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New Easter Dates
1997 - 2205


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Saturday 22 July 2017  •   29 Holly Moon 2017

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.

The Sunday after Passover

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.

Table of dates 1997 to 2205

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).

year Western Orthodox Astro- Sun after notes on astronomical calculations
  Gregorian   nomical Passover (all Jerusalem meridian times: GMT + 2h 21m)
1997 30 Mar 27 Apr 30 Mar 27 Apr  
1998 12 Apr 19 Apr 19 Apr 12 Apr Full Moon 00:45 Sunday 12 Apr, so Easter the following Sunday
1999 04 Apr 11 Apr 04 Apr 04 Apr  
2000 23 Apr 30 Apr 23 Apr 23 Apr  
2001 15 Apr 15 Apr 15 Apr 15 Apr  
2002 31 Mar 05 May 31 Mar 31 Mar  
2003 20 Apr 27 Apr 20 Apr 20 Apr  
2004 11 Apr 11 Apr 11 Apr 11 Apr  
2005 27 Mar 01 May 27 Mar 01 May  
2006 16 Apr 23 Apr 16 Apr 16 Apr  
2007 08 Apr 08 Apr 08 Apr 08 Apr  
2008 23 Mar 27 Apr 23 Mar 27 Apr  
2009 12 Apr 19 Apr 12 Apr 12 Apr  
2010 04 Apr 04 Apr 04 Apr 04 Apr  
2011 24 Apr 24 Apr 24 Apr 24 Apr  
2012 08 Apr 15 Apr 08 Apr 08 Apr  
2013 31 Mar 05 May 31 Mar 31 Mar  
2014 20 Apr 20 Apr 20 Apr 20 Apr  
2015 05 Apr 12 Apr 05 Apr 05 Apr  
2016 27 Mar 01 May 27 Mar 24 Apr  
2017 16 Apr 16 Apr 16 Apr 16 Apr  
2018 01 Apr 08 Apr 01 Apr 01 Apr  
2019 21 Apr 28 Apr 24 Mar 21 Apr Full Moon 04:05 21 Mar, Equinox 00:20 21 Mar
2020 12 Apr 19 Apr 12 Apr 12 Apr  
2021 04 Apr 02 May 04 Apr 04 Apr  
2022 17 Apr 24 Apr 17 Apr 17 Apr  
2023 09 Apr 16 Apr 09 Apr 09 Apr  
2024 31 Mar 05 May 31 Mar 28 Apr  
2025 20 Apr 20 Apr 20 Apr 20 Apr  
2026 05 Apr 12 Apr 05 Apr 05 Apr  
2027 28 Mar 02 May 28 Mar 25 Apr  
2028 16 Apr 16 Apr 16 Apr 16 Apr  
2029 01 Apr 08 Apr 01 Apr 01 Apr  
2030 21 Apr 28 Apr 21 Apr 21 Apr  
2031 13 Apr 13 Apr 13 Apr 13 Apr  
2032 28 Mar 02 May 28 Mar 28 Mar  
2033 17 Apr 24 Apr 17 Apr 17 Apr  
2034 09 Apr 09 Apr 09 Apr 09 Apr  
2035 25 Mar 29 Apr 25 Mar 29 Apr  
2036 13 Apr 20 Apr 13 Apr 13 Apr  
2037 05 Apr 05 Apr 05 Apr 05 Apr  
