Under the Gregorian calendar, what days can never be Easter?

Question

Obviously, October 31 can't be Easter any year whatsoever. Indeed no day in October can be Easter. But can February 28 be Easter? What about February 29? May 1? Is there a single consecutive range of days that can't be Easter, like say for example April 17 wrapping around past December to January and over to March 12?

Bonus question: using the Julian calendar as it was observed in Russia until 1918, does the answer to this question change merely by a simple transposition?

@Lucian Do you have a more reliable source than that? Even if those Wikipedia articles are technically correct, the writing looks awful. — Robert Soupe, Apr 07 '15 at 02:44
Since the Julian calendar shifts with respect to the mean tropical year (hence with respect to the equinoctes) by one day every 128 years, there is no day in the Julian calendar that isn't eventually an Easter. — Eric Towers, Jul 14 '15 at 23:53
@Eric Yes, of course, which is why I wrote "as it was observed in Russia until 1918." I can't promise you David's bounty, but I do hope someone comes along to give a better answer so that Dave doesn't have to reluctantly let the system auto-award it to the reluctant mathematician. — Robert Soupe, Jul 15 '15 at 00:41

score 7 · Answer 1 · answered Apr 05 '15 at 23:47

7

Easter is defined (on the Gregorian calendar) as "the first Sunday following the first full moon after the spring equinox". The spring equinox ranges from Mar 20-21. The lunar cycle is 29.53 days. The dominical ranges from 1-7. Thus, Easter will be no later than Apr 25. The earliest is Mar 22.

answered Apr 05 '15 at 23:47

reluctant mathematician

856
6
12

So then each day between March 22 and April 25 (inclusive) will be Easter at least once within the next four centuries? – Robert Soupe Apr 07 '15 at 02:41
1

This calculation will work most of the time. In some religions, observers watch for the full moon and then name the date. Their full moon can be different from the astronomical full moon. (human error?) – Fred Daniel Kline Jul 11 '15 at 21:28
2

The Catholic Church computes Easter using the ecclesiastical full moon, a straightforward (though somewhat verbose) formula that obviates any need for observation or for detailed computation of when the Moon actually becomes full. – Brian Tung Jul 11 '15 at 22:27
(loosely stated) the first full moon on or after the vernal equinox; also, if that calculation coincides with Passover, then Easter will be a week later. – DDS Jun 28 '19 at 06:30
1

@mlchristians, is there any evidence that Easter is moved when it coincides with Passover? I've seen various calculations for the date of Easter, and can't see any evidence that Passover itself is calculated, let alone that it causes Easter to be moved. – Steve Feb 08 '21 at 14:45
@Steve I've seen it different places---one I recall, ``On the History and Practice of Ancient Astronomy'' by J. Evans. You bring up a good point about the calculation of Passover. – DDS Feb 08 '21 at 16:44
@mlchristians, yes certainly I've heard this claim before in my own research, but it appears possibly to be (and I mean no disrespect to you in saying this...) one of the misleading claims that swirls around this topic. It's possible that the calculation adopted by the Christian church inherently avoids Passover (perhaps by the rule that Easter is the Sunday after the full moon - that full-moon day perhaps being Passover itself by the Judaic calculation, idk), but there is definitely no ad-hoc exception to the calculation, or specific reference to Passover as part of the calculation. – Steve Feb 08 '21 at 16:56
@Steve Then I can only refer you to what was promulgated at the Council of Nicea in 325 A.D. if you can find an accurate reference to it. Note that in my original comment, I had said "loosely stated"---if you replace "vernal equinox" with "March 21" you will have a more accurate statement of what the Church decreed back in 325 A.D. I hope this helps. – DDS Feb 08 '21 at 19:14
@mlchristians, prior to Dionysius, who formalised the computus for Easter in around 500AD, the church possibly used a different method of reckoning. I can't speak offhand to what exactly preceded it. I can only tell you that I'm not aware of any such exception in the Gregorian system, or in the Julian system that immediately preceded it. As I say, a possible explanation is that the "Sunday after" rule inherently avoids Passover - because the Jewish scheme for calculating Passover, is similar if not identical to how the "Paschal full moon" is calculated in the Christian system. – Steve Feb 08 '21 at 19:49
That is, (and I speak as someone who is not familiar with the detail of the Jewish lunar calendar), if the Paschal full moon determined by the Christian computus is the same day as Passover in the Jewish calendar, then the rule which says Gregorian Easter is always the Sunday after the full moon (and this is not an exception, but an inherent part of the calculation, because the full moon itself is only occasionally on a Sunday, so Easter would usually be on the Sunday after the full moon, given that Easter axiomatically falls on Sunday), inherently avoids Easter falling on Passover itself. – Steve Feb 08 '21 at 19:54

