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The overall function, , normalizes the result to reside in the range of 0 to 6, which yields the index of the correct day of the week for the date being analyzed. The reason that the formula differs between calendars is that the Julian calendar does not have a separate rule for leap centuries and is offset from the Gregorian calendar by a fixed ...
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).
The Julian date (JD) of any instant is the Julian day number plus the fraction of a day since the preceding noon in Universal Time. Julian dates are expressed as a Julian day number with a decimal fraction added. [8] For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2 456 293.520 833. [9]
Note that Julian days begin at noon (hour = 12) and thus hours 0-11 of a solar day are one Julian day earlier than hours 12-23. The value may extend outside of the normal range and is considered as additional number of julian days (a Julian day is 24 hours or 86400 seconds exactly, ignoring any adjustment of leap seconds within the UTC calendar).
Note that Julian days begin at noon (hour = 12) and thus hours 0–11 of a solar day are one Julian day earlier than hours 12–23. The value may extend outside of the normal range and is considered as additional number of julian days (a Julian day is 24 hours or 86400 seconds exactly, ignoring any adjustment of leap seconds within the UTC ...
J transit is the Julian date for the local true solar transit (or solar noon). 2451545.0 is noon of the equivalent Julian year reference. 0.0053 sin M − 0.0069 sin ( 2 λ ) {\displaystyle 0.0053\sin M-0.0069\sin \left(2\lambda \right)} is a simplified version of the equation of time .
No guidance is provided about conversion of dates before March 5, -500, or after February 29, 2100 (both being Julian dates). For unlisted dates, find the date in the table closest to, but earlier than, the date to be converted. Be sure to use the correct column. If converting from Julian to Gregorian, add the
Use the Julian portion of the table of paschal full moons. Use the "week table" (remembering to use the "Julian" side) to find the day of the week on which the paschal full moon falls. Easter is the following Sunday and it is a Julian date. Call this date JD. Subtract 100 from the year. Divide the result by 100.