Easter paradox
An Easter paradox or an Easter paradox exists if the actual beginning of spring and / or the spring full moon do not occur on the days that are used for this in the calculation method for the Easter date , and the calculated Easter date thus deviates from the date that would follow from the actual events.
In the Julian calendar , the difference between actual astronomical events and their calendar reproduction in the year of the calendar reform in 1582 was more than a week, which in retrospect can be described as a major systematic error . From an Easter paradox that i. d. Usually refers to a deviation of only one day, can therefore only be spoken of when using the Gregorian calendar .
The causes of the Easter paradox
The definition for the Easter date is: Easter is the first Sunday after the first full moon in spring.
The first full moon in spring is the full moon from March 21st, which is used in the Easter bill as a fixed reference day instead of March 20th or 19th, which is also astronomically possible for the beginning of spring . The day on which the full moon actually takes place is also not used as the full moon day, but a cyclically predetermined day .
In the first centuries of Easter it was not easy to accurately predict the beginning of spring and the full moon to the exact day. On the basis of centuries of observations, however, good average values had been obtained for their chronological sequence, with which their future arrival was determined. The two average periods used are the solar year and the lunar month . The events determined with the help of these periods are called cyclic . Depending on the calculation method, they deviate to a tolerable extent from the astronomical events that actually occur .
With this cyclical approach , disagreements were minimized and it was possible to plan well into the future. Because of the organizational advantage, the Gregorian calendar reform did not deviate from it, although it was now possible to specify more precise dates ( astronomical procedure ) for the future.
The beginning of spring varies slowly and relatively little. Its cyclical date is March 21st. Astronomical dates within the Gregorian calendar cycle of 400 years are the 21st (until 2100 for the last time in 2011), the 20th and 2044 to 2097 sometimes also the 19th of March. The lunar month varies relatively quickly between the values of 29.272 and 29.833 days. The accumulation leads to the fact that the astronomical spring full moon deviates from the cyclical scheme ( lunar circle ) by a maximum of ± 1 day .
Types of Easter Paradoxes
The Easter paradoxes were first examined in detail by Ludwig Lange . The given classification was suggested by him.
- An Easter paradox is only caused by the difference between an astronomical and a cyclical full moon date, where only the days of the week Saturday and Sunday play a role.
a) • An Easter paradox exists when the astronomical full moon is on a Saturday, but the cyclical full moon is not until the next day (a Sunday) and the cyclical Easter is therefore only a week later: Positive Hebdomadal paradox (H +) ( hebdomadal in the Meaning of weekly),
b) • An Easter paradox exists when an astronomical full moon is on a Sunday, but the cyclical full moon is on the Saturday before and the cyclical Easter is already on this Sunday: Negative Hebdomadal paradox (H-) .
- a) An Easter paradox is only caused by the difference between an astronomical and a cyclical full moon date, whereby only the reference to the beginning of spring fixed on March 21st plays a role:
• An Easter paradox exists when the cyclical full moon is on March 21st but the astronomical one is earlier and the cyclical Easter is not set after the next full moon date.
Lange does not include this limiting case in his classification.
b) An Easter paradox is caused both by the difference between an astronomical and a cyclical full moon date and by the difference between an astronomical and a cyclical beginning of spring date. The reference to March 21 does not apply. The astronomical data at and near the beginning of spring are compared directly with one another:
• An Easter paradox exists if this comparison leads to a different result than the cyclical method: Positive equinox paradox (A +) (term refers to the spring equinox ), Note:
In the cyclical Easter calculation, only calendar days are taken into account as times for the beginning of spring and full moon, which are also set once and for all in advance. If one wanted to adhere to this regulation, the astronomical times would also have to be "rounded off" to the respective calendar or weekday. Lange is more strict by z. B. the order of the two events is also evaluated if they take place within a day.
The Easter paradox was originally part of the criticism of the Gregorian calendar and its Easter calculation. It took place in Christian Europe, so that the assignment of astronomical times to calendar dates was unquestionable. There was implicit reference to the Christian center of Rome . Additional cases of Easter paradoxes can be constructed (as Lange does, for example ) if one does not refer to Rome (or to another city of similar geographical length ). The day change (important, whether it is Saturday or Sunday or whether it is midnight between the astronomical beginning of spring and the full moon) takes place around the world at different times.