score 4 · Accepted Answer · edited Apr 13 '17 at 12:56

TL;DR: Gregorian Easters (eventually) fall on each date in [22 March, 25 April]. Greek Orthodox (Julian) Easters (eventually) fall on each date in the year, including 29 February.

In the years 1919 through 2285, the following years will be the first occurrence of Easter (Gregorian) for each date:

22 March, 2285
23 March, 2008
24 March, 1940
25 March, 1951
26 March, 1967
27 March, 1921
28 March, 1937
29 March, 1959
30 March, 1975
31 March, 1929
1 April, 1923
2 April, 1961
3 April, 1983
4 April, 1920
5 April, 1931
6 April, 1947
7 April, 1985
8 April, 1928
9 April, 1939
10 April, 1955
11 April, 1971
12 April, 1925
13 April, 1941
14 April, 1963
15 April, 1979
16 April, 1922
17 April, 1927
18 April, 1954
19 April, 1981
20 April, 1919
21 April, 1935
22 April, 1962
23 April, 2000
24 April, 2011
25 April, 1943

Consequently, every date in the range given by @reluctant mathematician in his answer occurs by 2285.

We could credibly argue whether 22 March will ever actually be a Gregorian Easter since the shortening of times that calendars in use suggests that the Gregorian calendar may be replaced by that time. No other dates are Easters through they year 10000 under the Gregorian Calendar.

Greek Orthodox Easter is celebrated according to the Julian Calendar. (This may or may not be the same calendar as in use in Russia up to 1918, I am unable to get definitive data from the implementation described below.) It takes about 10000 years for this calendar to shift just under three months, so I used the same method but on a time window from 1919 to 50000. This gives the table of all 366 dates (including 29 February in 42460):

