Christmas always falls on December 25, but Easter is quite another matter.
The holiday can fall on any date between March 22 and April 25, a five-week window.
Every leap year has two dominical letters, one for January and February and the other for the remaining months. The church considers March 21 to be the perennial date of the vernal equinox, but the real astronomical equinox can occur as early as March 19 (as will happen in 2096).
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(Dante, the medieval Italian poet, pointed out that eventually January would cease to be part of winter.) Finally, in 1582 Pope Gregory XIII reformed the calendar by omitting the leap day in all years that are multiples of 100, except for years that are multiples of 400 (such as the year 2000, for example).
To correct for the previous slippage, the Gregorian calendar for 1582 skipped the 10 days between October 4 and 15.
It was a tidy system, but unfortunately it did not accurately account for the true lengths of the lunar month and solar year.
As the centuries passed, the calendar started to slip relative to the seasons.
The first flawless algorithm was presented in 1876 in the journal (Oxford University Press).
O’Beirne’s method puts the various cycles and adjustments into an arithmetical scheme.
The lunar month is currently about 29.53 days long, and the solar year about 365.24 days long.
This leads to 12.37 lunar months per year, an inconvenient relationship because it is not an integer. 325 at the Council of Nicaea, church leaders decided that Easter should fall on the first Sunday after the first full moon occurring on, or after, the spring equinox (the date in March on which day and night have equal length).
It so happens that 235 lunar months are very close to 19 solar years, and the church’s system for assigning a date to Easter exploits this coincidence. The year was based on the Julian calendar back then, with one leap year in every four.