Күн және Ай тұтылуының 54 жылдық циклы

An exeligmos (ἐξελιγμός (lit=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). 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:
3
669
725.996
56.996 (114)
716.976

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.

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.

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).