Encylopaedia Britannica on the Metonic cycle:
Metonic cycle, in chronology, a period of 19 years in which there are 235 lunations, or synodic months, after which the Moon’s phases recur on the same days of the solar year, or year of the seasons. The cycle was discovered by Meton (fl. 432 bc), an Athenian astronomer.
Calendar Wiki’s opening paragraphs on the Metonic cycle say:
The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal i.e. tropical year) and the synodic month. Nineteen tropical years differ from 235 synodic months by about 2 hours. The Metonic cycle’s error is one full day every 219 years, or 12.4 parts per million.
19 tropical years = 6939.602 days
235 synodic months = 6939.688 days
It is helpful to recognize that this is an approximation of reality. The period of the Moon’s orbit around the Earth and the Earth’s orbit around the Sun (ignoring also exact definition of the year) are independent and have no known physical resonance. Examples of a real harmonic lock would be Mercury, with its 3:2 spin-orbit resonance or other orbital resonance.
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Wiki: no known physical resonance
But is there really an error? If we look hard enough, such a ‘physical resonance’ is found at 6441 tropical years, which is 19*339 as the chart on the right taken from this Talkshop post shows.
Wiki: Nineteen tropical years differ from 235 synodic months by about 2 hours.
In 339 occurrences of 19 years, we have ‘339*235, minus 1’ synodic months i.e. 79664 SM. If we break down the one lost month:
1 SM = 29.530589 days = 708.73413 hours
708.73413 / 339 = 2.0906611 hours — which is ‘about 2 hours’, so our chart is accurate enough in that regard.
6441 tropical years(TY) is about a quarter of the current axial precession period of the Earth:
6441*4 = 25764 TY = 25763 sidereal years
Precession is believed to be 25770 years approx. and declining.
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Fun with numbers: 79664 = 339*235,-1 or 766*104.
235+104 = 339
via Tallbloke’s Talkshop
April 3, 2020 at 12:03PM
Iowa Climate Science Education 