So the first allowable date of Easter is March 22 + d + 0, as Easter is to celebrate the Sunday after the ecclesiastical full moon; that is, if the full moon falls on Sunday 21 March, Easter is to be celebrated 7 days after, while if the full moon falls on Saturday 21 March, Easter is the following 22 March.

The first part consists of determining the variable d, the number of days (counting from 22 March) to the day after the full moon. The formula for d contains the terms 19 a and the constant M. a is the year's position in the 19-year lunar phase cycle, in which by assumption the moon's movement relative to Earth repeats every 19 calendar years. In older times, 19 calendar years were equated to 235 lunar months (the Metonic cycle), which is remarkably close since 235 lunar months are approximately 6939.6813 days and 19 years are on average 6939.6075 days.This raises the question why the Gregorian lunar calendar has separate solar and lunar corrections, which sometimes cancel each other. Lilius's original work has not been preserved, but his proposal was described in the Compendium Novae Rationis Restituendi Kalendarium circulated in 1577, in which it is explained that the correction system he devised was to be a perfectly flexible tool in the hands of future calendar reformers, since the solar and lunar calendar could henceforth be corrected without mutual interference. [50] An example of this flexibility was provided through an alternative intercalation sequence derived from Copernicus's theories, along with its corresponding epact corrections. [51] Butcher, Samuel (1877). The Ecclesiastical calendar: its theory and construction. Dublin: Hodges, Foster and Figgis. Archived from the original on 9 April 2023 . Retrieved 11 March 2016. In the example, this paschal full moon is on 16 April. If the dominical letter is E, then Easter day is on 20 April.

The Ptolemaic value of the length of the mean synodic month, established around the 4thcenturyBCE by the Babylonians, is 29 days 12 hr 44 min 3 + 1 / 3 s (see Kidinnu); the current value is 0.46s less (see New moon). In the same historic stretch of time the length of the mean tropical year has diminished by about 10s (all values mean solar time).The ratios of (mean solar) days per year and days per lunation change both because of intrinsic long-term variations in the orbits, and because the rotation of the Earth is slowing down due to tidal deceleration, so the Gregorian parameters become increasingly obsolete. Richards 2013, p.587: The day consists of 86,400 SI seconds, and the same value is given for the years 500, 1000, 1500, and 2000. Stern, Sacha, Calendar and Community: A History of the Jewish Calendar Second Century BCE – Tenth Century CE, Oxford University Press, Oxford, 2001.