As a moveable feast,[1][2] the date of Easter is determined in each year through a calculation known as computus (Latin for 'computation').[3] Easter is celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March (a fixed approximation of the March equinox). Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar.[4] The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified.[5]
The Old Farmer's Almanac 2018 Moon Calendar 228
DOWNLOAD: https://urlcod.com/2vFYO6
Easter commemorates the resurrection of Jesus, which is believed to have occurred on the third day (inclusive) after Passover. In the Hebrew calendar, Passover occurs on the 14th day of Nisan. Nisan is the first month of spring in the northern hemisphere, with the 14th corresponding to a full moon. Additionally, by the 2nd century, many Christians had chosen to observe Easter only on a Sunday.[9] The Hebrew calendar is a lunisolar one and does not have a simple relationship with the Christian calendars: it resynchronizes with the solar year by intercalating a leap month every two or three years, before the lunar new year on 1 Nisan. Later the Jews adopted the Metonic cycle to predict future intercalations.
A possible consequence of this intercalation is that 14 Nisan may occur before the equinox, which some third-century Christians considered unacceptable, although this cannot happen in the fixed calendar currently in use.[10] Consequently, they decided to separate the dating of Easter from the Hebrew calendar. To do so, it was necessary to identify the first full moon following the March equinox. By the time of the First Council of Nicaea, the Church of Alexandria had designated 21 March as an ecclesiastical date for the equinox, irrespective of actual astronomical observation. In 395, Theophilus published a table of future dates for Easter, validating the Alexandrian criteria.[11] Thereafter, the computus would be the procedure of determining the first Sunday after the first ecclesiastical full moon falling on or after 21 March.
The paschal or Easter-month is the first one in the year to have its fourteenth day (its formal full moon) on or after 21 March. Easter is the Sunday after its 14th day (or, saying the same thing, the Sunday within its third week). The paschal lunar month always begins on a date in the 29-day period from 8 March to 5 April inclusive. Its fourteenth day, therefore, always falls on a date between 21 March and 18 April inclusive, and the following Sunday then necessarily falls on a date in the range 22 March to 25 April inclusive. This is true of both the Western system (in the Gregorian calendar) and of the Eastern system (in the Julian calendar). In the solar calendar Easter is called a moveable feast since its date varies within a 35-day range. But in the lunar calendar, Easter is always the third Sunday in the paschal lunar month, and is no more "moveable" than any holiday that is fixed to a particular day of the week and week within a month, such as Thanksgiving.
The epacts are used to find the dates of the new moon in the following way: Write down a table of all 365 days of the year (the leap day is ignored). Then label all dates with a Roman numeral counting downwards, from "*" (0 or 30), "xxix" (29), down to "i" (1), starting from 1 January, and repeat this to the end of the year. However, in every second such period count only 29 days and label the date with xxv (25) also with xxiv (24). Treat the 13th period (last eleven days) as long, therefore, and assign the labels "xxv" and "xxiv" to sequential dates (26 and 27 December respectively). Finally, in addition, add the label "25" to the dates that have "xxv" in the 30-day periods; but in 29-day periods (which have "xxiv" together with "xxv") add the label "25" to the date with "xxvi". The distribution of the lengths of the months and the length of the epact cycles is such that each civil calendar month starts and ends with the same epact label, except for February and, one might say, for August, which starts with the double label "xxv"/"xxiv" but ends with the single label "xxiv". This table is called the calendarium. The ecclesiastical new moons for any year are those dates when the epact for the year is entered. If the epact for the year is for instance 27, then there is an ecclesiastical new moon on every date in that year that has the epact label "xxvii" (27). If the epact is 25, then there is a complication, introduced so that the ecclesiastical new moon will not fall on the same date twice during a Metonic cycle. If the epact cycle in force includes epact 24 (as does the cycle in use since 1900 and until 2199), then an epact of 25 puts the ecclesiastical new moon on April 4 (having the label "25"), otherwise it is on April 5 (having label "xxv").[42] In fact, an epact of 25 giving April 4 can only happen if the golden number is greater than 11 (in which case it will be 11 years after a year with epact 24). So for example, in 1954 the golden number was 17, the epact was 25, the ecclesiastical new moon was reckoned on April 4, the full moon on April 17, and Easter was on April 18 rather than April 25 as it would otherwise have been, such as in 1886 when the golden number was 6.
