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I know that JD0.0 is Jan. 1st 4713 BC at Noon, a year in the Julian calendar is 365.25 days and that the number after 'JD' is the number of days so...

I want to calculate the number of days between Jan1.2000AD and Jan1.4713BC and I do

$$ \text{# of years} = 4712+2000=6712 \text{ years (skipping the year 0)} $$ $$ \text{# of days} = 6712 \cdot 365.25 =2451558 $$

So I think it should be JD2451558. An extra 13 days. What's going on here? I thought maybe the length of a year in the Julian calendar is $2451545/6712=365.2480632\text{days}$ but I can't find anything to support that.

I imagine that people would have questioned whoever proposed J2000 as JD2451545.0 and got a satisfying answer but I can't find one! Help

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This Wikipedia article states (correctly) that

"The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar)"

The Julian year consists of 365.25 days while a Gregorian year consists of 365.2425 days.

Since the introduction of the Gregorian calendar, the difference between Gregorian and Julian calendar dates has increased by three days every four centuries (all date ranges are inclusive). In addition, 10 days were added to the Julian calendar to obtain the Gregorian calendar at the time of the calendar reform. The current difference between the Gregorian and Julian calendar dates is 13 days: 14 September 2016 Gregorian date is 1 September 2016 (Julian date).

This should explain the extra 13 days in your calculations.

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So I think it should be JD2451558. An extra 13 days. What's going on here?

British calendar for September 1752, where the first three days were Tuesday September 1, Wednesday September 2, and Thursday September 14

The switch from the Julian calendar to the Gregorian calendar involved two changes. One change was the frequency at which leap years occur. The Julian calendar had a leap year every four years, making a Julian year 365.25 days long on average. The Gregorian calendar has 97 leap years every 400 years, making a Gregorian year 365.2425 days long on average.

The other change was a one-time shortening of some year to bring the calendar back in line with the seasons in the third century AD. Different countries did this differently, some as early as 1582, others as late as 1923. As depicted above, Great Britain made this change in 1752 by making 3 September 1752 to 13 September 1752 vanish (that's eleven days). Since that change, both 1800 and 1900 would have been leap years in the Julian calendar but were not in the Gregorian calendar. Eleven days lost in September 1752 plus two more days for no February 29th in 1800 or 1900 exactly accounts for your thirteen day discrepancy.

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    $\begingroup$ The switch Julian to Gregorian calendars involved one more change, which was how the Roman Catholic Church calculates the day on which Easter falls. This third change has zero impact on the 13 day discrepancy. $\endgroup$ – David Hammen Sep 19 '16 at 11:47

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