The Date of Easter. Historical Information & Calculations. Easter Origins. The celebration of the Spring Equinox in pre-Christian times and even today has been know by many names – Ostra, Otara, Eostre , Easter
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The Date of Easter Historical Information & Calculations
Easter Origins • The celebration of the Spring Equinox in pre-Christian times and even today has been know by many names – Ostra, Otara, Eostre , Easter • Long before organized religion ,man celebrated the victory of spring over winter, life over death, with rituals to the Gods and Goddesses • From celebrating the revival of nature and the return of the sun’s warmth, Easter became the Christianized rebirth of mankind thru Christ’s death and resurrection • To convert the pagan celebrants to Christianity, early missionaries chose to spread their message of faith throughout the populations by taking many of the traditions of the Christian observance of the Resurrection which occurred at roughly the same time of year ,and folding it into the pagan feast of Ostara/Eostre
Background • Easter is an annual festival observed throughout the Christian world. The date for Easter shifts every year within the Gregorian Calendar. The Gregorian Calendar is the standard international calendar for civil use. In addition, it regulates the ceremonial cycle of the Roman Catholic and Protestant churches. The current Gregorian ecclesiastical rules that determine the date of Easter trace back to 325 CE at the First Council of Nicaea convened by the Roman Emperor Constantine. At that time the Roman world used the Julian Calendar (put in place by Julius Caesar).
The First Council of Nicaea • The Council decided to keep Easter on a Sunday, the same Sunday throughout the world. To fix incontrovertibly the date for Easter, and to make it determinable indefinitely in advance, the Council constructed special tables to compute the date. These tables were revised in the following few centuries resulting eventually in the tables constructed by the 6th century Abbot of Scythia, Dionysis Exiguus. Nonetheless, different means of calculations continued in use throughout the Christian world.
More HISTORY The aim of the Easter Dating Method is to maintain, for each Easter Sunday, the same season of the year and the same relationship to the preceding astronomical full moon that occurred at the time of Christ‘s resurrection in 30 A.D. • This was achieved in 1583 A.D. using skill and common-sense by Pope Gregory the 13th, and his astronomers and mathematicians, predominantly Lilius and Clavius by introducing their new larger (revised) PFM (Paschal Full Moon) Gregorian dates table. This replaced the (original) 326 A.D. "19 PFM dates" table in the Julian calendar. • Easter Sunday, from 326 A.D., is always one of the 35 dates March 22 to April 25. • From 31 A.D. to 325 A.D. Easter Day was celebrated either:(a) on or just after the first day of the Jewish Passover (no matter on which day of the week that Easter Day occurred), or(b) on a Sunday close to or on the first Passover Day.Both of these methods existed continuously throughout this period.
Julian Calendar • From 326 A.D. to 1582 A.D. Easter Sunday date was based on the Julian calendar in use at that time. It became defined as the Sunday following the Paschal Full Moon date for the year, using a simple "19 PFM dates" table. (Precise information on this subject can be found on pages 415 to 425 of the Explanatory Supplement to the 1961 Astronomical Ephemeris). • The Julian calendar was replaced by the Gregorian calendar in October 1582 to re-align March 20 (and therefore Easter) with the seasons by removing 10 dates October 5 to 14, 1582. This replacement did not occur until later in many countries e.g. in September 1752 in England.
The Julian Calendar • In 1582 Gregory XIII (Pope of the Roman Catholic Church) completed a reconstruction of the Julian calendar and produced new Easter tables. One major difference between the Julian and Gregorian Calendar is the "leap year rule".. Universal adoption of this Gregorian calendar occurred slowly. By the 1700's though, most of western Europe had adopted the Gregorian Calendar. The Eastern Christian churches still determine the Easter dates using the older Julian Calendar method. • The usual statement, that Easter Day is the first Sunday after the full moon that occurs next after the vernal equinox, is not a precise statement of the actual ecclesiastical rules. The full moon involved is not the astronomical Full Moon but an ecclesiastical moon (determined from tables) that keeps, more or less, in step with the astronomical Moon.
The Ecclesiastical Rules • Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after the day of the vernal equinox; • this particular ecclesiastical full moon is the 14th day of a tabular lunation (new moon); and • the vernal equinox is fixed as March 21 • resulting in that Easter can never occur before March 22 or later than April 25. The Gregorian dates for the ecclesiastical full moon come from the Gregorian tables. Therefore, the civil date of Easter depends upon which tables - Gregorian or pre-Gregorian - are used. The western (Roman Catholic and Protestant) Christian churches use the Gregorian tables; many eastern (Orthodox) Christian churches use the older tables based on the Julian Calendar.
