Gregorian calendar

The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull Inter gravissimas issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years slightly differently to make the average calendar year 365.2425 days long rather than the Julian calendar's 365.25 days, thus more closely approximating the 365.2422-day "tropical" or "solar" year that is determined by the Earth's revolution around the Sun.
The rule for leap years is that every year divisible by four is a leap year, except for years that are divisible by 100, except in turn for years also divisible by 400. For example, 1800 and 1900 were not leap years, but 1600 and 2000 were leap years.
There were two reasons to establish the Gregorian calendar. First, the Julian calendar was based on the estimate that the average solar year is exactly 365.25 days long, an overestimate of a little under one day per century, and thus has a leap year every four years without exception. The Gregorian reform shortened the average year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes. Second, in the years since the First Council of Nicaea in AD 325, the excess leap days introduced by the Julian algorithm had caused the calendar to drift such that the March equinox was occurring well before its nominal 21 March date. This date was important to the Christian churches, because it is fundamental to the calculation of the date of Easter. To reinstate the association, the reform advanced the date by 10 days: Thursday 4 October 1582 was followed by Friday 15 October 1582. In addition, the reform also altered the lunar cycle used by the Church to calculate the date for Easter, because astronomical new moons were occurring four days before the calculated dates.
The reform was adopted initially by the Catholic countries of Europe and their overseas possessions. Over the next three centuries, the Protestant and Eastern Orthodox countries also gradually moved to what they called the "Improved calendar", with Greece being the last European country to adopt the calendar in 1923. However, many Orthodox churches continue to use the Julian calendar for religious rites and the dating of major feasts. To unambiguously specify a date during the transition period, both notations were given, tagged as "Old Style" or "New Style" as appropriate. During the 20th century, most non-Western countries also adopted the calendar, at least for civil purposes.

Description

The Gregorian calendar, like the Julian calendar, is a solar calendar with 12 months of 28–31 days each. The year in both calendars consists of 365 days, with a leap day being added to February in the leap years. The months and length of months in the Gregorian calendar are the same as for the Julian calendar. The only difference is that the Gregorian calendar omits a leap day in three centurial years every 400 years and leaves the leap day unchanged in the fourth.
A leap year normally occurs every four years: the leap day, historically, was inserted by doubling 24 Februarythere were indeed two days dated 24 February. However, for many years it has been customary to put the extra day at the end of the month of February, adding a 29 February for the leap day. Before the 1969 revision of its General Roman Calendar, the Catholic Church delayed February feasts after the 23rd by one day in leap years; masses celebrated according to the previous calendar still reflect this delay.

No.	Name	Length in days
1	January	31
2	February	28
3	March	31
4	April	30
5	May	31
6	June	30
7	July	31
8	August	31
9	September	30
10	October	31
11	November	30
12	December	31

Gregorian years are identified by consecutive year numbers. A calendar date is fully specified by the year, the month, and the day of the month. Although the calendar year currently runs from 1 January to 31 December, at previous times year numbers were based on a different starting point within the calendar.
Calendar cycles repeat completely every 400 years, which equals 146,097 days. Of these 400 years, 303 are regular years of 365 days and 97 are leap years of 366 days. A mean calendar year is days = 365.2425 days, or 365 days, 5 hours, 49 minutes and 12 seconds. The cycle contains exactly 20,871 weeks.

Gregorian reform

The Gregorian calendar was a reform of the Julian calendar. It was instituted by the papal bull Inter gravissimas dated 24 February 1582 by Pope Gregory XIII, after whom the calendar is named. The motivation for the adjustment was to bring the date for the celebration of Easter to the time of year in which it was celebrated when it was introduced by the early Church. The error in the Julian calendar had led to the date of the equinox according to the calendar drifting from the observed reality, and thus an error had been introduced into the calculation of the date of Easter. Although a recommendation of the First Council of Nicaea in 325 specified that all Christians should celebrate Easter on the same day, it took almost five centuries before virtually all Christians achieved that objective by adopting the rules of the Church of Alexandria.

