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« Return to Thread: Lunisolar Cycle Multiples of Short Lunar Cycle
Re: Unhindered option RE: Cycles of interest RE: Lunisolar Cycle Multiples of Short Lunar Cycle
by Irv Bromberg
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On 2009 May 19, at 14:10 , Brij Bhushan Vij wrote:
But, my goal has been for correction of the Gregorian calendar, which is a 'solar day calendar':400-years =146089.68758679124 days BUT works with Mean Year =365+97/400 =365.2425 days (146097 days). Thus, the controversy of corrections needed now.
the Mean Year=365.2421875 days (365d5h48m45s.0)
=(365+31/128) days is a practical unhindered value.
Irv replies: OK, well the primary goal of the Gregorian calendar reform was to keep the vernal equinox on March 21st, so the relevant length of year to evaluate it against is not 365+31/128 days but rather the vernal equinox year, which is presently very close to 365+127/524 days, or 365d 5h 49m 0.5s (and getting slightly longer over the coming centuries), about 15.5 seconds per year longer than the mean year that you are using. The Gregorian mean year is 365d 5h 49m 12s, so it's mean year is about 11.5 seconds too long, and so the Gregorian mean year is actually more accurate with respect to the vernal equinox year than your proposed reform! Nevertheless, because of tidal slowing of the Earth rotation rate, in the long term it is better to have a mean year that is too short than a mean year that is too long.
For my calculations I use the value 29.53058881 days (29d 12h 44m 2s.873184). Mean values as shown by me: MeanLunation =29.5305893733 (29d12m 44m2s.92) is close enough to be practical, UNLESS there is a better value achievable, sir.
Irv replies: I looked into this further and found that improving on the accuracy is very method dependent, so I have to say that that lunation period is about as accurate as one can use. I was just suggesting that it is not ideal to use an accurate lunation period for a lunar calendar intended to be used today and into the future, because the astronomical mean lunation period is getting progressively shorter. Instead, I suggest intentionally using a slightly shorter lunation period, which will allow the lunar approximation to serve with better accuracy for a longer duration until correction is necessary.
I had suggested a shorter mean month somewhere in the range of 2.0 to 2.5 seconds in excess of 29d 12h 44m. Compare with the Gregorian Easter computus which is about 2.7 seconds in excess, or the even shorter mean month used for the Dee Easter computus which is less than 2.4 seconds in excess, or the shorter still mean month used for the modern Hindu lunisolar calendar (Arya) of less than 2.3 seconds in excess. These shorter cycles will endure further into the future, provided that they are set up to be a bit late in the present era, then in the future they will drift earlier until they are accurate, and later they will drift late again (when the astronomical mean synodic month gets shorter than the cycle mean month). These cycles are shown in my lunar calendar drift spreadsheet at:
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