1 January, 33809
2 January, 33972
3 January, 33904
4 January, 34189
5 January, 34341
6 January, 34436
7 January, 34531
8 January, 34626
9 January, 34721
10 January, 34968
11 January, 35063
12 January, 35158
13 January, 35405
14 January, 35500
15 January, 35595
16 January, 35785
17 January, 35937
18 January, 36032
19 January, 36127
20 January, 36222
21 January, 36317
22 January, 36564
23 January, 36659
24 January, 36754
25 January, 37001
26 January, 37096
27 January, 37191
28 January, 37381
29 January, 37533
30 January, 37628
31 January, 37723
1 February, 37818
2 February, 37913
3 February, 38160
4 February, 38255
5 February, 38350
6 February, 38749
7 February, 38692
8 February, 38787
9 February, 38977
10 February, 39129
11 February, 39224
12 February, 39319
13 February, 39414
14 February, 39509
15 February, 39756
16 February, 39851
17 February, 39946
18 February, 40345
19 February, 40288
20 February, 40383
21 February, 40573
22 February, 40725
23 February, 40820
24 February, 40915
25 February, 41010
26 February, 41105
27 February, 41352
28 February, 41447
29 February, 42460
1 March, 41542
2 March, 41884
3 March, 42047
4 March, 41979
5 March, 42169
6 March, 42321
7 March, 42579
8 March, 42511
9 March, 42606
10 March, 42701
11 March, 43100
12 March, 43043
13 March, 43138
14 March, 43480
15 March, 43643
16 March, 43575
17 March, 43765
18 March, 43917
19 March, 44175
20 March, 44107
21 March, 44202
22 March, 44544
23 March, 44859
24 March, 44639
25 March, 44734
26 March, 45076
27 March, 45239
28 March, 45171
29 March, 45361
30 March, 45513
31 March, 45771
1 April, 45703
2 April, 45893
3 April, 46140
4 April, 2010
5 April, 1942
6 April, 1980
7 April, 1991
8 April, 1923
9 April, 1939
10 April, 1966
11 April, 1920
12 April, 1931
13 April, 1947
14 April, 1963
15 April, 1928
16 April, 1922
17 April, 1955
18 April, 1971
19 April, 1925
20 April, 1919
21 April, 1946
22 April, 1979
23 April, 1995
24 April, 1927
25 April, 1943
26 April, 1970
27 April, 1924
28 April, 1935
29 April, 1951
30 April, 1967
1 May, 1921
2 May, 1926
3 May, 1959
4 May, 1975
5 May, 1929
6 May, 1945
7 May, 2051
8 May, 1983
9 May, 2173
10 May, 2268
11 May, 2583
12 May, 2515
13 May, 2610
14 May, 2705
15 May, 3104
16 May, 3047
17 May, 3142
18 May, 3332
19 May, 3647
20 May, 3579
21 May, 3769
22 May, 3864
23 May, 4179
24 May, 4111
25 May, 4206
26 May, 4301
27 May, 4700
28 May, 4643
29 May, 4738
30 May, 4928
31 May, 5243
1 June, 5175
2 June, 5365
3 June, 5460
4 June, 5775
5 June, 5707
6 June, 5802
7 June, 5992
8 June, 6459
9 June, 6239
10 June, 6334
11 June, 6524
12 June, 6839
13 June, 6771
14 June, 6961
15 June, 7056
16 June, 7371
17 June, 7303
18 June, 7493
19 June, 7588
20 June, 8055
21 June, 7835
22 June, 7930
23 June, 8120
24 June, 8435
25 June, 8367
26 June, 8557
27 June, 8652
28 June, 8899
29 June, 8994
30 June, 9089
1 July, 9184
2 July, 9499
3 July, 9431
4 July, 9526
5 July, 9716
6 July, 10031
7 July, 9963
8 July, 10153
9 July, 10248
10 July, 10495
11 July, 10590
12 July, 10685
13 July, 10780
14 July, 11095
15 July, 11027
16 July, 11122
17 July, 11312
18 July, 11627
19 July, 11559
20 July, 11749
21 July, 11844
22 July, 12091
23 July, 12186
24 July, 12281
25 July, 12376
26 July, 12691
27 July, 12623
28 July, 12718
29 July, 12908
30 July, 13223
31 July, 13155
1 August, 13345
2 August, 13440
3 August, 13687
4 August, 13782
5 August, 13877
6 August, 13972
7 August, 14287
8 August, 14219
9 August, 14314
10 August, 14504
11 August, 14819
12 August, 14751
13 August, 14941
14 August, 15036
15 August, 15283
16 August, 15378
17 August, 15473
18 August, 15568
19 August, 15883
20 August, 15815
21 August, 15910
22 August, 16100
23 August, 16415
24 August, 16347
25 August, 16537
26 August, 16632
27 August, 16879
28 August, 16974
29 August, 17069
30 August, 17164
31 August, 17479
1 September, 17411
2 September, 17506
3 September, 17848
4 September, 18011
5 September, 17943
6 September, 18133
7 September, 18228
8 September, 18475
9 September, 18570
10 September, 18665
11 September, 18760
12 September, 19075
13 September, 19007
14 September, 19102
15 September, 19444
16 September, 19607
17 September, 19539
18 September, 19729
19 September, 19824
20 September, 20071
21 September, 20166
22 September, 20261
23 September, 20356
24 September, 20671
25 September, 20603
26 September, 20793
27 September, 21040
28 September, 21203
29 September, 21135
30 September, 21325
1 October, 21420
2 October, 21667
3 October, 21762
4 October, 21857
5 October, 21952
6 October, 22199
7 October, 22294
8 October, 22389
9 October, 22636
10 October, 22799
11 October, 22731
12 October, 22921
13 October, 23016
14 October, 23263
15 October, 23358
16 October, 23453
17 October, 23548
18 October, 23795
19 October, 23890
20 October, 23985
21 October, 24232
22 October, 24395
23 October, 24327
24 October, 24517
25 October, 24612
26 October, 24859
27 October, 24954
28 October, 25049
29 October, 25144
30 October, 25391
31 October, 25486
1 November, 25581
2 November, 25828
3 November, 25991
4 November, 25923
5 November, 26113
6 November, 26208
7 November, 26455
8 November, 26550
9 November, 26645
10 November, 26740
11 November, 26987
12 November, 27082
13 November, 27177
14 November, 27424
15 November, 27587
16 November, 27519
17 November, 27709
18 November, 27804
19 November, 28051
20 November, 28146
21 November, 28241
22 November, 28336
23 November, 28583
24 November, 28678
25 November, 28773
26 November, 29020
27 November, 29183
28 November, 29115
29 November, 29305
30 November, 29400
1 December, 29647
2 December, 29742
3 December, 29837
4 December, 29932
5 December, 30179
6 December, 30274
7 December, 30369
8 December, 30616
9 December, 30779
10 December, 30711
11 December, 30901
12 December, 31148
13 December, 31243
14 December, 31338
15 December, 31433
16 December, 31528
17 December, 31775
18 December, 31870
19 December, 31965
20 December, 32212
21 December, 32375
22 December, 32307
23 December, 32592
24 December, 32744
25 December, 32839
26 December, 32934
27 December, 33029
28 December, 33124
29 December, 33371
30 December, 33466
31 December, 33561