Background

Because the date of Easter is a functionthe computusof the date of the spring equinox in the northern hemisphere, the Catholic Church considered the increasing divergence between the canonical date of the equinox and observed reality to be unacceptable. Easter is celebrated on the Sunday after the ecclesiastical full moon on or after 21 March, which was adopted as an approximation to the March equinox. European scholars had been well aware of the calendar drift since the early medieval period.
Bede, writing in the 8th century, showed that the accumulated error in his time was more than three days. Roger Bacon,, estimated the error at seven or eight days. Dante, writing, was aware of the need for calendar reform. An attempt to go forward with such a reform was undertaken by Pope Sixtus IV, who in 1475 invited Regiomontanus to the Vatican for this purpose. However, the project was interrupted by the death of Regiomontanus shortly after his arrival in Rome. The increase of astronomical knowledge and the precision of observations towards the end of the 15th century made the question more pressing. Numerous publications over the following decades called for a calendar reform, among them two papers sent to the Vatican by the University of Salamanca in 1515 and 1578, but the project was not taken up again until the 1540s, and implemented only under Pope Gregory XIII.

Preparation

In 1545, the Council of Trent authorised Pope Paul III to reform the calendar, 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 more consistent and accurate scheduling of the feast of Easter.
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. The reform adopted was a modification of a proposal made by the Calabrian doctor Aloysius Lilius.
Lilius's proposal included reducing the number of leap years in four centuries from 100 to 97, by making three out of four centurial years common instead of leap years. He also produced an original and practical scheme for adjusting the epacts of the Moon when calculating the annual date of Easter, solving a long-standing obstacle to calendar reform.
Ancient tables provided the Sun's mean longitude. The German mathematician Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the Sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies. The Gregorian leap year rule was put forward by Petrus Pitatus of Verona in 1560. He noted that it is consistent with the tropical year of the Alfonsine tables and with the mean tropical year of Copernicus and Erasmus Reinhold. The three mean tropical years in Babylonian sexagesimals as the excess over 365 days were 0;14,33,9,57, 0;14,33,11,12 and 0;14,33,9,24. In decimal notation, these are equal to 0.24254606, 0.24255185, and 0.24254352, respectively. All values are the same to two sexagesimal places and this is also the mean length of the Gregorian year. Thus Pitatus's solution would have commended itself to the astronomers.
Lilius's proposals had two components. First, he proposed a correction to the length of the year. The mean tropical year is 365.24219 days long. A commonly used value in Lilius's time, from the Alfonsine tables, is 365.2425463 days. As the average length of a Julian year is 365.25 days, the Julian year is almost 11 minutes longer than the mean tropical year. The discrepancy results in a drift of about three days every 400 years. Lilius's proposal resulted in an average year of 365.2425 days. At the time of Gregory's reform, there had already been a drift of 10 days since the Council of Nicaea, resulting in the vernal equinox falling on 10 or 11 March instead of the ecclesiastically fixed date of 21 March, and if unreformed it would have drifted further. Lilius proposed that the 10-day drift should be corrected by deleting the Julian leap day on each of its ten occurrences over a period of forty years, thereby providing for a gradual return of the equinox to 21 March.
Lilius's work was expanded upon by Christopher Clavius in a closely argued, 800-page volume. He would later defend his and Lilius's work against detractors. Clavius's opinion was that the correction should take place in one move, and it was this advice that prevailed with Gregory.
The second component consisted of an approximation that would provide an accurate yet simple, rule-based calendar. Lilius's formula was a 10-day correction to revert the drift since the Council of Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. The proposed rule was that "years divisible by 100 would be leap years only if they were divisible by 400 as well".
The 19-year cycle used for the lunar calendar required revision because the astronomical new moon was, at the time of the reform, four days before the calculated new moon. It was to be corrected by one day every 300 or 400 years along with corrections for the years that were no longer leap years In fact, a new method for computing the date of Easter was introduced. The method proposed by Lilius was revised somewhat in the final reform.
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 10 days. The Julian calendar day Thursday, 4 October 1582 was followed by the first day of the Gregorian calendar, Friday, 15 October 1582.