 - 223, because a Saros period contains exactly 223 lunations).

In a solar cycle, the solar eclipses that follow each other every 18 years “run” from pole to pole on the earth's surface. During the lunar eclipses of a lunar Saros cycle, the earth's shadow runs over the full moon that can be observed in the sky. With odd cycle numbers it runs from north to south (viewed from the northern hemisphere from top to bottom), with even numbers from south to north.

See also

• Meton cycle
• Lunar circle

literature

• George van den Bergh: Periodicity and variation of solar and lunar eclipses. Tjeenk Willink, Haarlem 1955.
• Jean Meeus : Mathematical Astronomy Morsels III. Willmann-Bell, Richmond 2004, ISBN 0-943396-81-6 , pp. 87-113.
• Jean Meeus : Mathematical Astronomy Morsels IV. Willmann-Bell, Richmond 2007, pp. 107–126.

Web links

• Hans-Dieter Gera: Moon orbit and Saros cycle. Retrieved January 16, 2009 . 
• Fred Espenak : Eclipses and the Saros. NASA Eclipse web site, accessed January 16, 2009 . 
• Fred Espenak: Solar Eclipses of Saros 0 to 180. NASA Eclipse web site, accessed January 16, 2009 . 
• Fred Espenak: Lunar Eclipses of Saros 1 to 175. NASA Eclipse web site, archived from the original on March 23, 2008 ; Retrieved January 16, 2009 . 
• solar-eclipse.de: List of active Saros cycles . Retrieved October 5, 2016 . 

Individual evidence

1. ↑ All data are average values, see eclipse cycles.
2. ^ Jean Meeus: Mathematical Astronomy Morsels III. Willmann-Bell 2004, ISBN 0-943396-81-6 , p. 111.
3. ↑ Naturalis Historia. II.10 [56].
4. ↑ Liz Brack-Bernsen: On the origin of the Babylonian moon theory. Franz-Steiner-Verlag, 1997, p. 5, p. 68.
5. ^ Otto Neugebauer: A history of ancient mathematical astronomy. Springer, 1975, p. 497.
6. ↑ George van den Bergh: Periodicity and Variation of Solar and Lunar Eclipses. Tjeenk Willink, Haarlem 1955.
7. ↑ Fred Espenak : Solar Eclipses of Saros 0 to 180.
8. ^ Jean Meeus: Mathematical Astronomy Morsels III. Willmann-Bell 2004, ISBN 0-943396-81-6 , p. 93 ff., TABLE 18.B.
9. ↑ Fred Espenak: Saros Series 136.
10. ^ Hans-Dieter Gera: Moon orbit and Saros cycle. Section: The course of the Saros cycle. 5th paragraph.
11. ↑ Fred Espenak: Saros Series 145.
12. ↑ Fred Espenak: Lunar Eclipses of Saros 1 to 175. ( Memento of the original from February 7, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
13. ↑ Fred Espenak: Lunar Eclipses of Saros 145.