Negative equinox (A-) represent the rarest form of Easter paradox and only occur in the period from 1583 to 4000 in the two years 2353 and 2372.
Years with the Easter paradox
List of all paradoxes from 1582 to 2200 for the Gregorian meridian according to Lange
- A +: 1590, 1666, 1685, 1924, 1943, 1962, 2019, 2038, 2057, 2076, 2095, 2114, 2133, 2152, 2171, 2190
- H + : 1629, 1700, 1724, 1744, 1778, 1798, 1876, 1974, 2045, 2069, 2089, 2096
- H- : 1598, 1609, 1622, 1693, 1802, 1805, 1818, 1825, 1829, 1845, 1900, 1903, 1923, 1927, 1954, 1967, 1981, 2049, 2076, 2106, 2119, 2133, 2147, 2150 , 2170, 2174
- In the years 2076 and 2133 the A + and the H- paradoxes occur combined ( double paradox ).
- In 2019, the last paradox so far, an equinox (A +), occurred (March 21, in the Easter calculation as a fixed calendar day for the beginning of spring and a cyclical full moon: March 20, i.e. one day too early for the cyclical method; astronomical full moon: March 21) March 02:43 am CET. However, the astronomical beginning of spring was March 20th 22:58 pm CET, i.e. on the day or 3 hours 45 minutes before the astronomical full moon). The paradox is that the full moon discussed was astronomically already a spring full moon and Easter Sunday should have been March 24th, but if the cyclical method is used, this full moon is still considered a winter full moon .
- In the year 2045 the astronomical spring full moon will be on Saturday April 1st, the cyclical one day later. Easter is therefore only celebrated on April 9th (H + paradox).
- In 2049 it will be the other way around: cyclical full moon on Saturday 17th April; astronomical full moon and Easter the next day (H- paradox) .:
Consideration of the equinox paradoxes from 1583 to 2200
The following table compares the hypothetical Easter dates determined according to an exact astronomical calculation with the real Easter dates determined according to the cyclical method of the Gregorian calendar. ΔT is the difference between Dynamic Time (TD) and Universal Time (UT).
| year | ΔT
[min] |
Spring
equinox [TD] [UT] |
Full moon
[UT] |
hypothetical,
astronomical Easter date |
Gregorian
Easter date |
difference
Gregorian and astronomical Easter date |
|---|---|---|---|---|---|---|
| 1590 | 2 | March 20 22h 44m
March 20 22h 42m |
21.03. 05h 06m | 25.03. | 04/22 | 4 weeks |
| 1666 | 0 | March 20 08h 44m | March 20 18h01m | 21.03. | 04/25 | 5 weeks |
| 1685 | 0 | 19.03. 23h 15m | March 20 17h 46m | 25.03. | 04/22 | 4 weeks |
| 1924 | 0 | March 20 21h 20m | 21.03. 04h 30m | 23.03. | April 20 | 4 weeks |
| 1943 | 0 | 21.03. 12h 03m | 21.03. 22h 08m | 28.03. | 04/25 | 4 weeks |
| 1962 | 1 | 21.03. 02h 30m
21.03. 02h 29m |
21.03. 07h 55m | 25.03. | 04/22 | 4 weeks |
| 2019 | 1 | March 20 22h 00m
March 20 21h 59m |
21.03. 01h 43m | 24.03. | 04/21 | 4 weeks |
| 2038 | 1 | March 20 12h 42m
March 20 12h 41m |
21.03. 02h 09m | 28.03. | 04/25 | 4 weeks |
| 2057 | 1 | March 20 03h 10m
March 20 03h 09m |
21.03. 00h 45m | 25.03. | 04/22 | 4 weeks |
| 2076 | 2 | 19.03. 17h 42m
19.03. 17h 40m |
March 20 16h 38m | 22.03. | April 19 | 4 weeks |
| 2095 | 3 | March 20 08h 19m
March 20 08h 16m |
21.03. 01h 11m | 27.03. | 04/24 | 4 weeks |
| 2133 | 5 | March 20 13h 20m
March 20 13h 15m |
21.03. 00h 20m | 22.03. | April 19 | 4 weeks |
| 2152 | 6th | March 20 03h 44m
March 20 03h 38m |
March 20 22h 27m | 26.03. | 04/23 | 4 weeks |
| 2171 | 6th | March 20 18h 15m
March 20 18h 09m |
21.03. 22h 59m | 24.03. | 04/21 | 4 weeks |
| 2190 | 7th | March 20 08h 51m
March 20 08h 44m |
21.03. 20h 35m | 28.03. | 04/25 | 4 weeks |
Scope of Paradoxes
While equinox paradoxes in principle occur globally (unlimited), Hebdomadal paradoxes can occur either globally or locally. The following considerations are based on the mean local time and the civil day change at midnight as in Lange. The respective longitude for which midnight is at the time of the full moon under consideration is the paradoxical limit. Positive Hebdomadal paradoxes (H +) that are localized apply from a paradoxical line (longitude) westward to the date line. Localized negative Hebdomadal paradoxes (H-), on the other hand, apply from a paradox line eastward to the date line . No paradox occurs on the other sides of the paradox boundary (east at H +, west at H-). H. the cyclical and astronomical Easter calculations lead to the same result. Global (unrestricted) Hebdomadal paradoxes have no paradox limit and occur worldwide.
