# DETERMINATION OF EASTER DATE - THE COMPUT

## ABOUT THE ECCLESIASTICAL COMPUT :

The comput is used to regulate time for the ecclesiastical uses. In particular for the calculation of the Easter date.

## DEFINITION OF THE EASTER DATE :

The current definition of the Easter date is that defined in 325 at the time of the Nicée council "Easter is Sunday which follows the fourteenth day of the Moon which reaches this age at March 21 or immediately after". The fourteenth day of the Moon being the day of Full moon and on March 21 corresponding to the date of the vernal equinox, this definition is often translated in the following way: Easter is first Sunday which follows first Full moon of Spring. This second definition is misleading because it implies that the Easter date is the result of an astronomical calculation based on the determination of the vernal equinox and first Full moon according to this equinox. Actually it of it is nothing, the calculation of the Easter date is done using a lunar everlasting calendar using the fictitious average Moon (the ecclesiastical Moon). This method of calculation has the ecclesiastical name of comput.
There are two ecclesiastical Computs : the Julian comput used until 1582 and the Gregorian comput in use since 1583. The Gregorian comput corrects certain imperfections of the Julian comput. The Julian comput has two elements : the Sunday letter and the golden number. The Gregorian comput also has two elements : the Sunday letter and the epact. Sometimes we also give for the Julian comput an epact (the Julian epact) which is directly related to the golden number.
By extension we call Julian Easter the Gregorian date of Easter calculated using the Julian comput and Gregorian Easter the date of Easter calculated using the Gregorian comput.

## ELEMENTS OF THE COMPUT :

- dominical letter : from the 1st January, we associates to the days of the year the 7 letters A, B, C, D, E, F, G, then again A, B, C, etc... In the case of the leap years the operation is carried out in two times : until February 29, to which the letter D corresponds, and from the 1st March, in which the letter D is assigned. The Sunday letter indicates Sundays. If the year is bissextile, we give two Sunday letters for the year, the first one is valid until February 29 and the second one is valid from the 1st March.
- epact : during the middle Age, in the Julian comput, before the Gregorian reform of the Easter date calculation, the epact was the age of the Moon at March 22nd; in the Gregorian comput, therefore after the Gregorian reform of 1582, the epact is the age of the Moon at the 1st January decreased by a unit. It is this definition which is used in the above results.
The age of the Moon is equal to one each New moon. In these computs, we remind users that it is not the true Moon which is used but the fictitious average one called the ecclesiastical Moon.
- Solar cycle (1 to 28) : the position of the year in a 28 years cycle, (return of the week days to the same dates in the Julian calendar).
- Golden number (1 to 19) : the position of the year in the Metonic cycle, 235 lunations. The golden number is used in the Julian comput calculation of the Easter date and it is replaced by the epact in the Gregorian comput.
- Roman indiction (1 to 15) : the position of the year in a 15 years cycle, without astronomical significance, this element is not used for the calculation of the Easter date.

## EXPLAINING THE PROVIDED DATA :

For the years earlier to the Gregorian reform : we give the Julian Easter date, in the Julian calendar then we give the date of the Jewish Easter in the Jewish and Julian calendars.
For the following years to the Gregorian reform (after 1582) : we give the Gregorian Easter date in the Gregorian calendar, it is the date used by the catholic church since 1583, then we give the Julian Easter date, in the Julian and Gregorian calendars, this date is still in use nowadays by certain orthodox churches and finally we give the date of the Jewish Easter in the Jewish and Julian calendars.

## VALIDITY OF THE RESULTS :

This program allows calculating the Easter dates since year 325, time of the definition of the Easter date by the council of Nicée. It uses the ecclesiastical comput elaborate by Denis Le Petit in year 525 before our era. This comput is based on average fictive Moon according to the Metonic cycle. In this comput, we find the same Easter dates every 532 years (19 X 28, product of the Metonic cycle by the solar cycle). This comput was used by the whole Christian community only starting from second half of the VIII

^{th} century. The values found for the earlier years to that time are thus purely indicative and can be, according to the areas and Christian communities considered, in disagreement with the real dates of the celebrations. In the same way the Jewish calendar in its current form date from the IV

^{th} century, but it was indeed of use in all the Jewish community only several centuries after its creation (approximately the VIII

^{th} century). Therefore the results obtained for the earlier years to that time are also purely indicative.
To have historical data for these distant times it is better to see historical sources and not to accept only the results provided by this program.

| The determination of Easter date (in french) |

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