An exeligmos () 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). The exeligmos is an eclipse cycle that is a triple saros, three 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 eight hours later in the day or about 120° to the west of the eclipse that occurred one saros earlier.
It corresponds to:
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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.
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.
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). It also corresponds to 114 eclipse seasons. The first two factors make this a long-lasting eclipse series. The latter factor is what makes all the 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 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 Path Map (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 Path Map Visibility (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 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.
SarosMemberDateGregorian Calendar is used for dates after 1582 Oct 15. Julian Calendar is used for dates before 1582 Oct 04.Time(Greatest)UTCTypeLocationLat,LongGammaMag.Width(km)Duration(min:sec)Ref1363July 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 32s13612October 11, 155814:58:55Annular56.5S 90.3W-0.82890.9971180m 12s13615November 22, 161216:04:35Hybrid65.7S 98.4W-0.76911.000210m 1s13618December 25, 166617:59:16Hybrid71.6S 98.3W-0.74521.0058300m 24s13621January 27, 172120:05:11Total64S 102.4W-0.72691.0158791m 7s13624March 1, 177521:39:20Total47.9S 124.8W-0.67831.03041392m 20s13627April 3, 182922:18:36Total28.5S 142.6W-0.58031.04741924m 5s13630May 6, 188321:53:49Total8.1S 144.6W-0.4251.06342295m 58s13633June 8, 193720:41:02Total9.9N 130.5W-0.22531.07512507m 4s13636July 11, 199119:07:01Total22N 105.2W-0.00411.082586m 53s13639August 12, 204517:42:39Total25.9N 78.5W0.21161.07742566m 6s13642September 14, 209916:57:53Total23.4N 62.8W0.39421.06842415m 18s13645October 17, 215317:12:18Total18.8N 65.7W0.52591.0562144m 36s13648November 20, 220718:30:26Total15.8N 87.8W0.60271.04341803m 56s13651December 22, 226120:38:50Total16.1N 124.2W0.6361.03371473m 17s13654January 25, 231623:05:17Total21.4N 166W0.65261.02821262m 42s13657February 27, 23701:07:02Total33.2N 157E0.68651.02621212m 17s13660March 31, 24242:10:10Total51.3N 131.9E0.76521.02541331m 55s13663May 3, 24781:55:59Total75.7N 107.7E0.90341.02181761m 20s13666June 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.NASA Eclipse Website Fred Espenak
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).
See also Eclipse cycle Saros Full moon cycle
References