Exeligmos

An exeligmos (Greek: ἐξέλιγμοςturning of the wheel) 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 close to the eclipse before it. For a lunar eclipse the same part of the earth will view an eclipse that is very similar to the one that occurred one exeligmos before it (see main text for visual examples). It is an eclipse cycle that is a triple saros, 3 saroses (or saroi) long, with the advantage that it has nearly an integer number of days so the next eclipse will be visible at locations and times near the eclipse that occurred one exeligmos earlier. In contrast, each saros, an eclipse occurs about 8 hours later in the day or about 120° to the west of the eclipse that occurred one saros earlier.[1]

Details

The Greeks had knowledge of the exeligmos by at latest 100 BC. A Greek astronomical clock called the Antikythera mechanism used epicyclic gearing to predict the dates of consecutive exeligmoses.[2]

The exeligmos is 669 synodic months (every eclipse cycle must be an integer number of synodic months), almost exactly 726 draconic months (which ensures the sun and moon are in alignment during the new moon), and also almost exactly 717 anomalistic months[3] (ensuring the moon is at the same point of its elliptic orbit). The first two factors make this a long lasting eclipse series. The latter factor is what makes each eclipse in an exeligmos so similar. The near integer number of anomalistic months ensures that the apparent diameter of the moon will be nearly the same with each successive eclipse. The fact that it is very nearly a whole integer of days ensures each successive eclipse in the series occurs very close to the previous eclipse in the series. For each successive eclipse in an exeligmos series the longitude and latitude can change significantly because an exeligmos is over a month longer than a calendar year, and the gamma increases/decreases because an exeligmos is about three hours shorter than a draconic month. The sun's apparent diameter also changes significantly in one month, affecting the length and width of a solar eclipse.[1]

Solar exeligmos example

Here is a comparison of two annular solar eclipses one exeligmos apart:

April 19, 1958 May 20, 2012
Path Map
(annular eclipse is red path)
(green lines represent limits of partial eclipse)
SE1958Apr19A SE2012May20A
Duration 7 minutes 7 seconds 5 minutes 46 seconds
Max width of annular eclipse path 138 kilometers 184 kilometers
Latitude of greatest eclipse 26° North 49° North
Time of greatest eclipse (UTC) 03:27 23:54

Lunar exeligmos example

Here is a comparison of two partial lunar eclipses one exeligmos apart:

July 16, 1954 August 16, 2008
Path Map
Lunar eclipse chart close-1954Jul16 Lunar eclipse chart close-2008Aug16
Visibility
(side of earth eclipse is visible from)
Lunar eclipse from moon-1954Jul16 Lunar eclipse from moon-2008Aug16
Duration (Partial eclipse) 141 minutes 188 minutes
Time of greatest eclipse (UTC) 00:20 21:11

Sample series of solar exeligmos

Exeligmos table of solar saros 136. Each eclipse occurs at roughly the same longitude but moves about 5-15 degrees in latitude with each successive cycle.[1]

