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Astronomers often need to know difference between two dates, or be able to calculate next date of some periodic event. For events which are quite far one from another, like comet appearance, regular calendar is not well suited, due to different number of days in months, leap years, calendar reforms (Julian/Gregorian) and so on.
Thus, Joseph Justus Scaliger, french astronomer (1540 - 1609) invented Julian Dates or Julian Days, named after his father, Julius Scaliger. And it is not about Julian calendar at all.
Julian days is the counter, each day incremented by one. So, if you know value of Julian day for one date and value of Julian day for another, you can simply subtract one from another and find out the difference.
The start of Julian days, called the start of the Julian era, is defined as noon of January, 1st, 4713 B.C. in the Julian calendar. With this date, all known historical astronomical observations have positive Julian day numbers, so all calculations are simple additions and subtractions.
Julian day is a fractional number, where whole part corresponds to 12:00 AM, 0.25 is 6:00 PM, 0.5 - 12:00 PM, 0.75 - 6:00 AM, etc.
Because first two digits of Julian day remain constant for about three centuries, sometimes more short version of Julian day, Modified Julian Date is used. The start of Modified Julian days is defined as midnight of November, 17th, 1858, and