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{{Short description|Period of 54 years and 33 days}}
An '''exeligmos''' ({{lang-elgrc-gre|ἐξέλιγμος}} — ''ἐξελιγμός|lit=turning of the wheel''}}) is a period of 54 years, 33 days that can be used to predict successive [[eclipse]]s 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). ItThe exeligmos is an [[eclipse cycle]] that is a triple [[saros (astronomy)|saros]], 3three 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 8eight hours later in the day or about 120° to the west of the eclipse that occurred one saros earlier.<ref name=Totality>{{cite book|last=Littman|display-authors=etal|first=Mark|title=Totality: eclipses of the sun|year=2008|publisher=[[Oxford University Press]]|isbn=978-0-19-953209-4|pages=325–326}}</ref>
 
It corresponds to:
*{{val|3|u=[[saros (astronomy)|saroses]]}}
*669 [[synodic month]]s
*725.996 {{val|669|u=[[draconicsynodic month]]s}}
*{{val|725.996|u=[[draconic month]]s}}
*{{val|56.996 |u=eclipse years}} ({{val|114 |u=[[eclipse season]]s}})
*{{val|716.976 |u=[[anomalistic month]]s}}
 
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 [[lunar node|node]] of the [[orbit of the Moon]], and under these circumstances another eclipse can occur.
 
== 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.<ref>{{Cite journal
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|bibcode = 2006Natur.444..587F }}</ref>
 
The exeligmos is 669 [[month#Synodic month|synodic months]] (every eclipse cycle must be an integer number of synodic months), almost exactly 726 [[month#Draconic month|draconic months]] (which ensures the sun and moon are in alignment during the new moon), and also almost exactly 717 [[month#Anomalistic month|anomalistic months]]<ref>{{cite book|url=https://books.google.com/books?id=tAhZT5jRTwgC&pg=PA301|title=From Aristotle to Augustine|first=Furley|last=David|date=11 February 1999|publisher=Psychology Press|via=Google Books|isbn=978-0-415-06002-8|page=301}}</ref> (ensuring the moon is at the same point of its elliptic orbit). AndIt also corresponds to 114 eclipse seasons. The first two factors make this a long -lasting eclipse series. The latter factor is what makes eachall eclipsethe eclipses 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 (eclipse) |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.<ref name=Totality />
 
=== Solar exeligmos example ===
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| Duration (Partial eclipse)|| 204 minutes || 203 minutes
|-
| Time of greatest eclipse (UTC) || 11:0706 || 13:3129
|}
 
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|136||42||[[Solar eclipse of September 14, 2099|September 14, 2099]]||16:57:53||Total||23.4N 62.8W||0.3942||1.0684||241||5m 18s||[http://eclipse.gsfc.nasa.gov/5MCSEmap/2001-2100/2099-09-14.gif]
|- align=center bgcolor=#e0ffe0
|136||45||[[Solar eclipse of October 17, 2153|October 17, 2153]]||17:12:18||Total||18.8N 65.7W||0.5259||1.056||214||4m 36s||[http://eclipse.gsfc.nasa.gov/5MCSEmap/2101-2200/2153-10-17.gif]
|- align=center bgcolor=#e0ffe0
|136||48||November 20, 2207||18:30:26||Total||15.8N 87.8W||0.6027||1.0434||180||3m 56s||[http://eclipse.gsfc.nasa.gov/5MCSEmap/2201-2300/2207-11-20.gif]
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|}
 
== Solar Exeligmosexeligmos Animationanimation ==
 
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.<ref name="NASA">[http://eclipse.gsfc.nasa.gov/eclipse.html NASA Eclipse Website] Fred Espenak</ref>
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==See also==
* [[Solar eclipse]]
* [[Eclipse cycle]]
* [[Saros (astronomy)|Saros]]
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[[Category:Eclipses]]
[[Category:Time in astronomy]]
[[Category:Ancient Greek astronomy]]