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« Return to Thread: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
by Irv Bromberg
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On 2009 Apr 6, at 08:39 , gerry_lowry (alliston ontario canada) wrote:
I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
That was not part of the Gregorian reform, nor was it adopted at the recent 400th anniversary of the Gregorian calendar reform.
With the Gregorian mean year of 365+97/400 days = 365d 5h 49m 12s the calendar season is at about March 3rd, or nearly 18 days before the northward equinox. The Gregorian calendar mean year will "expire" around 4500 AD, that is when it will be longer than all points in the solar cycle.
Calendar seasons are explained under the topic heading "Calendar Seasons: Stable points in the solar cycle" at <http://www.sym454.org/leap/>.
Omitting year 4000 as a leap year would greatly increase the long-term equinox jitter as others have mentioned, and it also changes the calendar mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting the calendar season to a position that is 10 days beyond the northward equinox, about March 31st.
The calendar season concept is not too realistic in the context of such a long leap cycle with such high jitter. It works best with smoothly spread leap cycles that are under 1000 years long. Nevertheless this analysis of the calendar mean years serves to make the point that that proposed reform of the Gregorian calendar would not be particularly helpful.
Furthermore, by the time that the next year 4000 leap day would be omitted in 8000 AD the northward equinoctial year will be appreciably shorter than it is today, so there will not be any point in the solar cycle that has a mean year as long as even this shorter 365+369/4000 mean year. The 4000-year cycle will thus "expire" around the year 6000. Thus it is rather silly to even consider a reform proposal for a leap rule modification that most likely would be invoked only once in the far future.
On the other hand, if the 4000-year cycle were implemented as a cycle having its leap years as smoothly spread as possible then numerical integration (SOLEX) shows that relative to the Gregorian epoch the northward equinox will reach a maximum of about 1/2 day late around year 5000 AD, and by around 8000 AD it will have close to zero drift, but will already drift >1/2 day early by year 9000 AD, by which time the drift will be exponentially migrating towards earlier dates. Overall, this is not bad at all, but would require that leap years be as smoothly spread as possible, a very different situation from the present Gregorian leap rule or this proposed year 4000 modification.
A reasonably short and smoothly spread leap cycle would greatly reduce the calendar equinox jitter and would also greatly reduce the long-term equinox drift, particularly if an appropriate calendar mean year is selected.
Although the mean northward equinoctial year is presently just a fraction of a second shorter than 365+127/524 days = 365d 5h 49m 60/131s, which accordingly has its calendar season just a fraction of a day before the northward equinox, for calendrical purposes the 524-year leap cycle is not as good as a cycle with a slightly shorter calendar mean year because:
1. Traditionally dates are calculated relative to the Gregorian epoch, and for the past 2000 years the northward equinoctial year has been shorter than it is today.
2. The present era mean northward equinoctial year is near its maximum and in about 1000 years will start to get progressively shorter, which will make the 524-year cycle mean year too long for future dates. The northward equinoctial year will never again be as long as it will be around the year 3000 AD.
For further information see my "Lengths of the Seasons" web page at <http://www.sym454.org/seasons/>, especially the row #6 figures.
« Return to Thread: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
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