2038 25 Apr 25 Apr 28 Mar 25 Apr Full Moon 04:31 Sunday 21 Mar, Equinox 15:02 20 Mar
2039 10 Apr 17 Apr 10 Apr 10 Apr  
2040 01 Apr 06 May 01 Apr 01 Apr  
2041 21 Apr 21 Apr 21 Apr 21 Apr  
2042 06 Apr 13 Apr 06 Apr 06 Apr  
2043 29 Mar 03 May 29 Mar 26 Apr  
2044 17 Apr 24 Apr 17 Apr 17 Apr  
2045 09 Apr 09 Apr 02 Apr 09 Apr Full Moon 21:04 Saturday 1 April
2046 25 Mar 29 Apr 25 Mar 22 Apr  
2047 14 Apr 21 Apr 14 Apr 14 Apr  
2048 05 Apr 05 Apr 05 Apr 05 Apr  
2049 18 Apr 25 Apr 25 Apr 18 Apr  
2050 10 Apr 17 Apr 10 Apr 10 Apr  
2051 02 Apr 07 May 02 Apr 02 Apr  
2052 21 Apr 21 Apr 21 Apr 21 Apr  
2053 06 Apr 13 Apr 06 Apr 06 Apr  
2054 29 Mar 03 May 29 Mar 26 Apr  
2055 18 Apr 18 Apr 18 Apr 18 Apr  
2056 02 Apr 09 Apr 02 Apr 02 Apr  
2057 22 Apr 29 Apr 25 Mar 22 Apr Full Moon 03:12 21 Mar, Equinox 05:31 20 Mar
2058 14 Apr 14 Apr 14 Apr 14 Apr  
2059 30 Mar 04 May 30 Mar 30 Mar  
2060 18 Apr 25 Apr 18 Apr 18 Apr  
2061 10 Apr 10 Apr 10 Apr 10 Apr  
2062 26 Mar 30 Apr 26 Mar 30 Apr  
2063 15 Apr 22 Apr 15 Apr 15 Apr  
2064 06 Apr 13 Apr 06 Apr 06 Apr  
2065 29 Mar 26 Apr 29 Mar 26 Apr  
2066 11 Apr 18 Apr 11 Apr 11 Apr  
2067 03 Apr 10 Apr 03 Apr 03 Apr  
2068 22 Apr 29 Apr 22 Apr 22 Apr previous Full Moon 01:20 19 Mar, before Equinox at 21:15
2069 14 Apr 14 Apr 14 Apr 07 Apr  
2070 30 Mar 04 May 30 Mar 30 Mar  
2071 19 Apr 19 Apr 19 Apr 19 Apr  
2072 10 Apr 10 Apr 10 Apr 10 Apr  
2073 26 Mar 30 Apr 26 Mar 23 Apr  
2074 15 Apr 22 Apr 15 Apr 15 Apr  
2075 07 Apr 07 Apr 07 Apr 07 Apr  
2076 19 Apr 26 Apr 22 Mar 19 Apr Full Moon 19:04 20 Mar, Equinox 20:01 19 Mar
2077 11 Apr 18 Apr 11 Apr 11 Apr  
2078 03 Apr 08 May 03 Apr 03 Apr  
2079 23 Apr 23 Apr 23 Apr 23 Apr  
2080 07 Apr 14 Apr 07 Apr 07 Apr  
2081 30 Mar 04 May 30 Mar 27 Apr  
2082 19 Apr 19 Apr 19 Apr 19 Apr  
2083 04 Apr 11 Apr 04 Apr 04 Apr  
2084 26 Mar 30 Apr 26 Mar 23 Apr  
2085 15 Apr 15 Apr 15 Apr 15 Apr  
2086 31 Mar 07 Apr 31 Mar 31 Mar  
2087 20 Apr 27 Apr 20 Apr 20 Apr previous Full Moon on 19 Mar, before Equinox on 20 Mar
2088 11 Apr 18 Apr 11 Apr 11 Apr  
2089 03 Apr 01 May 27 Mar 27 Mar Full Moon on Saturday 26 March
2090 16 Apr 23 Apr 16 Apr 16 Apr  
