Exeligmos

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.[1]

Details

The exeligmos was known by the Greeks as earlier than 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

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)
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

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

February 9, 1990 March 13, 2044
Path Map
Visibility
(side of earth eclipse is visible from)
Duration (Partial eclipse) 204 minutes 209 minutes
Time of greatest eclipse (UTC) 19:12 19:38

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]

SarosMemberDate[4]Time
(Greatest)
UTC		TypeLocation
Lat,Long		GammaMag.Width
(km)		Duration
(min:sec)		Ref
1363July 5, 139619:37:40Partial63.9S 147.2W-1.35680.3449
1366August 7, 145016:48:49Partial61.8S 132.8W-1.12860.756
1369September 8, 150415:12:15Annular55.3S 102.6W-0.94860.9924830m 32s
13612October 11, 155814:58:55Annular56.5S 90.3W-0.82890.9971180m 12s
13615November 22, 161216:04:35Hybrid65.7S 98.4W-0.76911.000210m 1s
13618December 25, 166617:59:16Hybrid71.6S 98.3W-0.74521.0058300m 24s
13621January 27, 172120:05:11Total64S 102.4W-0.72691.0158791m 7s
13624March 1, 177521:39:20Total47.9S 124.8W-0.67831.03041392m 20s
13627April 3, 182922:18:36Total28.5S 142.6W-0.58031.04741924m 5s
13630May 6, 188321:53:49Total8.1S 144.6W-0.4251.06342295m 58s
13633June 8, 193720:41:02Total9.9N 130.5W-0.22531.07512507m 4s
13636July 11, 199119:07:01Total22N 105.2W-0.00411.082586m 53s
13639August 12, 204517:42:39Total25.9N 78.5W0.21161.07742566m 6s
13642September 14, 209916:57:53Total23.4N 62.8W0.39421.06842415m 18s
13645October 17, 215317:12:18Total18.8N 65.7W0.52591.0562144m 36s
13648November 20, 220718:30:26Total15.8N 87.8W0.60271.04341803m 56s
13651December 22, 226120:38:50Total16.1N 124.2W0.6361.03371473m 17s
13654January 25, 231623:05:17Total21.4N 166W0.65261.02821262m 42s
13657February 27, 23701:07:02Total33.2N 157E0.68651.02621212m 17s
13660March 31, 24242:10:10Total51.3N 131.9E0.76521.02541331m 55s
13663May 3, 24781:55:59Total75.7N 107.7E0.90341.02181761m 20s
13666June 5, 25320:28:58Partial67.5N 1.3E1.09620.8224
13669July 7, 258622:07:07Partial64.5N 7.2E1.3270.3957

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]

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]

See also

References

  1. 1 2 3 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. ↑ 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. ↑ Gregorian Calendar is used for dates after 1582 Oct 15. Julian Calendar is used for dates before 1582 Oct 04.
  5. 1 2 NASA Eclipse Website Fred Espenak
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