thumb|250px|right|heliocentric solar system for astronomy and calendar studies, the metonic cycle or enneadecaeteris (from , "nineteen years") is a period of very close to 19 years that is remarkable for being nearly a common multiple of the solar year and the synodic (lunar) month. the greek astronomer meton of athens (fifth century bc) observed that a period of 19 years is almost exactly equal to 235 synodic months and, rounded to full days, counts 6,940 days. the difference between the two periods (of 19 years and 235 synodic months) is only a few hours, depending on the definition of the year. considering a year to be  of this 6,940-day cycle gives a year length of 365&nbsp;+&nbsp;&nbsp;+&nbsp; days (the unrounded cycle is much more accurate), which is slightly more than 12 synodic months. to keep a 12-month lunar year in pace with the solar year, an intercalary 13th month would have to be added on seven occasions during the nineteen-year period (235 = 19 Ã 12 + 7). when meton introduced the cycle around 432&nbsp;bc, it was already known by babylonian astronomers. a mechanical computation of the cycle is built into the antikythera mechanism. the cycle was used in the babylonian calendar, ancient chinese calendar systems (the 'rule cycle' ç« ) and the medieval computus (i.e. the calculation of the date of easter). it regulates the 19-year cycle of intercalary months of the hebrew calendar. ==mathematical basis== at the time of meton, axial precession had not yet been discovered, and he could not distinguish between sidereal years (currently: 365.256363 days) and tropical years (currently: 365.242190 days). most calendars, like the commonly used gregorian calendar, are based on the tropical year and maintain the seasons at the same calendar times each year. nineteen tropical years are about two hours shorter than 235 synodic months. the metonic cycle's error is, therefore, one full day every 219 years, or 12.4 parts per million. :19 tropical years = 6,939.602 days (12 Ã 354-day years + 7 Ã 384-day years + 3.6 days). :235 synodic months (lunar phases) = 6,939.688 days (metonic period by definition). :254 sidereal months (lunar orbits) = 6,939.702 days (19 + 235 = 254). :255 draconic months (lunar nodes) = 6,939.1161 days. note that the 19-year cycle is also close (to somewhat more than half a day) to 255 draconic months, so it is also an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses. the octon is  of a metonic cycle (47 synodic months, 3.8 years), and it recurs about 20 to 25 cycles. this cycle seems to be a coincidence. the periods of the mo
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