Julian dates (abbreviated JD) are simply a continuous count of days and fractions since noon Universal Time on January 1, 4713 BC (on the Julian calendar).
Almost 2.5 million days have transpired since this date.
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More information on calendars and their histories can be found in E. Richards' "Calendars" chapter of the Explanatory Supplement to The Astronomical Almanac (ed. For more information on the API, please see the documentation page.
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Thus, the day of the week can be obtained from the remainder of the division of the Julian date by 7.
Calendar dates — year, month, and day — are more problematic.
Thus, there is a ten-day gap in calendar dates, but no discontinuity in Julian dates or days of the week: 4 October 1582 (Julian) is a Thursday, which begins at JD 2299159.5; and 15 October 1582 (Gregorian) is a Friday, which begins at JD 2299160.5.
The omission of ten days of calendar dates was necessitated by the astronomical error built up by the Julian calendar over its many centuries of use, due to its too-frequent leap years.
Julian dates are widely used as time variables within astronomical software.