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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 7, at 10:50 , Palmen, KEV (Karl) wrote:
The 69/389 leap week cycle has an extremely low mean year of 365.241645 days.
The mean year is 365+94/389 days ≡ 365d 5h 47m 58+58/389s and is just a few seconds longer than the shortest solar year length that presently exists at aphelion, which I have reckoned using the Find Calendar Seasons spreadsheet at approximately 365 days 5 hours 47 minutes 52 seconds or about 365+43/178 days. This means that it has recently (within the past millennium) become a stable calendar season starting at aphelion, and its calendar season is now migrating towards perihelion at the same time that perihelion is migrating towards it, keeping it quite stable and very near to the north solstice. It is actually slightly too long for the present era mean north solstitial year (calendar season slightly before the north solstice), but in the future the mean north solstitial year will spend quite a few millennia at an even longer mean year, so overall the 389-year cycle will remain an excellent average approximation for the next 10-11 millennia, as shown as the dashed orange horizontal line on this chart:
Because of the expected near-maximal longevity of this cycle and the fact that the stability of the mean northward equinoctial year is about 2/3 of the way towards its expiration era, I have been very seriously considering switching Symmetry454 to use the 389-year cycle with 69 leap weeks as the preferred leap cycle. If adopted then a fixed arithmetic Easter computus would be out of the question due to the cycle tracking the north solstice rather than the northward equinox. Therefore it would have to use either the astronomical Uniform Easter as recommended by the World Council of Churches, or the proposed fixed Easter date of Sunday April 7th on the Symmetry454 calendar. Yesterday I checked and found that Symmetry454 Sunday April 7th remains the median astronomical Easter date with this 389-year leap cycle even for thousands of years into the future, despite the cycle's comparatively short calendar mean year.
This chart shows the predicted long-term drift of the cycle relative to the north solstice, based on the numerical integration of SOLEX:
(The drift chart depicts the cycle performance before adopting the K value that makes this cycle fully symmetrical, but the only difference is the vertical alignment. Since the north solstice at the epoch occurred at about 3/4 hour before midnight Jerusalem local time at the end of Symmetry454 Friday, June 19, 1 AD, therefore with the fully symmetrical cycle the green line average would shift later by about 2+1/2 days. This doesn't affect the interpretation of the calendar drift performance.)
« 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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