The compilation is based on the times of the full moons according to L. Lange (until 2000) and F. Espenak (after 2001). The paradoxical limits were specified and adopted by Lange up to 2000. Since the full moon dates are given to the nearest minute, the paradoxical limits can be given to a quarter of a degree as in Lange. Paradoxical limits from 2001 onwards can easily be calculated from the given full moon dates. Example: Full moon at 00h 00m UT, results in paradoxical limit 0.00 degrees (zero meriadians); every hour after midnight (from Saturday to Sunday) the paradoxical limit shifts by 15.00 ° to the west or every hour before midnight by 15.00 ° to the east.
Gregorian H + paradoxes from 1801 to 2200: paradoxically west of the stated paradox limit
| year | Full moon
[UT] until 2000 From 2001 onwards |
Paradoxical limit | hypothetical,
astronomical Easter date |
Gregorian
Easter date (see above) |
Remarks |
|---|---|---|---|---|---|
| 1876 | Sa 08.04. 19h 38m | 65.50 ° E | 9th April | April 16 | |
| 1974 | Sa 06.04. 20h 58m | 45.50 ° E | 7th of April | April 14th | |
| 2045 | Sa 04/01 18h 43m | 79.25 ° E | 2nd of April | 9th April | |
| 2069 | Sa 06.04. 16h 13m | 116.75 ° E | 7th of April | April 14th | |
| 2089 | Sa 26.03. 09h 21m | 27th of March | 3rd of April | globally unlimited paradox | |
| 2096 | Sa 07.04. 18h 19m | 85.25 ° E | April 8th | April 15th |
Gregorian H- paradoxes from 1801 to 2200: paradox east of the stated paradox limit
| year | Full moon
[UT] until 2000 From 2001 onwards |
Paradoxical limit | hypothetical,
astronomical Easter date |
Gregorian
Easter date (see above) |
Remarks |
|---|---|---|---|---|---|
| 1802 | Sun 18.04. 02h 33m | 38.25 ° W | April 25 | April 18 | |
| 1805 | Sa 13.04. 23h 43m | 4.25 ° E | April 21 | April 14th | |
| 1818 | Sun 22.03. 14h 07m | 211.75 ° W (148.25 ° E) | March 29 | March 22 | almost global paradox; not paradoxical only for small areas, west of the paradoxical line, which were east (on the American side) of the then strongly shifted westward date line, z. B. Philippines, Mariana Islands |
| 1825 | Sun 03.04. 06h 25m | 96.25 ° W | 10th of April | 3rd of April | |
| 1829 | Sun 19.04. 06h 19m | 94.75 ° W | 26th of April | April 19th | |
| 1845 | Sun 23.03. 16h 18m | March 30 | March 23 | globally unlimited paradox | |
| 1900 | Sun April 15th 01h 02m | 15.50 ° W | April 22 | April 15th | |
| 1903 | Sun 04/12 00h 18m | 4.50 ° W | April 19th | 12. April | |
| 1923 | Sun 04/01 13h 08m | April 8th | April 1st | globally unlimited paradox | |
| 1927 | Sun 04/17 03h 34m | 53.50 ° W | April 24th | 17th April | |
| 1954 | Sun 04/18 05h 47m | 86.75 ° W | April 25 | April 18 | |
| 1967 | Sun 26.03. 03h 19m | 49.75 ° W | 2nd of April | 26th of March | |
| 1981 | Sun 19.04. 07h 56m | 119.00 ° W | 26th of April | April 19th | |
| 2049 | Sun 04/18 01h 05m | 16.25 ° W | April 25 | April 18 | |
| 2076 | Fri 20.03. 16h 38m Sun 19.04 . 06h 30m |
97.50 ° W |
March 22nd (A +) April 26th (H-) |
April 19th |
additional global A + paradox, d. H. Double paradox (A + and H- paradox) east of the paradox limit, otherwise only A + paradox |
| 2106 | Sun 04/18 08h 22m | 125.50 ° W | April 25 | April 18 | |
