Easter moons, 2019–2038

Easter by hand: the church's moon against the sky's

The question

Gregorian Easter is the Sunday after the "Paschal full moon", but that moon is a table, not the sky: the 14th day of an ecclesiastical lunation, from the epact, against a fixed equinox of March 21. How far off is the table's moon now, and how often does it change Easter?

Method

Anonymous Gregorian algorithm (Meeus/Butcher). For 2000–2099, b = 20, d = 5, g = 6, so b − d − g + 15 = 24 and h = (19a + 24) mod 30 with a = Y mod 19, and the table's PFM is March 21 + h. Exceptions (my reading of the Gregorian epact rule): h = 29 gives April 18 (not 19); h = 28 with a over 10 gives April 17 (not 18). Easter = March 22 + h + l − 7m.

Checked by hand against known Easters: 2024 Mar 31, 2025 Apr 20, 2026 Apr 5, 2027 Mar 28. All right.

Sky: USNO API moon/phases (UTC), and seasons for the equinox.

Table, 2019–2038 (UTC dates)

| year | a | h | table PFM | real full moon (UTC) | table − real | |---|---|---|---|---|---| | 2019 | 5 | 29 | Apr 18 | Mar 21 01:43 (equinox Mar 20 21:58) | different lunation | | 2020 | 6 | 18 | Apr 8 | Apr 8 02:35 | 0 | | 2021 | 7 | 7 | Mar 28 | Mar 28 18:48 | 0 | | 2022 | 8 | 26 | Apr 16 | Apr 16 18:55 | 0 | | 2023 | 9 | 15 | Apr 5 | Apr 6 04:34 | −1 | | 2024 | 10 | 4 | Mar 25 | Mar 25 07:00 | 0 | | 2025 | 11 | 23 | Apr 13 | Apr 13 00:22 | 0 | | 2026 | 12 | 12 | Apr 2 | Apr 2 02:12 | 0 | | 2027 | 13 | 1 | Mar 22 | Mar 22 10:44 | 0 | | 2028 | 14 | 20 | Apr 10 | Apr 9 10:26 | +1 | | 2029 | 15 | 9 | Mar 30 | Mar 30 02:26 | 0 | | 2030 | 16 | 28 | Apr 17 (exc.) | Apr 18 03:20 | −1 | | 2031 | 17 | 17 | Apr 7 | Apr 7 17:21 | 0 | | 2032 | 18 | 6 | Mar 27 | Mar 27 00:46 | 0 | | 2033 | 0 | 24 | Apr 14 | Apr 14 19:17 | 0 | | 2034 | 1 | 13 | Apr 3 | Apr 3 19:19 | 0 | | 2035 | 2 | 2 | Mar 23 | Mar 23 22:42 | 0 | | 2036 | 3 | 21 | Apr 11 | Apr 10 20:22 | +1 | | 2037 | 4 | 10 | Mar 31 | Mar 31 09:53 | 0 | | 2038 | 5 | 29 | Apr 18 | Mar 21 02:09 (equinox Mar 20 12:40) | different lunation |

In the 2019 lunation itself the table's moon is Mar 20, the sky's Mar 21: −1. Same in 2038.

What it shows

• In UTC, the table's moon lands on the sky's date in 14 of the 18 ordinary years, and is a day off in 4 (2023 and 2030 early, 2028 and 2036 late). Nothing is off by more than a day.
• None of the one-day misses change Easter: 2023 (Wed vs Thu, both to Apr 9), 2028 (sky's moon on Sunday Apr 9, table's on Monday, both give Apr 16), 2030 (both to Apr 21), 2036 (both to Apr 13). The 2030 exception moves the table a day away from the sky and changes nothing.
• The two years that do change are 2019 and 2038, which are one Metonic cycle apart (same a, same h). The mechanism is two small errors pointing the same way. The table's moon is a day early (Mar 20 vs Mar 21), and the table's equinox is a day late (Mar 21 vs Mar 20). So the table puts the full moon before the equinox, and the sky puts it after. Each error is a day. Together they cost a month.
  • 2019: the sky says Easter Mar 24, the church Apr 21.
  • 2038: the sky's full moon falls on Sunday Mar 21, so the sky says Mar 28. The church says Apr 25, the latest date Easter can have.

Caveats

• These are UTC dates. A reckoning on the Jerusalem meridian (2–3 h ahead) would move only late-evening UTC moons, to the next day: 2035 (22:42) would go to Mar 24 and become −1. 2019 and 2038 don't change, because a time zone moves the equinox and the moon together, and the sky's order (equinox first, by about 4 h and 13 h) holds everywhere.
• The 2030 exception rule is from memory of the epact table. It doesn't affect any Easter here.
• Before computing, I half-remembered that 2019 and 2038 differ from astronomical Easter. The table is what I'd stand behind, not the memory.