How is the date of Easter set on the Orthodox calendar?

The Orthodox Churches continue to use the Julian Calendar with the result the equinox is assumed to be 13 days later than it really is. March 21 Julian is April 3 in the Gregorian Calendar commonly used. This is fairly well known, but less known is that the Eastern Churches continue to use the Dionysian tabulation for the dates of full moons, whereas in the West this too was changed, beginning in Catholic countries in the 16th century.

In the 6th century a 19 year cycle of paschal full moon dates was constructed. If a year is divisible by 19 it has a Golden Number of 1, otherwise the Golden Number is one more than the remainder. 532 was divisible by 19. The Full Moon was April 5th. The next year the moon is said to be 11 days earlier on March 25th. This is because twelve lunar months are about 11 days less than a year. For the year 534 there would be a full moon on March 14 but this is too early, so instead of counting back 11 days to the twelfth moon we count forward 19 days to the thirteenth moon on April 13. This is repeated over the 19 year cycle, going back 11 days, or forward 19. When the Golden Number reaches 19 we get to April 17th and then go back 12 days to start the 19 year cycle again on April 5th.

Starting with years divisible by 19 (Golden Number 1) and going forward the cycle is 1) April 5th, 2) March 25th, 3) April 13th, 4) April 2nd, 5) March 22nd, 6) April 10th, 7) March 30th, 8) April 18th, 9) April 7th, 10) March 27th, 11) April 15th, 12) April 4th, 13) March 24th, 14) April 12th, 15) April 1st, 16) March 21st, 17) April 9th, 18) March 29th, 19) April 17th.

But how accurate is this cycle? Because 19 years can have 4 or 5 leap years, it is better to consider 4 such cycles. In 76 years there are 4 19 year cycles and always 19 leap years ( in the Julian Calendar). This period contains 365.25 x 76 days, which is 27, 759. The 4 cycles contain 940 lunar months averaging 29.530588 days, which in all is 27, 758.75 days, a discrepancy of about 6 hours. After 76 years each full moon actually happens 6 hours earlier, amounting to one day every 300 years (approximately).

By now the real full moon occurs 4 or 5 days earlier than the tabulated one used in the East, or we could express it , the tabulated day is 4 days late.

In 2018 the Golden Number is 5 giving a full moon on March 22 Julian. Because the Gregorian Calendar is 13 days ahead, this works out to April 4th in the Gregorian Calendar, and so Easter in the East is the following Sunday.

Adjustments to the Western tabulation give the current 19 year cycle as follows: 1) April 14, 2) April 3, 3) March 23, 4) April 11, 5) March 31, 6) April 18, 7) April 8, 8) March 28, 9) April 16, 10) April 5, 11) March 25, 12) April 13, 13) April 2 14) March 22, 15) April 10, 16) March 30, 17) April 17, 18) April 7, 19) March 27.

This tabulation is constructed as for the East, going back 11 days or forward 19, except it starts with April 14th when the Golden Number is 1; and what would work out to April 18 or 19 is instead tabulated 17 or 18 respectively.

Omitting leap years three times ever 400 years should keep the equinox close to March 21 in the West, while in the East Easter moves closer to the Summer.

The lunar tabulation in the West is planned for further adjustment. The date of the full moon s will become 1 day later every time a leap year is missed. But it will be adjusted 1 day earlier every 300 years, starting 2100 , to account for the 76 year cycle leaving the moon 6 hours earlier.

So for Golden Number years 1 the tabulated moon is April 14. in 2100 it would move forward a day, to offset the missed leap year, but also back because of the 300 year rule, so it will remain April 14 until 2200. In 2200 it goes to April 15 and in 2300 to April 16, because 2200 and 2300 are not leap years. in 2400, which is a leap year it moves back to April 15 under the 300 year rule and so on.

All the other Golden Number dates move im tandem.

But in the East no adjustments are planned for sun or moon. In the very long term Orthodox Easter could be any time of year and any phase of month. There has been some talk of an agreed common date, but whether that happens remains to be seen.