Saros Member Date[4] Time
(Greatest)
UTC
Type Location
Lat,Long
Gamma Mag. Width
(km)
Duration
(min:sec)
Ref
136 3 July 5, 1396 19:37:40 Partial 63.9S 147.2W -1.3568 0.3449 [1]
136 6 August 7, 1450 16:48:49 Partial 61.8S 132.8W -1.1286 0.756 [2]
136 9 September 8, 1504 15:12:15 Annular 55.3S 102.6W -0.9486 0.9924 83 0m 32s [3]
136 12 October 11, 1558 14:58:55 Annular 56.5S 90.3W -0.8289 0.9971 18 0m 12s [4]
136 15 November 22, 1612 16:04:35 Hybrid 65.7S 98.4W -0.7691 1.0002 1 0m 1s [5]
136 18 December 25, 1666 17:59:16 Hybrid 71.6S 98.3W -0.7452 1.0058 30 0m 24s [6]
136 21 January 27, 1721 20:05:11 Total 64S 102.4W -0.7269 1.0158 79 1m 7s [7]
136 24 March 1, 1775 21:39:20 Total 47.9S 124.8W -0.6783 1.0304 139 2m 20s [8]
136 27 April 3, 1829 22:18:36 Total 28.5S 142.6W -0.5803 1.0474 192 4m 5s [9]
136 30 May 6, 1883 21:53:49 Total 8.1S 144.6W -0.425 1.0634 229 5m 58s [10]
136 33 June 8, 1937 20:41:02 Total 9.9N 130.5W -0.2253 1.0751 250 7m 4s [11]
136 36 July 11, 1991 19:07:01 Total 22N 105.2W -0.0041 1.08 258 6m 53s [12]
136 39 August 12, 2045 17:42:39 Total 25.9N 78.5W 0.2116 1.0774 256 6m 6s [13]
136 42 September 14, 2099 16:57:53 Total 23.4N 62.8W 0.3942 1.0684 241 5m 18s [14]
136 45 October 17, 2153 17:12:18 Total 18.8N 65.7W 0.5259 1.056 214 4m 36s [15]
136 48 November 20, 2207 18:30:26 Total 15.8N 87.8W 0.6027 1.0434 180 3m 56s [16]
136 51 December 22, 2261 20:38:50 Total 16.1N 124.2W 0.636 1.0337 147 3m 17s [17]
136 54 January 25, 2316 23:05:17 Total 21.4N 166W 0.6526 1.0282 126 2m 42s [18]
136 57 February 27, 2370 1:07:02 Total 33.2N 157E 0.6865 1.0262 121 2m 17s [19]
136 60 March 31, 2424 2:10:10 Total 51.3N 131.9E 0.7652 1.0254 133 1m 55s [20]
136 63 May 3, 2478 1:55:59 Total 75.7N 107.7E 0.9034 1.0218 176 1m 20s [21]
136 66 June 5, 2532 0:28:58 Partial 67.5N 1.3E 1.0962 0.8224 [22]
136 69 July 7, 2586 22:07:07 Partial 64.5N 7.2E 1.327 0.3957 [23]

Solar Exeligmos Animation

Here is an animation of an exeligmos series. Note the similar paths of each total eclipse, and how they fall close to the same longitude of the earth.[5]

Exeligmos

Exeligmos

Solar Saros Animation (for comparison)

This next animation is from the entire saros series of the exeligmos above. Notice how each eclipse falls on a different side of the earth (120 degrees apart).[5]

Saros 136 animation

Saros 136 animation

See also

References

  1. ^ a b c Littman, Mark; et al. (2008). Totality: eclipses of the sun. Oxford University Press. pp. 325–326. ISBN 0-19-953209-5.
  2. ^ Freeth, Tony; Y. Bitsakis; X. Moussas; M.G. Edmunds (November 30, 2006). "Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism". Nature. 444 (7119): 587–591. Bibcode:2006Natur.444..587F. doi:10.1038/nature05357. PMID 17136087.
  3. ^ https://books.google.com/books?id=tAhZT5jRTwgC&pg=PA301&lpg=PA301&dq=exeligmos+717+669&source=bl&ots=sFcx9lkg0x&sig=RBi98OvhkiwSnAhaMBmI-upYh6M&hl=en&sa=X&ei=JgWbUOuNDqmQ0AWtnoGgCw&ved=0CCoQ6AEwAg#v=onepage&q&f=false
  4. ^ Gregorian Calendar is used for dates after 1582 Oct 15. Julian Calendar is used for dates before 1582 Oct 04.
  5. ^ a b NASA Eclipse Website Fred Espenak
54 (number)

54 (fifty-four) is the natural number following 53 and preceding 55.

Antikythera mechanism

The Antikythera mechanism (, ) is an ancient Greek analogue computer and orrery used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad, the cycle of the ancient Olympic Games.The artefact was retrieved from the sea in 1901, and identified on 17 May 1902 as containing a gear wheel by archaeologist Valerios Stais, among wreckage retrieved from a wreck off the coast of the Greek island Antikythera. The instrument is believed to have been designed and constructed by Greek scientists and has been variously dated to about 87 BC, or between 150 and 100 BC, or to 205 BC, or to within a generation before the shipwreck, which has been dated to approximately 70-60 BC.The device, housed in the remains of a 34 cm × 18 cm × 9 cm (13.4 in × 7.1 in × 3.5 in) wooden box, was found as one lump, later separated into three main fragments which are now divided into 82 separate fragments after conservation works. Four of these fragments contain gears, while inscriptions are found on many others. The largest gear is approximately 14 centimetres (5.5 in) in diameter and originally had 223 teeth.It is a complex clockwork mechanism composed of at least 30 meshing bronze gears. A team led by Mike Edmunds and Tony Freeth at Cardiff University used modern computer x-ray tomography and high resolution surface scanning to image inside fragments of the crust-encased mechanism and read the faintest inscriptions that once covered the outer casing of the machine.