2091 08 Apr 08 Apr 08 Apr 08 Apr  
2092 30 Mar 27 Apr 30 Mar 27 Apr  
2093 12 Apr 19 Apr 12 Apr 12 Apr  
2094 04 Apr 11 Apr 04 Apr 04 Apr  
2095 24 Apr 24 Apr 27 Mar 24 Apr Full Moon 03:37 21 Mar, Equinox 10:38 20 Mar
2096 15 Apr 15 Apr 08 Apr 08 Apr Full Moon on Saturday 7 April
2097 31 Mar 05 May 31 Mar 31 Mar  
2098 20 Apr 27 Apr 20 Apr 20 Apr  
2099 12 Apr 12 Apr 12 Apr 12 Apr  
2100 28 Mar 02 May 28 Mar 25 Apr  
2101 17 Apr 24 Apr 17 Apr 17 Apr  
2102 09 Apr 09 Apr 09 Apr 09 Apr  
2103 25 Mar 29 Apr 25 Mar 29 Apr  
2104 13 Apr 20 Apr 13 Apr 13 Apr  
2105 05 Apr 05 Apr 05 Apr 05 Apr  
2106 18 Apr 25 Apr 25 Apr 25 Apr  
2107 10 Apr 17 Apr 10 Apr 10 Apr  
2108 01 Apr 06 May 01 Apr 01 Apr  
2109 21 Apr 21 Apr 21 Apr 21 Apr  
2110 06 Apr 13 Apr 06 Apr 06 Apr  
2111 29 Mar 03 May 29 Mar 26 Apr  
2112 17 Apr 17 Apr 17 Apr 17 Apr  
2113 02 Apr 09 Apr 02 Apr 02 Apr  
2114 22 Apr 29 Apr 25 Mar 22 Apr  
2115 14 Apr 14 Apr 14 Apr 14 Apr  
2116 29 Mar 03 May 29 Mar 29 Mar  
2117 18 Apr 25 Apr 18 Apr 18 Apr  
2118 10 Apr 17 Apr 10 Apr 10 Apr  
2119 26 Mar 30 Apr 02 Apr 30 Apr  
2120 14 Apr 21 Apr 21 Apr 14 Apr  
2121 06 Apr 13 Apr 06 Apr 06 Apr  
2122 29 Mar 03 May 29 Mar 26 Apr  
2123 11 Apr 18 Apr 11 Apr 18 Apr  
2124 02 Apr 09 Apr 02 Apr 02 Apr  
2125 22 Apr 29 Apr 22 Apr 22 Apr  
2126 14 Apr 14 Apr 14 Apr 14 Apr  
2127 30 Mar 04 May 30 Mar 30 Mar  
2128 18 Apr 25 Apr 18 Apr 18 Apr  
2129 10 Apr 10 Apr 10 Apr 10 Apr  
2130 26 Mar 30 Apr 26 Mar 30 Apr  
2131 15 Apr 22 Apr 15 Apr 15 Apr  
2132 06 Apr 06 Apr 06 Apr 06 Apr  
2133 19 Apr 26 Apr 22 Mar 26 Apr  
2134 11 Apr 18 Apr 11 Apr 11 Apr  
2135 03 Apr 08 May 03 Apr 03 Apr  
2136 22 Apr 22 Apr 22 Apr 22 Apr  
2137 07 Apr 14 Apr 07 Apr 07 Apr  
2138 30 Mar 04 May 30 Mar 27 Apr  
2139 19 Apr 19 Apr 19 Apr 19 Apr  
2140 03 Apr 10 Apr 03 Apr 03 Apr  
2141 26 Mar 30 Apr 26 Mar 23 Apr  
2142 15 Apr 22 Apr 15 Apr 15 Apr  
2143 31 Mar 07 Apr 07 Apr 07 Apr  
2144 19 Apr 26 Apr 19 Apr 19 Apr  
2145 11 Apr 18 Apr 11 Apr 11 Apr  
2146 03 Apr 08 May 03 Apr 03 Apr  
2147 16 Apr 23 Apr 23 Apr 16 Apr  
2148 07 Apr 14 Apr 07 Apr 07 Apr  
