from the series of short articles about calendars
One of the most demanding issues in the early Christianity was the computation of the date of the Easter. Among the main contributors were Cyril of Alexandria (378-444 AD), Dionysius Exiguus (470-544 AD), who introduced the reference "Anno Domini" for year numbering and Venerable Bede (672-735 AD). All of them exploited the ancient knowledge of the Metonic cycle, that is the 19-year period of realignment between year dates and moon phases. The Easter date was defined as "the first Sunday after the first full moon after the Spring Equinox". It is inspired from the Hebrew Pesach, occurring on the full moon after the Spring Equinox, in the Hebrew date 15th of Nisan, adding the element of the Sunday, the day of the glory of Jesus Christ in the form of the Spiritual Sun. The main reason for this addition is an attempt for differentiation from the celebration of the Easter by the Jews and their focus on the sacred Saturday. Considering as the date of Spring Equinox March 21st, occurred in 325 A.D. (the year of the First Ecumenical Synod in Nicaea), various algorithms had been proposed to estimate the date of the Easter. The algorithm finally adopted had the following steps: 1] computation of the Meton number of the year, through the formula α = year modulo 19 2] computation of the epact of the year (the number of the days of the synodic moon cycle) in the Jan. 1st of the year Epact = (8 + 11* α) modulo 30 3] computation of the date of the first full-moon after the Spring Equinox FM = 21 + (53-Epact) modulo 30 This is a number which means the order of day in March, and if it exceeds 31 it is transformed to a date in April. For example, FM = 28 means March 28th, while FM=44 means April 13th. Applying this algorithm after the Calendar reform of 1582, the dates must be transferred 13 days later, and after 2199, 14 days. 4] The Sunday after FM is the Easter Sunday. After the Calendar Reform by the Pope Gregory XIII in Oct. 5th/15th of 1582 A.D., obviously the date of the feast of the Easter was ceased to be celebrated in the same date, in the countries that had adopted the Gregorian Calendar and the countries that retained the Julian Calendar. The difference would be the number of days that Gregorian dates are in advance to the Julian dates, a difference that started as 10 days, nowadays is 13 days and in the future, of course, will increase more and more. Though, this is not the only difference in the computation of the Easter date between the Gregorians (Catholics) and the Julians (Orthodox). Gregorians, made also another correction which concerns the alignment of the computed Metonic dates of moon phases and the dates of the real moon phases. The first move-to-the-front correction in the yearly calendar introduced by the Gregorian reform is called solar correction and now amounts to 13 days). The second correction is called lunar correction and now amounts to 4 days. These corrections affect directly the true Epact of the year, as follows: The lunar correction must be added and the solar correction must be subtracted from the Julian Epact (the Epact computed in the initial algorithm of computation when the valid calendar was everywhere the Julian Calendar). Taking into account these two corrections one takes the real Epact, which is called Gregorian Epact (GEpact). Both the lunar correction and solar correction will increase in the future but not always uniformly to one another. Until 2099 A.D. l.correction = 4 and s.correction=13. In 2100 A.D. L.correction becomes 5 and s.correction becomes 14. 2] GEpact = Epact + l.correction – s.correction Therefore GEpact = Epact – 9 (for the years until 2099 Then 3] Gregorian Full Moon GFM = 21 + (53-Gepact) modulo 30 and 4] The Sunday after GFM is the Easter Sunday. According to the above algorithm, Julian and Gregorian full-moon dates differ 9 days (the Gregorian later) or 21 days (the Julian later) and after the Julian dates correction to adapt them to the Gregorian Calendar (13 days forwards), the corrected Julian full-moon date falls 4 or 34 days later than the Gregorian full-moon date. In the 4-days difference case, Julian Easter falls in the same day with Gregorian Easter or 1 week later. In the 34-days difference case, Julian Easter falls 4 or 5 weeks later than the Gregorian Easter. The true Easter Sunday is of course the one computed by the Gregorians, due to the true value of the epact. Catholic (Gregorian) Easter Sunday falls between March 22nd and April 25th. Orthodox (Julian) Easter Sunday falls, due to the transfer 13 days later, between April 4th and May 8th. This erroneous shift of the Orthodox Easter date forwards will take tremendous dimension on account of the gradual increase of the difference between a Julian and the corresponding Gregorian date century by century. You can test with the Orthodox and the Catholic Easter dates in the future centuries in the section "Compute the dates of Orthodox/ Catholic Easter" of our site. You can see there that the Catholic Easter will retain to fall in the spring interval between March 22nd and April 25th, while the Orthodox Easter will fall on July 20th in the year 15000 AD and in Sept. 28th in the year 25000 AD.
About the Metonic cycle
About the Easter Meton number
About the Calendar reform