| 2119 | Sun 26.03. 23h 58m | 2nd of April | 26th of March | globally unlimited paradox | |
| 2133 | Sat 21.03. 00h 20m Sun 19.04. 12h 36m |
189.00 ° W (171.00 ° E) |
March 22nd (A +) April 26th (H-) |
April 19th |
additional global A + paradox, d. H. global double paradox (A + and H- paradox). The westernmost bulge of the date line because of the Aleutian Islands only extends to 188 ° W (172 ° E) |
| 2147 | Sun 04/16 03h 13m | 48.25 ° W | April 23 | April 16 | |
| 2150 | Sun 04/12 00h 17m | 4.25 ° W | April 19th | 12. April | |
| 2170 | Sun 04/01 06h 40m | 100.00 ° W | April 8th | April 1st | |
| 2174 | Sun 04/17 07h 04m | 106.00 ° W | April 24th | 17th April |
The two programs listed under web links are suitable for checking. They are to be used together.
Web links
- Nikolaus A. Bär: Astronomical Easter calculator
- Mondkalender-online.de (for the years from 1800 to 2050)
Individual evidence
- ↑ Herbert Metz: The probable Easter paradoxes of the years 1600 - 5599 , [1]
- ↑ a b c d e f g h i j k l m n o p q r s t u Ludwig Lange: "Paradoxical" Easter dates in the Gregorian calendar and their significance for the modern calendar reform . In: Verlag der Bayerische Akademie der Wissenschaften (Ed.): Reports from the meetings of the Bavarian Academy of Sciences; Philosophical-philological and historical class . 9. Treatise. Munich 1928. [2]
- ↑ Ludwig Lange: "Paradoxes" Easter dates in the Gregorian calendar and their significance for the modern calendar reform , page 13: “... if you already consider the true astronomical full moon to be decisive, but it is only logical, also the equinox in the strictly astronomical one To grasp the senses ... "
- ↑ Since 2007, the astronomical beginning of spring is no longer later than March 20; in the second half of the 21st century it is often on March 19th. See Siegfried Wetzel: Alternatives to the Gregorian calendar , Fig. 1, [3]
- ↑ a b Lange considers negative equinox paradoxes (A-) to be possible in principle, but found none in the period he examined. This is not surprising, because the astronomical beginning of spring is never later than March 21, and thus the cyclical date is by no means set too early. The astronomical beginning of spring is even premature in the long term, namely by one day in the calendar in about 3320 years because of the Gregorian calendar year, which is slightly too long. Cf. Siegfried Wetzel: Alternatives to the Gregorian calendar , Fig. 2, [4]
- ↑ Klaus Peter Zeyer: Frequency of Easter paradoxes: Negative equinox paradoxes of the years 2353 and 2372 as the rarest variant. In: Regiomontanusbote . tape 33 , no. 2 . Nuremberg Astronomical Working Group, Nuremberg 2020, p. 5-10 .
- ↑ Ludwig Lange: "Paradoxes" Easter dates in the Gregorian calendar and their significance for the modern calendar reform , page 35
- ↑ a b This is what awaits you in the starry sky in 2019 - there will be an Easter paradox in 2019 , Hans-Ulrich Keller, T-Online, January 2, 2019, accessed January 3, 2019
- ↑ a b c d e f Fred Espenak: Six millennium catalog of phases of the moon. Retrieved August 12, 2017 .
- ^ A b Jean Meeus: Astronomical tables of the sun, moon and planets . Ed .: Willmann-Bell Inc. Willmann Bell Inc., Richmond, VA, USA 1983.