The Paschalion Question – Historical, Canonical, Mathematical and Astronomical Aspects

Den Ortodokse Kirkes Kalender

F. dia­kon Irakli har fået publi­ce­ret en dyb­de­gå­en­de arti­kel i  tids­skrif­tet Inter­na­tio­nal Jour­nal of Ort­ho­dox The­o­lo­gy, num­mer 8/1, 2017 med tit­len “Histo­ri­cal, Cano­ni­cal, Mat­he­ma­ti­cal and Astro­no­mi­cal Aspects of the Pas­cha­li­on Question”.

An arti­c­le by f. dea­con Irakli with the tit­le of “Histo­ri­cal, Cano­ni­cal, Mat­he­ma­ti­cal and Astro­no­mi­cal Aspects of the Pas­cha­li­on Question” was recent­ly publis­hed in a a sci­en­ti­fic, peer-review and open access jour­nal – Inter­na­tio­nal Jour­nal of Ort­ho­dox The­o­lo­gy, issue 8/1, 2017.

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 29% 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%. 

The Calendar of the Orthodox Church

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.

Based on an arti­c­le by Fr. Dr. V.F. Khu­lap.