The Gregorian calendar is the calendar currently used in the Western world. It is 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 was a little too long so causing the Vernal equinox to drift earlier in the calendar year. This was why the Gregorian calendar was invented.
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 days 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.
Years are counted from the initial epoch defined by Dionysius Exiguus, and are divided into two classes: common years and leap years. A common year is 365 days in length; a leap year is 366 days, with an intercalary day, designated February 29, preceding March 1. Leap years are determined according to the following rule:
these centurial years are leap years only if they are exactly divisible by 400.
As a result the year 2000 is a leap year, whereas 1900 and 2100 are not leap years. These rules can be applied to times prior to the Gregorian reform to create a proleptic Gregorian calendar. In this case, year 0 (1 B.C.) is considered to be exactly divisible by 4, 100, and 400; hence it is a leap year.
The Gregorian calendar is thus based on a cycle of 400 years, which comprises 146097 days. Since 146097 is evenly divisible by 7, the Gregorian civil calendar exactly repeats after 400 years. Dividing 146097 by 400 yields an average length of 365.2425 days per calendar year, which is a close approximation to the length of the tropical year. Comparison with Equation 1.1-1 reveals that the Gregorian calendar accumulates an error of one day in about 2500 years. Although various adjustments to the leap-year system have been proposed, none has been instituted.
Within each year, dates are specified according to the count of days from the beginning of the month. The order of months and number of days per month were adopted from the Julian calendar.
| 1. January | 31 | 7. July | 31 |
| 2. February | 28* | 8. August | 31 |
| 3. March | 31 | 9. September | 30 |
| 4. April | 30 | 10. October | 31 |
| 5. May | 31 | 11. November | 30 |
| 6. June | 30 | 12. December | 31 |
* In a leap year, February has 29 days.
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) along with corrections for the years (1700, 1800, 1900, 2100 etc.) that are no longer leap years. In fact, a new method for computing the date of Easter was introduced.
sources:
http://astro.nmsu.edu/~lhuber/leaphist.html,
http://www.knowledgerush.com/kr/encyclopedia/Gregorian_Calendar/