A Modified Gregorian Calendar • In a congress held in 1923, the eastern churches adopted a modified Gregorian Calendar and decided to set the date of Easter according to the astronomical Full Moon for the meridian of Jerusalem. However, a variety of practices remain among the eastern churches. • Inevitably then, the date of Easter occasionally differs from a date that depends on the astronomical Full Moon and vernal equinox. In some cases this difference may occur in some parts of the world and not in others because two dates separated by the International Date Line are always simultaneously in progress on the Earth. • For example, take the year 1962. In 1962, the astronomical Full Moon occurred on March 21, UT=7h 55m - about six hours after astronomical equinox. The ecclesiastical full moon (taken from the tables), however, occurred on March 20, before the fixed ecclesiastical equinox at March 21. In the astronomical case, the Full Moon followed its equinox; in the ecclesiastical case, it preceded its equinox. Following the rules, Easter, therefore, was not until the Sunday that followed the next ecclesiastical full moon (Wednesday, April 18) making Easter Sunday, April 22.
Gregorian Calendar cont • The Gregorian calendar very closely maintains the alignment of seasons and calendar dates by having leap years in only 1 of every 4 century years, namely, those divisible exactly by 400. One additional February 29 date will need to be removed in about 4140 A.D., therefore Easter calculations will need to use the changed Days of Week of PFM dates when the exact year for this removal is decided. • From 326 A.D., the Easter Sunday Date for any given year is NOT determined by the March Equinox date for that year. March 20 (not March 21) is the most common Gregorian Equinox date from 1583 to 4099 A.D. • Historically, references to March 21 have caused mistakes in calculating Easter Sunday dates. March 20 has become the important date in recent Easter dating methods. Despite frequent references to March 21, this date has no special significance to any recent Easter dating methods. • The present method describing the Easter Dating Procedure can be found in Christian Prayer Books.
Computing the Date of Easter • There are just as many ways to calculate Easter as there are calendars • But in all cases Easter is calculated relating to the moon cycles • In North America we follow the ecclesiastical method • The rule is that Easter is the first Sunday after the first ecclesiastical full moon that occurs on or after March 21. The lunar cycles used by the ecclesiastical system are simple to program.
The Lunar Calendar • The calculation of the moon’s phases was based on the so called Metonic cycle • This cycle is named after the Greek astronomer and mathematician Meton who lived in Athens in the 5th Century BCE • Babylonian astronomers had discovered earlier that 235(syndodic) lunar months have about the same length as 19 (tropical) years, therefore it was concluded that the new moon must fall on the same dates every 19 years • To designate the years with this 19 year cycle, the so called Golden Number was calculated. • That is the remainder of the division of the number of the year by 19, then increased by 1
The Golden Number Method • In the Lunar calendar the mean length of a month was 29.53085 days • The true length of a lunar month - the time between two consecutive new moons is 29.53059 • The difference between the cyclic calendar and the true phases of the moon amounted to a whole day in about 310 years • Using the lunar calendar the new moons were determined relating to a 19 year Metonic cycle • Behind the names of the months, the days on which new moons occur to each of the 19 years are given • The new moons of the seven leap months are given in bold letters • December 24 of year 19 was the cyclic new moon with which each 19 year cycle began
Applying Algorithms • The following algorithm will compute the date of Easter in the Gregorian Calendar system. Note it uses the 19 year cycle • This is an integer calculation. All variables are integers and all remainders from division are dropped. • The algorithm uses the year, y, to give the month, m, and day, d, of Easter. The symbol * means multiply. • c = y / 100 • n = y - 19 * ( y / 19 ) • k = ( c - 17 ) / 25 • i = c - c / 4 - ( c - k ) / 3 + 19 * n + 15 • i = i - 30 * ( i / 30 ) • i = i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) ) * ( ( 21 - n ) / 11 ) ) • j = y + y / 4 + i + 2 - c + c / 4 • j = j - 7 * ( j / 7 ) • l = i - j m = 3 + ( l + 40 ) / 44 d = l + 28 - 31 * ( m / 4 )
Applying the Calculations • For example, using the year 2010, y=2010, c=2010/100=20,n=2010 - 19 x (2010/19) = 15,etc. resulting in Easter on April 4, 2010.
Sources • Sources for the presentation: • The algorithm - J.M. Oudin (1940) and is reprinted in the Explanatory Supplement to the Astronomical Almanac, ed. P. K. Seidelmann (1992) • Astronomical Society of South Australia www.assa.org.au