Gregorian calendar

The Gregorian calendar is the internationally accepted civil calendar. Introduction to Calendars. United States Naval Observatory. Accessed 15 January 2009. Calendars by L. E. Doggett. Section 2.The international standard for the representation of dates and times ISO 8601 uses the Gregorian calendar. Section 3.2.1. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter gravissimas.See of the (Latin) 1582 papal bull ' Inter gravissimas' instituting Gregorian calendar reform. The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries. The need for the Gregorian reform stemmed from the fact that the Julian calendar system assumes time between vernal equinoxes is 365.25 days, when in fact it is about 11 minutes less. The accumulated error between these values was about 10 days when the reform was made, resulting in the equinox occurring on March 11 and moving steadily earlier in the calendar. Since the equinox was tied to the celebration of Easter, the reform in the calendar was undertaken by the Roman Catholic Church. The Gregorian calendar reform contained two parts, a reform of the Julian calendar as used up to Pope Gregory's time, together with a reform of the lunar cycle used by the Church along with the Julian calendar for calculating dates of Easter. The reform was a modification of a proposal made by the Calabrian doctor Aloysius Lilius (or Lilio).G Moyer (1983), "Aloisius Lilius and the 'Compendium novae rationis restituendi kalendarium'", pages 171-188 in G.V. Coyne (ed.), The Gregorian Reform of the Calendar: Proceedings of the Vatican conference to commemorate its 400th anniversary, Vatican City (Specola Vaticana) 1983. Lilius' proposal included reducing the number of leap years in four centuries from 100 to 97, by making 3 out of 4 centurial years common instead of leap years: this part of the proposal had been suggested before by, among others, Pietro Pitati. Lilio also produced an original and practical scheme for adjusting the epacts of the moon for completing the calculation of Easter dates, solving a long-standing difficulty that had faced proposers of calendar reform. The Gregorian calendar continues the previous year-numbering system based on the Anno Domini system, which counts years from the traditional Incarnation of Jesus, and which had spread throughout Europe during the Middle Ages. This year-numbering system is the predominant international standard today.This era was created in the year 525 by the Roman monk Dionysius Exiguus. See Nineteen-Year Cycle of Dionysius. Introduction and first argumentum. The Gregorian calendar modifies the Julian calendar's regular cycle of leap years, years exactly divisible by four,Stating the rule this way is an anachronism, since the Anno Domini year numbering was not invented until about 570 years after Julius Caesar established his calendar including all centurial years, as follows: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year. Introduction to Calendars. (13 September 2007). United States Naval Observatory. In addition to the modification of mean length of the calendar year from 365.25 days to 365.2425 days, the Gregorian calendar was required to deal with the fact that the error due to the difference between these lengths (10.8 minutes) had been accumulating steadily. Due mostly to this discrepancy,The Gregorian calendar came within 11 seconds of correctly modelling the vernal equinox year of AD 2000, and 30 seconds of modelling the vernal equinox year of AD 1, so it was not perfect. Nevertheless, most of the calendrical shift of the equinox can be attributed to the difference in the two calendars, since the Gregorian calendar corrected almost all of the problem. between AD 325 (when the Roman Catholic Church thought the First Council of Nicaea had fixed the vernal equinox on 21 March), and the time of Gregory's edict in 1582, the vernal equinox had moved backward in the calendar, until it was occurring on about 11 March, 10 days early. The Gregorian calendar therefore began by dropping 10 calendar days, to synchronise the calendar and seasons again. Because of the Protestant Reformation, however, many Western European countries did not initially follow the Gregorian reform, and maintained their old style systems. Eventually, necessity won out, but by the time the last adherents of the Julian calendar in Eastern Europe (Russia and Greece) changed to the Gregorian system in the 20th century, they were required to drop 13 days from their calendars, due to the additional accumulated error from the Julian system by then.

