Gregorian calendar

 

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Proleptic Gregorian calendar

The Gregorian calendar can, for certain purposes, be extended backwards to dates preceding its official introduction, producing the proleptic Gregorian Calendar. However, this proleptic calendar should be used with great caution.

 

For ordinary purposes, the dates of events occurring prior to 15 October 1582 are generally shown as they appeared in the Julian calendar, and not converted into their Gregorian equivalents.

However, events occurring in countries where the Gregorian calendar was introduced later than 4 October 1582 are a little more contentious. For example, in Britain and its overseas possessions (then including the American colonies), the new calendar was not introduced until 14 September 1752. How, then, would people date events occurring in Britain and her possessions in the 170 years between 1582 and 1752? The answer depends very much on the context, but writers who want to avoid confusion make it absolutely clear which calendar is being used. People have avoided changing historical records in Britain deriving from this period; however, it is often highly desirable to translate particular Old Style dates into their New Style equivalents, such as where the context includes reference to other countries that had already converted to New Style before Britain did. Astronomers avoid this ambiguity by the use of the Julian day number.

If comparisons of dates are done using different calendars, we can encounter logical absurdities such as William and Mary of Orange seeming to arrive in London to accept the English crown, a week or so before they left the Netherlands; and Shakespeare and Cervantes apparently dying on exactly the same date (23 April 1616), when in fact Cervantes predeceased Shakespeare by 10 days in real time. This coincidence however has allowed UNESCO to make 23 April the International Day of the Book.

For dates before the year 1, unlike the proleptic Gregorian calendar used in the international standard ISO 8601, the traditional proleptic Gregorian calendar (like the Julian calendar) does not have a year 0 and instead uses the counting numbers 1, 2, … both for years AD and BC and for CE and BCE. Thus the traditional timeline is 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses astronomical year numbering which includes a year 0 and negative numbers before it. Thus the ISO 8601 timeline is -0001, 0000, 0001, and 0002.

Confusion with British versus American usage

Dates of events in Britain prior to 1752 are usually now shown in their original Old Style form, whereas dates of events in (then British) America prior to 1752 are usually now shown in the New Style form.

For example, Shakespeare died on 23 April (OS), and it is rare to see this converted to 3 May (NS). But while George Washington was born on 11 February (OS), his birthday is now celebrated on 22 February (NS). (He changed its celebration date himself, as a twenty one year old surveyor.)
However, neither of these practices is universal in either country, so it is sometimes very unclear which calendar is being used, and this can lead to false assumptions, which can lead to dates being inaccurately converted from one calendar to the other. Since the resurgence of interest in the history of the calendar, more information about the real dates (according to various calendars) of events has been forthcoming and many previous errors have been corrected. While these changes are welcome, there is still much scope for confusion; therefore, noting the calendar being used in transitional periods would help the reader understand the dates involved.

Accuracy

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long, which has an error of about one day per 3300 years with respect to the mean tropical year of 365.24219 days but less than half this error with respect to the vernal equinox year of 365.24237 days. Both are substantially more accurate than the one day in 128 years error of the Julian calendar (average year 365.25 days).

On timescales of thousands of years, the Gregorian calendar falls behind the seasons drastically because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration. The equinox will occur earlier than now by a number of days approximately equal to [years into future/5000]2. This is a problem that the Gregorian calendar shares with any rule-based calendar.

Numerical facts

When leap years and common years are taken into account, there are a total of 14 possible Gregorian calendars.

When different dates of Easter are also taken into account, there are a total of 70 possible Gregorian calendars.

An average year is 365.2425 days = 52.1775 weeks = 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.

(Some years may also contain a leap second, which can be positive or negative.)

See also common year starting on Sunday and dominical letter.

The 400-year cycle of the Gregorian calendar has 146,097 days and hence exactly 20,871 weeks. So, for example, the days of the week in Gregorian 1603 were exactly the same as for 2003. This also causes more months to begin on a Sunday (and hence have Friday 13) than any other day of the week. 688 out of every 4800 months (or 172/1200) begin on a Sunday, while only 684 out of every 4800 months (171/1200) begin on each of Saturday and Monday, the least common cases.

A smaller cycle is 28 years (1,461 weeks), provided that there is no dropped leap year in between. Days of the week in years may also repeat after 6, 11, 12, 28 or 40 years. Intervals of 6 and 11 are only possible with common years, while intervals of 28 and 40 are only possible with leap years. An interval of 12 years can occur with either type, but only when there is a dropped leap year in between.

The Doomsday algorithm is a method by which you can discern which of the 14 calendar variations should be used in any given year (after the Gregorian reformation). It is based on the last day in February, referred to as the Doomsday.

Number of leap years starting on a given day of the week

Because there are 97 leap years in every 400 in the Gregorian Calendar, there should, in each "cycle", be either 13 or 14 leap years starting on each day of the week. However, the effects of the "common" centennial years (1700, 1800, 1900, 2100, 2200 etc.) cause major alterations.

This is because the absence of an extra day in such years causes the following leap year (1704, 1804, 1904, 2104 etc.) to start on the same day of the week as the leap year twelve years before (1692, 1792, 1892, 2092 etc.). Similarly, the leap year eight years after a "common" centennial year (1708, 1808, 1908, 2108 etc.) starts on the same day of the week as the leap year immediately prior to the "common" centennial year (1696, 1796, 1896, 2096 etc.). Thus, those days of the week on which such leap years begin gain an extra year or two in each cycle. In each cycle there are:

13 leap years starting on Monday
14 leap years starting on Tuesday
14 leap years starting on Wednesday
13 leap years starting on Thursday
15 leap years starting on Friday
13 leap years starting on Saturday
15 leap years starting on Sunday