An exeligmos (Greek: ἐξέλιγμος — turning 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.
It corresponds to:
- 669 synodic months
- 725.996 draconic months
- 56.996 eclipse years (114 eclipse seasons)
- 716.976 anomalistic months
The 57 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one exeligmos a New Moon (resp. Full Moon) will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur.
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 (ensuring the moon is at the same point of its elliptic orbit). And also corresponds to 114 eclipse seasons. 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.
Solar exeligmos example
Here is a comparison of two annular solar eclipses one exeligmos apart:
|May 20, 1966||June 21, 2020|
(annular eclipse is red path)
(light blue lines are lines of obscuration of 0%, 20%, 40%, 60% and 80% covered)
|Duration||0 minutes 5 seconds||0 minutes 38 seconds|
|Max width of annular eclipse path||3 kilometers||21 kilometers|
|Latitude of greatest eclipse||39° North||31° North|
|Time of greatest eclipse (UTC)||09:38||06:40|
Lunar exeligmos example
Here is a comparison of two total lunar eclipses one exeligmos apart:
|December 30, 1963||January 31, 2018|
(side of earth eclipse is visible from)
|Duration (Partial eclipse)||204 minutes||203 minutes|
|Time of greatest eclipse (UTC)||11:06||13:29|
Sample series of solar exeligmos
|136||3||July 5, 1396||19:37:40||Partial||63.9S 147.2W||-1.3568||0.3449|||
|136||6||August 7, 1450||16:48:49||Partial||61.8S 132.8W||-1.1286||0.756|||
|136||9||September 8, 1504||15:12:15||Annular||55.3S 102.6W||-0.9486||0.9924||83||0m 32s|||
|136||12||October 11, 1558||14:58:55||Annular||56.5S 90.3W||-0.8289||0.9971||18||0m 12s|||
|136||15||November 22, 1612||16:04:35||Hybrid||65.7S 98.4W||-0.7691||1.0002||1||0m 1s|||
|136||18||December 25, 1666||17:59:16||Hybrid||71.6S 98.3W||-0.7452||1.0058||30||0m 24s|||
|136||21||January 27, 1721||20:05:11||Total||64S 102.4W||-0.7269||1.0158||79||1m 7s|||
|136||24||March 1, 1775||21:39:20||Total||47.9S 124.8W||-0.6783||1.0304||139||2m 20s|||
|136||27||April 3, 1829||22:18:36||Total||28.5S 142.6W||-0.5803||1.0474||192||4m 5s|||
|136||30||May 6, 1883||21:53:49||Total||8.1S 144.6W||-0.425||1.0634||229||5m 58s|||
|136||33||June 8, 1937||20:41:02||Total||9.9N 130.5W||-0.2253||1.0751||250||7m 4s|||
|136||36||July 11, 1991||19:07:01||Total||22N 105.2W||-0.0041||1.08||258||6m 53s|||
|136||39||August 12, 2045||17:42:39||Total||25.9N 78.5W||0.2116||1.0774||256||6m 6s|||
|136||42||September 14, 2099||16:57:53||Total||23.4N 62.8W||0.3942||1.0684||241||5m 18s|||
|136||45||October 17, 2153||17:12:18||Total||18.8N 65.7W||0.5259||1.056||214||4m 36s|||
|136||48||November 20, 2207||18:30:26||Total||15.8N 87.8W||0.6027||1.0434||180||3m 56s|||
|136||51||December 22, 2261||20:38:50||Total||16.1N 124.2W||0.636||1.0337||147||3m 17s|||
|136||54||January 25, 2316||23:05:17||Total||21.4N 166W||0.6526||1.0282||126||2m 42s|||
|136||57||February 27, 2370||1:07:02||Total||33.2N 157E||0.6865||1.0262||121||2m 17s|||
|136||60||March 31, 2424||2:10:10||Total||51.3N 131.9E||0.7652||1.0254||133||1m 55s|||
|136||63||May 3, 2478||1:55:59||Total||75.7N 107.7E||0.9034||1.0218||176||1m 20s|||
|136||66||June 5, 2532||0:28:58||Partial||67.5N 1.3E||1.0962||0.8224|||
|136||69||July 7, 2586||22:07:07||Partial||64.5N 7.2E||1.327||0.3957|||
Solar Exeligmos Animation
Solar Saros Animation (for comparison)
- Littman, Mark; et al. (2008). Totality: eclipses of the sun. Oxford University Press. pp. 325–326. ISBN 978-0-19-953209-4.
- 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.
- David, Furley (11 February 1999). From Aristotle to Augustine. Psychology Press. p. 301. ISBN 978-0-415-06002-8 – via Google Books.
- Gregorian Calendar is used for dates after 1582 Oct 15. Julian Calendar is used for dates before 1582 Oct 04.
- NASA Eclipse Website Fred Espenak