The label "25" (as distinct from "xxv") is used as follows: Within a Metonic cycle, years that are 11 years apart have epacts that differ by one day. A month beginning on a date having labels xxiv and xxv written side by side has either 29 or 30 days. If the epacts 24 and 25 both occur within one Metonic cycle, then the new (and full) moons would fall on the same dates for these two years. This is possible for the real moon[i] but is inelegant in a schematic lunar calendar; the dates should repeat only after 19 years. To avoid this, in years that have epacts 25 and with a Golden Number larger than 11, the reckoned new moon falls on the date with the label 25 rather than xxv. Where the labels 25 and xxv are together, there is no problem since they are the same. This does not move the problem to the pair "25" and "xxvi", because the earliest epact 26 could appear would be in year 23 of the cycle, which lasts only 19 years: there is a saltus lunae in between that makes the new moons fall on separate dates.
However, 19 uncorrected Julian years are a little longer than 235 lunations. The difference accumulates to one day in about 310 years. Therefore, in the Gregorian calendar, the epact gets corrected by adding 1 eight times in 2,500 (Gregorian) years, always in a century year: this is the so-called lunar correction (historically called "lunar equation"). The first one was applied in 1800, the next is in 2100, and will be applied every 300 years except for an interval of 400 years between 3900 and 4300, which starts a new cycle. At the time of the reform, the epacts were changed by 7, even though 10 days were skipped, in order to make a three-day correction to the timing of the new moons.[42]
Every other lunar month has only 29 days, so one day must have two (of the 30) epact labels assigned to it. The reason for moving around the epact label "xxv/25" rather than any other seems to be the following: According to Dionysius (in his introductory letter to Petronius), the Nicene council, on the authority of Eusebius, established that the first month of the ecclesiastical lunar year (the paschal month) should start between 8 March and 5 April inclusive, and the 14th day fall between 21 March and 18 April inclusive, thus spanning a period of (only) 29 days. A new moon on 7 March, which has epact label "xxiv", has its 14th day (full moon) on 20 March, which is too early (not following 20 March). So years with an epact of "xxiv", if the lunar month beginning on 7 March had 30 days, would have their paschal new moon on 6 April, which is too late: The full moon would fall on 19 April, and Easter could be as late as 26 April. In the Julian calendar the latest date of Easter was 25 April, and the Gregorian reform maintained that limit. So the paschal full moon must fall no later than 18 April and the new moon on 5 April, which has epact label "xxv". 5 April must therefore have its double epact labels "xxiv" and "xxv". Then epact "xxv" must be treated differently, as explained in the paragraph above.
The relation between lunar and solar calendar dates is made independent of the leap day scheme for the solar year. Basically the Gregorian calendar still uses the Julian calendar with a leap day every four years, so a Metonic cycle of 19 years has 6,940 or 6,939 days with five or four leap days. Now the lunar cycle counts only 19 354 + 19 11 = 6,935 days. By not labeling and counting the leap day with an epact number, but having the next new moon fall on the same calendar date as without the leap day, the current lunation gets extended by a day,[j] and the 235 lunations cover as many days as the 19 years (so long as the 19 years do not include a "solar correction" as in 1900). So the burden of synchronizing the calendar with the moon (intermediate-term accuracy) is shifted to the solar calendar, which may use any suitable intercalation scheme, all under the assumption that 19 solar years = 235 lunations (creating a long-term inaccuracy if not corrected by a "lunar correction"). A consequence is that the reckoned age of the moon may be off by a day, and also that the lunations that contain the leap day may be 31 days long, which would never happen if the real moon were followed (short-term inaccuracies). This is the price of a regular fit to the solar calendar.
The "solar corrections" approximately undo the effect of the Gregorian modifications to the leap days of the solar calendar on the lunar calendar: they (partially) bring the epact cycle back to the original Metonic relation between the Julian year and lunar month. The inherent mismatch between sun and moon in this basic 19-year cycle is then corrected every three or four centuries by the "lunar correction" to the epacts. However, the epact corrections occur at the beginning of Gregorian centuries, not Julian centuries, and therefore the original Julian Metonic cycle is not fully restored. 2ff7e9595c
Commentaires