Is the true difference between the Julian Calendar and a Gregorian calendar working back from any point after AD 1901 actually 15 days instead of 13?

Question

When the Gregorian Calendar was implemented, it was decided that the date should be advanced by 10 days to account for the extra time accumulated by the Julian Calendar.

However, A.D. 325 was used as the reference point, as the makers of the Gregorian Calendar wanted to realign the vernal equinox to roughly where it was in A.D. 325 (i.e., during the time of the Council of Nicaea).

Since then, the difference between the Gregorian Calendar and Julian Calendar has grown to be 13 days, as the three years A.D. 1700, A.D. 1800, and A.D. 1900 are leap years in the Julian Calendar but not in the Gregorian Calendar.

However, if we were to to use any Gregorian Calendar after A.D. 1901 to compare with the Julian Calendar, wouldn't the difference between the two actually be 15 days since the calendar reform in A.D. 1582 failed to account for the two other leap years found in the Julian Calendar that don't fit the Gregorian Calendar's leap year rule (A.D. 100 and A.D. 200)?

From A.D. 325 to A.D. 1582, there were 9 leap years in the Julian Calendar that wouldn't have fit the Gregorian calendar's leap year rule: A.D. 500, A.D. 600, A.D. 700, A.D. 900, A.D. 1000, A.D. 1100, A.D. 1300, A.D. 1400, and A.D. 1500.

However, if we were to truly account for the number of extra days accumulated by the Julian Calendar since its inception, wouldn't 2 more days need to be accounted for when calculating the true difference between the Gregorian Calendar and Julian Calendar? Though there were only 9 leap years in the Julian Calendar that wouldn't have fit the Gregorian calendar's leap year rule from A.D. 325 to A.D. 1582, the fact that the date was advanced by 10 days in 1582 could be thought of as covering the extra day from the Julian Calendar's leap year of A.D. 300. Thus, the two extra days that need to be accounted for are the Julian Calendar leap days in years A.D. 100 and A.D. 200.

Though intercalation was off in the early stages of the Julian Calendar, doesn't the fact that the date of the solar eclipse (and thus the New Moon) that was predicted to happen in Rome on August 1, A.D. 45 according to Roman calculations (as documented in Dio Cassius Book 60, Section 26) aligns with our Julian date calculations of when the New Moon should have occurred if the rules of the Julian calendar were followed correctly since inception attest to the fact that the corrections brought on by Augustus's termination of leap years between 8 B.C. and A.D 8 brought the calendar back on track by this point? It's to my understanding that these moon dates we retrospectively calculate wouldn't need adjusting, as, being astronomical observations calculated using Julian Ephemeris Days (JDE), they are independent of this whole 15 day difference conversation.

I've brought up the last point to highlight the fact that 15 days should be all we need (nothing more and nothing less), as the Julian Calendar seemed to have recovered from that period of irregular leap years from 42 B.C. to 9 B.C.

With all of this being said, is it true that the difference between the Julian Calendar and Gregorian Calendar is actually 15 days (which should matter a lot as far as assigning the appropriate days of the week when converting between proleptic Gregorian Calendar and historical Julian Calendar dates goes)? Thanks for any insight!

Answer 1

That the calendar reform in A.D. 1582 did not account for the two leap years in the Julian Calendar that didn't fit the Gregorian Calendar's leap year rule and occurred before A.D. 300 (A.D. 100 and A.D. 200) was according to its design, as I explain below.

On the one hand, the Julian calendar had been designed so that at the time of its enactment in 45 B.C. the spring equinox would fall on March 23. From the list of equinoxes (and solstices) linked in answer [1] at ASE, I paste below the GMT dates and times of the spring equinoxes since 45 B.C. to 21 B.C., from which you can see that 21 B.C. was the first year in which the spring equinox fell on March 22 using Rome Mean Time (RMT) = GMT + 49' 56" (which BTW corresponds to the exact longitude of Piazza del Campidoglio on the top of Capitoline Hill).

 Greenwich Mean Time (GMT) - Rome Mean Time (RMT) 
                             = GMT + 49' 56"
B.C.     45-03-23 03:20:17
B.C.     44-03-23 09:03:44
B.C.     43-03-23 14:56:27
B.C.     42-03-23 20:48:37
B.C.     41-03-23 02:26:34
B.C.     40-03-23 08:21:36
B.C.     39-03-23 14:11:26
B.C.     38-03-23 19:48:46
B.C.     37-03-23 01:42:21
B.C.     36-03-23 07:28:24
B.C.     35-03-23 13:19:38
B.C.     34-03-23 19:12:18
B.C.     33-03-23 00:49:02
B.C.     32-03-23 06:47:11
B.C.     31-03-23 12:44:35
B.C.     30-03-23 18:28:36
B.C.     29-03-23 00:27:10
B.C.     28-03-23 06:16:04
B.C.     27-03-23 12:04:44
B.C.     26-03-23 17:55:18
B.C.     25-03-22 23:30:38 - 25-03-23 00:20:34
B.C.     24-03-23 05:21:05
B.C.     23-03-23 11:12:06
B.C.     22-03-23 16:45:49
B.C.     21-03-22 22:35:24 - 21-03-22 23:25:20