Detailed imaging of the mechanism suggests that it had 37 gear wheels enabling it to follow the movements of the moon and the sun through the zodiac, to predict eclipses and even to model the irregular orbit of the moon, where the moon's velocity is higher in its perigee than in its apogee. This motion was studied in the 2nd century BC by astronomer Hipparchus of Rhodes, and it is speculated that he may have been consulted in the machine's construction.The knowledge of this technology was lost at some point in antiquity, and technological works approaching its complexity and workmanship did not appear again until the development of mechanical astronomical clocks in Europe in the fourteenth century. All known fragments of the Antikythera mechanism are kept at the National Archaeological Museum in Athens, along with a number of artistic reconstructions/replicas of how the mechanism may have looked and worked.

April 2033 lunar eclipse

A total lunar eclipse will take place on April 14, 2033.

April 2051 lunar eclipse

A total lunar eclipse will take place on April 26, 2051.

This will be the third lunar eclipse in the 2050-2051 tetrad.

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.

February 1943 lunar eclipse

A partial lunar eclipse took place on February 20, 1943.

March 1961 lunar eclipse

A partial lunar eclipse took place on March 2, 1961.

March 1979 lunar eclipse

A partial lunar eclipse took place on March 13, 1979.

This event followed the total solar eclipse of February 26, 1979.

March 1997 lunar eclipse

A partial lunar eclipse took place on March 24, 1997, the first of two lunar eclipses in 1997.

This partial lunar eclipse was nearly total; however, it occurred 3 days after the lunar apogee, so the umbral shadow is smaller.

This is the 29th member of Lunar Saros 132, and the last of the first set of partial eclipses. The next event is the April 2015 lunar eclipse, which is the first of 12 total eclipses.

May 2087 lunar eclipse

A total lunar eclipse will take place on May 17, 2087. The moon will pass through the center of the Earth's shadow.

Solar eclipse of April 30, 2060

A total solar eclipse will occur on April 30, 2060. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

Solar eclipse of February 14, 1934

A total solar eclipse occurred on February 14, 1934. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide. Totality was visible from the Dutch East Indies (today's Indonesia), North Borneo (now belonging to Malaysia), and South Pacific Mandate in Japan (the part now belonging to FS Micronesia).

Solar eclipse of February 25, 1952

A total solar eclipse occurred on February 25, 1952. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

The path of totality crossed Africa, the Middle East, and Asia.

Solar eclipse of February 3, 1916

A total solar eclipse occurred on February 3, 1916. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

Totality was visible in Colombia, Venezuela, and the whole Guadeloupe except Marie-Galante, Saint Martin and Saint Barthélemy.

Solar eclipse of July 5, 2168

A total solar eclipse will occur on July 5, 2168. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

Lasting a maximum of 7 minutes, 26 seconds, it will be the longest eclipse since the 11th century, which lasted 7 minutes and 20 seconds, as well with the next two occurrences.

Solar eclipse of June 13, 2132

A total solar eclipse will occur on June 13, 2132. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

Solar eclipse of June 25, 2150

A total solar eclipse will occur on June 25, 2150. It will be the longest total eclipse since the 11th century. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

This will be the first total solar eclipse to exceed 7 minutes in term of duration since June 30, 1973. Totality will start in the Lesser Sunda Islands in Indonesia, continue across the northern Pacific Ocean, and end in the eastern Pacific.

Solar eclipse of June 3, 2114

There will be a total solar eclipse on June 3, 2114. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

Solar eclipse of May 22, 2096

A total solar eclipse will occur on May 22, 2096. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.

This will be the first eclipse of saros series 139 to exceed series 136 in length of totality. The length of totality for saros 139 is increasing, while that of Saros 136 is decreasing.

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