Moonwise Calendars and Diaries

New Easter Dates
Proposal for astronomical calculation of Easter

Up to now in most years, Christians have had the embarrassment of two different dates of Easter. In response to this, the World Council of Churches and the Middle East Council of Churches co-sponsored a consultation held at Aleppo in Syria in March 1997. This proposed an end to the current Western and Orthodox calculations in favour of astronomical prediction: the Sunday following the Jerusalem meridian day of the first Full Moon after the March Equinox. Jerusalem meridian time is 2 hours and 21 minutes ahead of Greenwich. Read more about this in an updated World Council of Churches article.

I have constructed a table of dates of Easter from 1997, the year of the Aleppo consultation, to 2205. Note that in most years the proposed dates co-incide with the current Western Gregorian calculation. The current Orthodox calculations use for the Equinox the fixed date of 21 March in the Julian Calendar, which is 3 April in the Gregorian Calendar until 2099, 4 April from 2100 and 5 Apr from 2200, whereas the Gregorian calculations use the fixed date of 21 March in the Gregorian Calendar, which is much nearer to the actual Equinox date. It is not surprising therefore that the proposed dates agree more with the Western ones, though this may make it a greater hurdle for some Orthodox Churches. I understand that the Greek Orthodox Church decided to use this calculation (or maybe a very similar one) back in the 1920s, but didn’t then put it into regular practice.

It should also be noted that the current Easter calculations of both West and East use differing 19-year cycles of Full Moon dates, that are not the same as the actual Full Moon dates (based on the Jerusalem meridian). The Western formula currently results in dates from two days earlier to one day later than Full Moon in Jerusalem, whereas the Orthodox formula gives dates 3-5 days later.

If you have any more information about this, do let me know.

An objection to the Aleppo astronomical definition among some Orthodox Churches is that it sometimes (about a fifth of the time) makes Easter fall on or before the first day of Passover (15 Nisan in the Jewish Calendar), which clearly conflicts with the synoptic gospels (Matthew, Mark and Luke). However, as it is, Orthodox Pascha / Easter is about half the time more than a week after the start of Passover, and that conflicts with the gospels, too.

May I humbly propose that as a way of finding agreement between all the churches, and as a sign of reconciliation with the Jewish religion, Easter is defined as the Sunday after 15 Nisan (when 15 Nisan is a Sunday, then Easter is the following Sunday). I understand that early Christians used this definition.

The range of dates for the years around now is 28 March to 1 May; this compares to 22 March to 25 April for the current Western dates, 4 April to 8 May in the current Orthodox dates and 22 March to 26 April (for a few centuries ahead*) for the astronomical definition. The Sunday after Passover is usually the current Western date of Easter, but when not it is often the current Orthodox date. When the current Western and Orthodox dates co-incide, they fall on the Sunday after Passover in all but two years of the 21st century (2069 and 2096), and every year in the 22nd century. *Christian Catsanos points out that the astronomical definition puts Easter Day on 21 March in 2877. See the website Calendars Through the Ages.

Unfortunately, there are two serious objections to this proposal:

1. The Jewish Calendar, despite its lunar accuracy, moves ahead relative to the equinox at about half the rate of the Julian Calendar. While this means that the Sunday after Passover will continue to be an excellent compromise between the Western and Eastern Easters, it means that very gradually the Sunday after Passover will creep ahead relative to the equinox, and to the Gregorian Calendar. In the Gregorian year 9035, admittedly a long way off, the Sunday after Passover will for the first time fall in June, if no change is made to the calendars in the mean time.

2. It abandons the Nicene definition of Easter: the Sunday after the first full moon of spring.

The second of these will probably mean my proposal has no hope, for many (especially Orthodox Christians) believe the declaration of Nicaea cannot be set aside. However, there seems no way both to keep the Nicene definition and ensure that Easter is after Passover without holding on to the old Julian Calendar. Given the obvious advantage of a return to Christianity’s gospel roots in Judaism, I still think it is worth giving the Sunday after Passover serious consideration.

My understanding is that a non-Jewish formula was needed because the Jewish Calendar was at the time hard to predict, and that there was perhaps a desire to distinguish Christian practice from Jewish practice. If we assume that the Nicene definition was essentially a reformulation of “the Sunday after Passover”, my proposal would not be going against its spirit. Moreover, the Jewish Calendar’s slippage relative to the seasons is very slow, and there is plenty of time for it to be revised. Would it not be good to trust in the good faith of the Jewish people?

While I make this proposal, I will nevertheless be very pleased if the astronomical proposal from the Aleppo consultation is implemented. I merely offer the Sunday after Passover as an alternative, especially in case the astronomical definition is rejected.

To create the table I have used the Gregorian system of Epacts (which I have called the Gregorian Lunar Calendar); the Orthodox dates are calcul ated according to two different-looking, but equivalent, formulae (see below). For the astronomical definition I am assuming that it is OK for the full moon and the equinox to be on the same Jerusalem meridian day, but that it is not OK for the full moon to occur before the equinox (even if on the same day).

Easter formulas:

The Gregorian calculation used by the Western Church sets up a whole lunar calendar, and the Paschal Full Moon is the 14th day of the Paschal Moon. Easter Day is the Sunday after the Paschal Full Moon (and if the Paschal Full Moon is on a Sunday, it is still the Sunday after).

The Orthodox Churches also celebrate Easter (Pascha) on the Sunday after the Paschal Full Moon. The date of the Paschal Full Moon may be arrived at by two equivalent formulas, which both use the Julian Calendar.

Gauss’ formula for the Orthodox Paschal Full Moon (thanks to Marcos Montes) boils down to
Julian 20 March + (((YR MOD 19)*19+16) MOD 30)

The formula given by Reingold and Dershowitz in Calendrical Calculations becomes
Julian 19 April - (((YR MOD 19)*11+14) MOD 30)

Julian 20 March is Gregorian 2 April until 2099, 3 April from 2100 and 4 Apr from 2200.
(YR MOD 19) means the remainder left after dividing YR (the year number) by 19, and can thus have the values 0 to 18.
Expressions in brackets are evaluated first; otherwise multiplication(*) is understood to be carried out before addition(+).

The two expressions can be shown to be equivalent: substitute n for (YR MOD 19), J for Julian 20 March and (J + 30) for Julian 19 April.
Now, when dealing with non-negative whole numbers a, b and x, (a MOD x) + (b MOD x) is equivalent to ((a + b) MOD x) + x((a + b) >= x),
where ((a + b) >= x) evaluates to one if (a + b) is greater than or equal to x, and evaluates to zero otherwise.
Look at the difference between the two formulas:
(J + ((19n + 16) MOD 30)) - (J + 30 - ((11n + 14) MOD 30))
= J - J - 30 + ((19n + 16) MOD 30) + ((11n + 14) MOD 30)
= -30 + ((19n + 16 + 11n + 14) MOD 30) + 30 * ((19n + 16 + 11n + 14) >= 30)
= -30 + ((30n + 30) MOD 30) + 30 * ((30n + 30) >= 30)
= -30 + 0 + 30 * ((30n + 30) >= 30)   ((30n + 30) MOD 30) = 0 where n is a whole number as here
= -30 + 0 + 30 * 1         ((30n + 30) must be at least 30 where n is a non-negative number as here
= 0

Given that n can be one of only nineteen whole numbers, 0 to 18, this equivalence can also be shown readily using a spreadsheet.