2149 30 Mar 04 May 30 Mar 27 Apr  
2150 12 Apr 19 Apr 19 Apr 19 Apr  
2151 04 Apr 11 Apr 04 Apr 04 Apr  
2152 23 Apr 30 Apr 26 Mar 23 Apr  
2153 15 Apr 15 Apr 15 Apr 15 Apr  
2154 31 Mar 05 May 31 Mar 31 Mar  
2155 20 Apr 27 Apr 20 Apr 20 Apr  
2156 11 Apr 11 Apr 11 Apr 11 Apr  
2157 27 Mar 01 May 27 Mar 01 May  
2158 16 Apr 23 Apr 16 Apr 16 Apr  
2159 08 Apr 08 Apr 08 Apr 08 Apr  
2160 23 Mar 27 Apr 23 Mar 27 Apr  
2161 12 Apr 19 Apr 12 Apr 12 Apr  
2162 04 Apr 11 Apr 04 Apr 04 Apr  
2163 24 Apr 24 Apr 24 Apr 24 Apr  
2164 08 Apr 15 Apr 08 Apr 08 Apr  
2165 31 Mar 05 May 31 Mar 31 Mar  
2166 20 Apr 20 Apr 20 Apr 20 Apr  
2167 05 Apr 12 Apr 05 Apr 05 Apr  
2168 27 Mar 01 May 27 Mar 24 Apr  
2169 16 Apr 23 Apr 16 Apr 16 Apr  
2170 01 Apr 08 Apr 08 Apr 08 Apr  
2171 21 Apr 28 Apr 24 Mar 21 Apr  
2172 12 Apr 19 Apr 12 Apr 12 Apr  
2173 04 Apr 09 May 04 Apr 04 Apr  
2174 17 Apr 24 Apr 24 Apr 17 Apr  
2175 09 Apr 16 Apr 09 Apr 09 Apr  
2176 31 Mar 05 May 31 Mar 28 Apr  
2177 20 Apr 20 Apr 20 Apr 20 Apr  
2178 05 Apr 12 Apr 05 Apr 05 Apr  
2179 28 Mar 02 May 28 Mar 25 Apr  
2180 16 Apr 16 Apr 16 Apr 16 Apr  
2181 01 Apr 08 Apr 01 Apr 01 Apr  
2182 21 Apr 28 Apr 21 Apr 21 Apr  
2183 13 Apr 13 Apr 13 Apr 13 Apr  
2184 28 Mar 02 May 28 Mar 28 Mar  
2185 17 Apr 24 Apr 17 Apr 17 Apr  
2186 09 Apr 09 Apr 09 Apr 09 Apr  
2187 25 Mar 29 Apr 25 Mar 29 Apr  
2188 13 Apr 20 Apr 13 Apr 13 Apr  
2189 05 Apr 12 Apr 05 Apr 05 Apr  
2190 25 Apr 25 Apr 28 Mar 25 Apr  
2191 10 Apr 17 Apr 10 Apr 10 Apr  
2192 01 Apr 06 May 01 Apr 01 Apr  
2193 21 Apr 28 Apr 21 Apr 21 Apr  
2194 06 Apr 13 Apr 06 Apr 06 Apr  
2195 29 Mar 03 May 29 Mar 26 Apr  
2196 17 Apr 24 Apr 17 Apr 17 Apr  
2197 09 Apr 09 Apr 09 Apr 09 Apr  
2198 25 Mar 29 Apr 25 Mar 22 Apr  
2199 14 Apr 21 Apr 14 Apr 14 Apr  
2200 06 Apr 06 Apr 06 Apr 06 Apr  
2201 19 Apr 26 Apr 26 Apr 26 Apr  
2202 11 Apr 18 Apr 11 Apr 11 Apr  
2203 03 Apr 08 May 03 Apr 03 Apr  
2204 22 Apr 22 Apr 22 Apr 22 Apr  
2205 07 Apr 14 Apr 07 Apr 07 Apr  

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.

William Morris
updated March 2017
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