It is of course exceedingly unlikely that any calendrical system, even the Julian system, will remain in use until 46140, the first (Gregorian) year Easter will fall on (Gregorian) 3 April.

Appendix

I used the Mathematica functions EasterSunday[] and EasterSundayGreekOrthodox[]. As of Version 10, these functions were crippled by Wolfram. Mathematica documentation claims "As of Version 10.0, calendar functionality is built into the Wolfram Language". However, there is no equivalent facility, nor is there documentation of a workaround. I have consequently used https://mathematica.stackexchange.com/questions/75281/eastersunday-replacement-in-mathematica-10 to workaround Wolfram's stupidity.

The Greek Orthodox version of the above was created using

dates = DataPaclets`CalendarDataDump`EasterSundayGreekOrthodox /@ Range[1919, 50000]
days = Sort[DeleteDuplicates[dates[[All, {2, 3}]]]]
findDates[day_] := Select[dates, #[[2]] == day[[1]] && #[[3]] == day[[2]] &][[1]]
result = findDates /@ days)
Length[result]
Max[result[[All, 1]]]
months = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"}
StringJoin @@ (" * " <> ToString[#[[3]]] <> " " <> months[[#[[2]]]] <> ", " <> ToString[#[[1]]] <> "\n" &) /@ result

Side question: if humans are still living on this planet in 2285, what sort of calendar do you think they'll be using? Stardates? Or just some tweaks on the Gregorian calendar just major enough to be considered different from Gregorian? — David R., Jul 15 '15 at 21:11
@DavidR. : We could just keep using Gregorian to 2285, but it seems likely that something will change. Perhaps the fallout of global water warfare will return us to "Year 10 of Thog's rule" calendars. Optimistically, I like to imagine at some point the economic costs of civil time and astronomical calendars will drive the move to atomic timekeeping, eschewing of timezones, and some sort of uniformization of the calendar (i.e. all units a fixed multiple of other units). — Eric Towers, Jul 15 '15 at 22:31

Under the Gregorian calendar, what days can never be Easter?

2 Answers2

Appendix