Exeligmos


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. It is an eclipse cycle that is a triple saros, 3 saroses 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:
The 57 eclipse years means that if there is a solar eclipse, then after one exeligmos a New 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, almost exactly 726 draconic months, and also almost exactly 717 anomalistic months. 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, 1966June 21, 2020
Path Map

Duration0 minutes 5 seconds0 minutes 38 seconds
Max width of annular eclipse path3 kilometers21 kilometers
Latitude of greatest eclipse39° North31° North
Time of greatest eclipse 09:3806:40

Lunar exeligmos example

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


December 30, 1963January 31, 2018
Path Map
Visibility
Duration 204 minutes203 minutes
Time of greatest eclipse 11:0613:29

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.
SarosMemberDateTime
UTC		TypeLocation
Lat,Long		GammaMag.Width
Duration
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.

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.