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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Eclipse cycle | 6/12 | https://en.wikipedia.org/wiki/Eclipse_cycle | reference | science, encyclopedia | 2026-05-05T11:12:34.827205+00:00 | kb-cron |
Macdonald cycle An eclipse cycle equal to 299 years and about ten and a half months, always occurring on the same node. Peter Macdonald found that a series of eclipses of especially long duration visible from Britain occurs with this interval in the period AD 1 to 3000. A Macdonald series has around ten eclipses and lasts about 3000 years. All or most are on the same day of the week, since the interval is only about an hour less than a whole number of weeks and the length is fairly constant becauses the anomaly of the moon is almost constant. Utting cycle The seventh convergent in the continued fractions development between the ratio of the eclipse year and synodic month, if this ratio is approximated as between 2.17039173 and 2.17039179. Discussed by James Utting in 1827. Selebit An eclipse cycle where the number of eclipse years (354.5) closely matches (by chance) the number of days in a lunar year (354.371). It equals approximately 336 years 5 months 6 days or 4161 lunations. It is a convergent in the continued fractions development of the ratio between the eclipse year and the synodic month, giving a series of eclipses one selebit apart a life expectancy of thousands of years. Cycle of Hipparchus Not a long-lasting eclipse cycle, but Hipparchus constructed it to closely match an integer number of synodic and anomalistic months, years (345), and days. Because of it being close to a whole number of both anomalistic months and anomalistic years, its length is always within about an hour of 126007 days and half an hour. (See graphs lower down of semester and Hipparchic cycle.) This means that at the time of the second eclipse same side of the earth will be facing the sun as at the first eclipse (but the value of gamma will be different). By comparing his own eclipse observations with Babylonian records from 345 years earlier, Hipparchus could verify the accuracy of the various periods that the Chaldeans used. Ptolemy points out that dividing it by 17 still gives a whole number of synodic months (251) and anomalistic months (269), but this is not an eclipse interval because it is not near a whole or half integer number of draconic months. Square year An eclipse cycle where the number of solar years (365.371) closely matches (by chance) the number of days in 1 solar year (365.242), lasting 365 years 4.5 months or 4519 lunations. It is the eighth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month, giving a series of eclipses one square year apart a life expectancy of thousands of years. Many eclipses of our day belong to square year series (or Utting or selebit series) that have been going for over 13,000 years, and many will continue for over 13,000 years. For example, the solar eclipse of September 21, 2025 (saros series 154, inex series 25) was preceded by at least 35 eclipses in its square year series (back to saros series −266, inex series −10 in 10,764 BC) and will be followed by at least 35 more (till saros series 574, inex series 60 in AD 14,813). Gregoriana Known for returning toward the same day of the week and Gregorian calendar date, as approximately an integer number of years, months, and weeks, are achieved, usually moving only a quarter day later in the Gregorian calendar. Hexdodeka Equal to six Unidos or two Trihex. Useful for giving accurate calculations of the timing of lunisolar syzygies. Grattan Guinness cycle The shortest cycle that gives eclipses on the same date (more or less) in both the Gregorian and in a 12-month lunar calendar, because it is almost exactly a whole number of Gregorian years (391.00029) as well as being exactly 403 12-month lunar years. Discovered by Henry Grattan Guinness in a speculative interpretation of Revelation 9:15. Hipparchian Fourteen inex plus two saros. The Almagest attributes this cycle to Hipparchus. George van den Bergh called it the "Long Babylonian Period" or the "Old Babylonian Period", but there is no evidence that the Babylonians were aware of it. Basic period Achieves nearly an integer number (521) of Julian years, anomalistic years (521 anomalistic years minus 5 days), and weeks (27185 weeks plus 0.1 day), leading to eclipses on the same day of the Julian calendar and week. Chalepe Equals 18 inex plus 2 saros, therefore 557 years plus about 1 month.