Abstract: There are different calendar systems in use among Orthodox Churches worldwide. Non-movable Orthodox Christian feasts like Nativity, Annunciation, Transfiguration, and so on, are celebrated according to two different — Julian and Revised Julian — calendars. However, when it comes to the question of the Easter date, most of the churches with some exception celebrate the feast of the Resurrection of our Lord Jesus Christ on the same Sunday. Despite different calendar systems, it is precisely the Easter date determination question on which all calendar systems are based. Presented paper studies the Easter date (also known as Paschal) related question from historical, canonical, mathematical and astronomical points of view. Two existing paschal systems — Alexandrian and Gregorian — are presented here. According to these systems, the dates of the Easter for the period of 2000 — 2050 are calculated and compared with the astronomical dates defined by the Church canonical requirements for the Easter date determination. Obtained results reveal that the Alexandrian method used in most Orthodox churches often deviate from the astronomical reality and canonical rules, and its accuracy can reach only 31% for the given period of years. On the other hand, the accuracy of the Gregorian method used in the Catholic/Protestant world can be as high as 92%.

Nedenfor kan høres et foredrag som f. diakon Irakli Tsakadze holdt lørdag den 15. maj 2010 i Gudsmoders Beskyttelses Menighed om Den Ortodokse Kirkes kalender. Under lydafspilleren kan man læse nogle noter til særlige emner i foredraget.

Tropical year Year, representing a time interval between two successive vernal equinox. Its duration is 365.242199 days. This quantity is not a multiple of 24 hours, so after 365 days there is a remaining of 5 hours 48 minutes and 46 seconds.

Egyptian calendar It, predecessor of Julian calendar, consisted of 365 days. So this calendar gave an error in one day every four years (1 / (365,242199–365) ~ =3D 4), where 365.242199 is the duration of the Tropical year. In this system, a certain fixed date (e.g. the vernal equinox) was gradually shifted in the calendar, moving from spring to summer, autumn, winter and, having made a full cycle in 1460 years, was returning to its original location.

Julian calendar It was officially introduced on the 1st of January, 45 BC. In order to improve the accuracy of the Egyptian calendar, every 4th year of the calendar was a leap year, i.e. one extra day was added to it. By this scheme the duration of this new calendar became 365+1/4=3D365.25 days. But this improvement was just another approximation, as it carried its own inaccuracy, namely it accumulated error in 1 day during 128 years (1/ (365.25 — 365,242199) ~ =3D 128). Note that if the year in the Egyptian calendar was shorter than the Tropical year, the year in the Julian calendar was longer than the Tropical one. However, this calendar was 30 times more accurate than previous Egyptian one.

Gregorian calendar Introduced in 1582 by the pope Gregory. Calendar reform was implemented in such a way that in that year 10 days had been “thrown out” and October 15 went immediately after October 4. The system of inserting the leap days was changed. In particular, over 400 years, their number decreased by 3, i.e. 100, 200 and 300 years of every 400 years were not leap years, while year 400 remained a leap year. In the result another, improved approximation to the length of the tropical year had been obtained: 365 +97 / 400 =3D 365.2425, where 97 is amount of leap years over 400 years. Error of this calendar was 1 day in 3322 years, (1 / (365,2425–365,242199) ~ =3D 3322). Currently, the difference between the Julian and Gregorian calendar is 13 days, and it will increase up to 14 days in 2100, which according to the Julian calendar will be leap year, but according to the Gregorian one =96 non a leap year.

Revised Julian calendar Another important calendar improvement was made in 1923 during the meeting of the Orthodox Churches in Constantinople (not all Orthodox churches were presented in that meeting). The members of the council approved the improved or “Revised” Julian calendar. It has a period of 900 years, during which the number of leap years is reduced by 7. The new leap year rule was adopted, which differs from that of the Gregorian calendar: years evenly divisible by four are leap years, except that years evenly divisible by 100 are not leap years, unless they leave a remainder of 200 or 600 when divided by 900, then they are leap years. This means that the two calendars will first differ in 2800, which will be a leap year in the Gregorian calendar, but a common year in the new calendar. The duration of the year defined by the Revised calendar is 365 +218 / 900 =3D 365.24222, where 218 is amount of leap years in 900 years. Error in 1 day will be accumulated in 47619 years (1 / (365.24222 — 365.242199) ~ =3D 47619) suggesting that this calendar is more precise than previous ones.