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These formulas are based on the observation that the day of the week progresses in a predictable manner based upon each subpart of that date. Each term within the formula is used to calculate the offset needed to obtain the correct day of the week. For the Gregorian calendar, the various parts of this formula can therefore be understood as follows:
In order to correct for calendar drift, 10 days were skipped, so doomsday moved back 10 days (i.e. 3 days): Thursday, October 4 (Julian, doomsday is Wednesday) was followed by Friday, October 15 (Gregorian, doomsday is Sunday). The table includes Julian calendar years, but the algorithm is for the Gregorian and proleptic Gregorian calendar only.
The basic approach of nearly all of the methods to calculate the day of the week begins by starting from an "anchor date": a known pair (such as 1 January 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week.
A calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics. Some examples of calendrical calculations: Converting a Julian or Gregorian calendar date to its Julian day number and vice versa (see § Julian day number calculation within that article for details).
Leap years have two letters, so for January and February calculate the day of the week for January 1 and for March to December calculate the day of the week for October 1. Leap years are all years that divide exactly by four, with the following exceptions: Gregorian calendar – all years divisible by 100, except those that divide exactly by 400.
Rata Die (R.D.) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Latin ablative feminine singular for "from a fixed date") by Howard Jacobson. [1] [2]
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The Lilian day number is a count of days of the Gregorian calendar and not defined relative to the Julian Date. It is an integer applied to a whole day; day 1 was October 15, 1582, which was the day the Gregorian calendar went into effect. The original paper defining it makes no mention of the time zone, and no mention of time-of-day. [26]