Description

The Gregorian solar calendar is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days; and repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day weeks.The repetition described applies to the solar, or civil, calendar. If the ecclesiastical (lunar) rules are also considered, the system repeats after 5,700,000 years of 2,081,882,250 days. (Seidelmann 1992, p. 582) Of these 400 years, 303 (the "common years") have 365 days, and 97 (the leap years) have 366 days. This gives an average calendar-year length of exactly 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds. A Gregorian year is divided into twelve months of irregular length, with no regular relationship among their lengths: A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1). Leap years add a 29th day to February, which normally has 28 days. The essential ongoing differentiating feature of the Gregorian calendar, as distinct from the Julian calendar with a leap day every four years, is that the Gregorian omits 3 leap days every 400 years. This difference would have been more noticeable in modern memory were it not that the year 2000 was a leap year in both the Julian and Gregorian calendar systems. The intercalary day in a leap year is known as a leap day. Since Roman times 24 February ( bissextile) was counted as the leap day,"Lastly, in consideration of the quarter of a day, which he regarded as completing the true year, he established the rule that, at the end of every four years, a single day should be intercalated where the month had been hitherto inserted, that is, immediately after the terminalia; which day is now called the bissextum". Censorinus:The Natal Day."Julius Caesar added ten days to the former number in order to complete the 365 days which the sun takes to pass through the zodiac; and to take account of the quarter of a day, he directed the pontiffs, who were entrusted with the months and days, to intercalate one day every four years in the same month and in the same place the ancients had intercalated, that is, before the last five days of February, hence this day was called bissextile." Macrobius: Saturnalia. but now 29 February is regarded as the leap day in most countries. Although the calendar year runs from 1 January to 31 December, sometimes year numbers were based on a different starting point within the calendar. Confusingly, the term "Anno Domini" is not specific on this point, and actually refers to a family of year numbering systems with different starting points for the years. (See the section below for more on this issue.)

Lunar calendar

The Catholic Church maintained a tabular lunar calendar, which was primarily to calculate the date of Easter, and the lunar calendar required reform as well. A perpetual lunar calendar was created, in the sense that 30 different arrangements (lines in the expanded table of epacts) for lunar months were created. One of the 30 arrangements applies to a century (for this purpose, the century begins with a year divisible by 100). When the arrangement to be used for a given century is communicated, anyone in possession of the tables can find the age of the moon on any date, and calculate the date of Easter.Coyne et al. (Eds), (1993), pp. 201–224.

History

Gregorian reform

The motivation of the Catholic Church in adjusting the calendar was to celebrate Easter at the time it thought the First Council of Nicaea had agreed upon in 325. Although a canon of the council implies that all churches used the same Easter, they did not. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the moon (computed using the Metonic cycle) that falls on or after the vernal equinox, which they placed on 21 March. However, the Church of Rome still regarded 25 March as the equinox (until 342) and used a different cycle to compute the day of the moon.O. Pedersen. (1983). "The ecclesiastical calendar and the life of the church." in G. V. Coyne et al., ed. 42–43. In the Alexandrian system, since the 14th day of the Easter moon could fall at earliest on 21 March its first day could fall no earlier than 8 March and no later than 5 April. This meant that Easter varied between 22 March and 25 April. In Rome, Easter was not allowed to fall later than 21 April, that being the day of the Parilia or birthday of Rome and a pagan festival. The first day of the Easter moon could fall no earlier than 5 March and no later than 2 April. Easter was the Sunday after the 15th day of this moon, whose 14th day was allowed to precede the equinox. Where the two systems produced different dates there was generally a compromise so that both churches were able to celebrate on the same day. By the tenth century all churches (except some on the eastern border of the Byzantine Empire) had adopted the Alexandrian Easter, which still placed the vernal equinox on 21 March, although Bede had already noted its drift in 725—it had drifted even further by the sixteenth century. Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19 year cycle. However, that approximation built up an error of one day every 310 years, so by the sixteenth century the lunar calendar was out of phase with the real Moon by four days. The Council of Trent approved a plan in 1563 for correcting the calendrical errors, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter. The fix was to come in two stages. First, it was necessary to approximate the correct length of a solar year. The value chosen was 365.2425 days in decimal notation.This is 365;14,33 days in sexagesimal notation—the length of the tropical year, rounded to two sexagesimal positions; this was the value used in the major astronomical tables of the day. Although close to the mean tropical year of 365.24219 days, it is even closer to the vernal equinox year of 365.2424 days; this fact made the choice of approximation particularly appropriate as the purpose of creating the calendar was to ensure that the vernal equinox would be near a specific date (21 March). (See Accuracy). The second stage was to devise a model based on the approximation which would provide an accurate yet simple, rule-based calendar. The formula designed by Aloysius Lilius was ultimately successful. It proposed a 10-day correction to revert the drift since Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. To implement the model, it was provided that years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300, 2500, 2600, 2700, 2900, and 3000, will not be leap years, but 2400, and 2800 will be. This theory was expanded upon by Christopher Clavius in a closely argued, 800 page volume. He would later defend his and Lilius's work against detractors. The 19-year cycle used for the lunar calendar was also to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years (1700, 1800, 1900, 2100 et cetera) that are no longer leap years. In fact, a new method for computing the date of Easter was introduced. In 1577 a Compendium was sent to expert mathematicians outside the reform commission for comments. Some of these experts, including Giambattista Benedetti and Giuseppe Moleto, believed Easter should be computed from the true motions of the sun and moon, rather than using a tabular method, but these recommendations were not adopted.Coyne et al. (Eds), 1983, p. 211, 214. Gregory dropped 10 days to bring the calendar back into synchronisation with the seasons. Lilius originally proposed that the 10-day correction should be implemented by deleting the Julian leap day on each of its ten occurrences during a period of 40 years, thereby providing for a gradual return of the equinox to 21 March. However, Clavius's opinion was that the correction should take place in one move and it was this advice which prevailed with Gregory. Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. The last day of the Julian calendar was Thursday, 4 October 1582 and this was followed by the first day of the Gregorian calendar, Friday, 15 October 1582 (the cycle of weekdays was not affected).

