The Gregorian Calendar, a modification of the Julian calendar, was first proposed by Neapolitan doctor Aloysius Lilius, and adopted by Pope Gregory XIII on February 24, 1582 (the document was dated 1581 on account of the pope starting the year in March).
The mean year in the Julian Calendar had exactly 365.25 days, but the mean tropical year duration is approximately 365.2422. As a result, every thousand years the calendar adds about 8 extraneous days, causing it to fall behind the solar year.

Accuracy

The Gregorian Calendar improves the approximation by skipping 3 Julian leap days in every 400 years, giving an average year of 365.2425 mean solar dayss long, which has an error of about 1 day per 3000 years with respect to the mean tropical year but less than half this error with respect to the vernal equinox tropical year of 365.2424 days. On any timescale over 3000 years it is expected that changes in the Earth's orbit and unpredictable rotation make it improbable that long term accuracy can be gained by rule changes requiring any further regular skipping of Julian leap days.

History

Invention

The motivation of the Catholic Church in adjusting the calendar was to have Easter celebrated at the time that had been agreed at the First Council of Nicaea in 325, i.e., at the Sunday after the 14th day of the Moon that falls on or after the vernal equinox - which fell approximately on March 21 at that time. By the time of this council, the drift of the equinox since the introduction of the Julian calendar had already been noticed. Instead of modifying the calendar, the equinox was standardised at March 21 instead of the original March 24 or March 25. However by the 16th century, the equinox had drifted noticeably further.

Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19-year cycle. However, that is an approximation that built up an error of 1 day every 310 years. So by the 16th century the lunar calendar was way out of sync with the real Moon too.

The fix for the equinox was to define that years divisible by 100 will be leap years only if they are divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. That gives a correction of 3 days. (Additionally, 10 dates were deleted at the time of introduction; see below.) This 3rd millennium will have 8 days corrected.

The Gregorian calendar also fixed the first day of the year as January 1, which was already the first day used in Italy, Germany, and other places, but not universally (England, for example, began the year on March 25). On January 1, 1622 January 1 was declared as the first day of the year.

When the new calendar was put in use, to correct the error already accumulated in the thirteen centuries since the council of Nicaea, a deletion of ten dates was made passing from October 4, 1582 directly to October 15, 1582. This created some consternation, and the church was accused of stealing days of people's lives.

The 19-year cycle used for the lunar calendar was also to be corrected by 1 day every 300 or 400 years (8 times in 2500 years). In fact, a new method for computing the date of Easter was introduced.

Adoption outside of Roman Catholic Nations

Not all countries accepted the new calendar immediately. Non-Catholic countries objected to adopting a Catholic invention. England, Scotland and thereby the rest of the British Empire (including part of what is now the United States) didn't adopt it until 1752, by which time it was necessary to correct by eleven dates (September 2, 1752 being followed by September 14, 1752). Again, people objected to the change--not because they literally thought days were being stolen from their lives, but because they were paid only for days actually worked, but were required to pay a full month's rent for the shortened September, causing hardship.

Denmark-Norway and the Protestantic parts of Germany adopted in 1700, due to the influence of Ole Rømer.

Sweden made an attempt to gradually introduce the Gregorian Calendar in 1700, by adopting a special Swedish calendar. However the change over didn't take place until 1753, where February 17 was followed by March 1.

Russia did not accept the new calendar until 1918, with January 31 followed by February 14. In consequence the anniversary of the October revolution now falls in November. Greece followed suit in 1924. The majority of Eastern Orthodoxy did not accept the change to the new calendar for liturgical purposes, regardless of the new civil date. This includes the Orthodox Church of Russia, which maintains the Julian calendar for religious purposes while accepting the use of the Gregorian for purely secular purposes. Some Orthodox Christians may go so far as to identify themselves as Old Calendarist and assert that under the Julian Calendar the eternal liturgy in Heaven was reflected on earth by the liturgical calendar and that the change meant that Heaven and Earth would be out of tune. However, most recognize that an ecclesiastic calendar need not be identical to the civil calendar.

Technically the Orthodox church does not use the Gregorian Calendar, but a Revised Julian calendar, but these will only start to differ in 2800.

Proleptic Gregorian Calendar

The Gregorian calendar can be extended to dates preceding its official introduction, producing the Proleptic Gregorian Calendar.

The Gregorian calendar's year is divided into 12 months:
No.NameLength (days)
1January31
2February28 or 29
3March31
4April30
5May31
6June30
7July31
8August31
9September30
10October31
11November30
12December31

An average year is 365.2425 days = 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds.

A common year is 365 days = 8,760 hours = 525,600 minutes = 31,536,000 seconds.

A leap year is 366 days = 8,784 hours = 527,040 minutes = 31,622,400 seconds.

(But some years may contain leap seconds.)

See also common year starting on Sunday and dominical letter.

The 400-year cycle of the Gregorian calendar has 146097 days and hence exactly 20871 weeks. So for example the days of week in Gregorian 1603 were exactly the same as for 2003. Also this causes more months to begin on a Sunday (and hence have Friday 13) than any other day of the week.

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