Exeligmos

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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[edit]

The exeligmos was known by the Greeks as early as 100 BC. A clock they made, called the Antikythera mechanism was able 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[edit]

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

March 7, 1970 April 8, 2024
Path Map
(total eclipse is blue path)
(green lines represent limits of partial eclipse)
1970-03-07 eclipse crop.png 2024-04-08 eclipse crop.png
Duration 3 minutes 28 seconds 4 minutes 28 seconds
Max width of total eclipse path 153 kilometers 199 kilometers
Latitude of greatest eclipse 18° North 25° North
Time of greatest eclipse (UTC) 17:38 18:17

Lunar exeligmos example[edit]

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

February 9, 1990 March 13, 2044
Path Map
Lunar eclipse chart close-1990Feb09.png Lunar eclipse chart close-2044Mar13.png
Visibility
(side of earth eclipse is visible from)
Lunar eclipse from moon-1990Feb09.png Lunar eclipse from moon-2044Mar13.png
Duration (Partial eclipse) 204 minutes 209 minutes
Time of greatest eclipse (UTC) 19:12 19:38

Sample series of solar exeligmos[edit]

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 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[edit]

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.[4]

Exeligmos.gif

Solar Saros Animation (for comparison)[edit]

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).[4]

Saros 136 animation.gif

See also[edit]

References[edit]

  1. ^ a b c Littman, et al., Mark (2008). Totality: eclipses of the sun. Oxford University Press. pp. 325–326. ISBN 0-19-953209-5. 
  2. ^ Freeth, Tony; Y. Bitsakis, X. Moussas..., and 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. ^ http://books.google.co.uk/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. ^ a b NASA Eclipse Website Fred Espenak