Adoption

Though Gregory's reform was enacted in the most solemn of forms available to the Church, in fact the bull had no authority beyond the Catholic Church and the Papal States. The changes which he was proposing were changes to the civil calendar over which he had no authority. The changes required adoption by the civil authorities in each country to have legal effect. The Nicene Council of 325 sought to devise rules whereby all Christians would celebrate Easter on the same day. In fact it took a very long time before Christians achieved that objective (see Easter for the issues which arose). However, the bull Inter gravissimas became the law of the Catholic Church. It was not recognised, however, by Protestant Churches nor by Orthodox Churches and others. Consequently, the days on which Easter and related holidays were celebrated by different Christian Churches again diverged.

Adoption in Europe

Only four Catholic countries adopted the new calendar on the date specified by the bull. Other Catholic countries experienced some delay before adopting the reform; and non-Catholic countries, not being subject to the decrees of the Pope, initially rejected or simply ignored the reform altogether, although they all eventually adopted it. Hence, the dates 5 October 1582 to 14 October 1582 (inclusive) are valid dates in many countries. Spain, Portugal, the Polish-Lithuanian Commonwealth, and most of Italy implemented the new calendar on Friday, 15 October 1582, following Julian Thursday, 4 October 1582. The Spanish and Portuguese colonies adopted the calendar later because of the slowness of communication. France adopted the new calendar on Monday, 20 December 1582, following Sunday, 9 December 1582. Toke Nørby. The Perpetual Calendar: What about France? The Dutch provinces of Brabant, Zeeland and the Staten-Generaal also adopted it on 25 December of that year, the provinces forming the Southern Netherlands (modern Belgium) on 1 January 1583, and the province of Holland followed suit on 12 January 1583. Many Protestant countries initially objected to adopting a Catholic invention; some Protestants feared the new calendar was part of a plot to return them to the Catholic fold.Gordon Moyer. (May 1982). "The Gregorian Calendar". Scientific American, May 1982, p. 144. In the , Protestants resisted the calendar imposed by the Habsburg Monarchy. In parts of Ireland, Catholic rebels until their defeat in the Nine Years' War kept the "new" Easter in defiance of the English-loyal authorities; later, Catholics practising in secret petitioned the Propaganda Fide for dispensation from observing the new calendar, as it signalled their disloyalty.