On the other hand, the Gregorian calendar was designed so that the spring equinox would fall on March 21 or earlier (i.e. 20 or 19). In fact, the very first spring equinox after the enactment of the Gregorian calendar fell on March 21:

 Greenwich Mean Time (GMT)

A.D.   1583-03-21 05:52:23

This goal was fully achieved. As can be checked at the list from [1], under the Gregorian calendar the latest time of occurrence of the spring equinox was and forever will be:

 Greenwich Mean Time (GMT) - Rome Mean Time (RMT) 
                             = GMT + 49' 56"
    
A.D.   1903-03-21 19:14:14 - 1903-03-21 20:04:10

Now, why was the Gregorian calendar designed with the goal that the spring equinox would fall on March 21 or earlier? Because that was exactly the case at the time of the Council of Nicaea:

 Greenwich Mean Time (GMT) - Rome Mean Time (RMT) 
                             = GMT + 49' 56"
A.D.    323-03-21 00:13:28
A.D.    324-03-20 06:02:57
A.D.    325-03-20 11:59:52
A.D.    326-03-20 17:41:10
A.D.    327-03-20 23:34:14 - 327-03-21 00:24:10

In fact, A.D. 327 was the very last year in which the spring equinox fell on March 21 (using Rome Mean Time) under the Julian calendar.

[1] https://astronomy.stackexchange.com/a/13009

Answer 2

Without any doubt, your question is very interesting. You have counted correctly, you are right: if the clerical of the 16th century really wanted all jubilees to happen in the same astronomic conditions, as they happened in the year 1AD, 11-12 days had to be added. If they wanted to return to Caesar's calendar setting, they should add 0.0075*(1582+46)=12.2. Anyway, your 12 days are correct.

(0.0075 days - it is a difference between the years of Julian and Gregorian calendars)

But, as you surely know, the calendar had been changed for the "correct and sacred" setting of Easter. It couldn't be celebrated with the Jewish Passover or even later. At the Nicaean Council 325AC, the way of Easter dating was set officially. In 1AD, in 46BC, or even in 33AD Easter did not exist yet and neither of those years could not be taken as a zero point by the Christian clergy.

Before the 2nd century Christians celebrated Easter together with Jews celebrating their Passover.

In the 2nd century, they started to celebrate Easter a week after Passover. (Look at the letter of St. Polycarp to the Philippians, believed to have been written around AD 110-140.) And it was logical because Jesus' Last Supper with his disciples occurred during the Passover meal.

In 325, on the Nicaean Council, as we know, they officially set Easter before the Jewish Passover. But you surely understand, that the council only agreed on the already accepted practice or somewhere around it. (There were no significant discussions on that theme - look Nicaean Council). So, the "sacred" time setting of Easter had to be set before 325y. Somewhere between the 2nd century and 325y. And that was a serious step - for they cut the Christian tradition off the Jew one, breaking the logic. It couldn't happen fast, and it couldn't consolidate fast, both steps needed time. So, we are getting the 3rd century as the only possible time for the start of celebrating Easter before the Jewish Passover. 1582y clergy could count it, too, or they could have some existing records on the theme. And the move of Easter from the times of the 3rd century was 10 days in 1582.

The papers were probably destroyed later because they proved the existence of the common tradition with Jews in not-so-early Christianity. The Jews were deeply despised by Christians in the 16th century, and many years later. Apparently, the real reasons had to be hidden as shameful. It is really funny that in all sources, religious and scientific, we see these 10 days taken from nowhere, as a rabbit from a hat, and declared as something both scientific and sacred. While they are not.

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A point about one of yours.

Nobody counts and predicts eclipses using calendar time. I had my first higher education in astronomic geodesy, and I studied spherical astronomy as a part of the program. And I worked as a programmer for tens of years. And I cannot imagine a person who would count any astronomic task using the calendar time, even with a computer. Always all tasks are counted, using the physical time, the star time, or, at least, the solar time, and only after getting the final result, it can be transformed into the calendar time. So, the calendar in use has not even the slightest influence on the quality of astronomical predictions. Muslims publish the same predictions using their, very different calendar, without any problems or errors due to it.