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« Return to Thread: Lunisolar Cycle Multiples of Short Lunar Cycle
Re: Lunisolar Cycle Multiples of Short Lunar Cycle
by Irv Bromberg
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On 2009 May 15, at 16:55 , Brij Bhushan Vij wrote:
Elite 3000, Irv, CC sirs:
>On 2009 May 15, at 14:22 , ELITE 3000 wrote:But which cycles are the most accurate in terms of lunation period and mean year compared to the mean solar year (365.242 189 67 days (365 d 5 h 48 min 45 s))>Irv replies:>That is 365+31/128 days, which doesn't approximate any equinox or solstice -- why do you care about it?
Brij says: My arguments since 1980's have been directed towards a 128-year (2*64-year Metric calendar) cycleleading to LWks & Keplers' LWks, NEVER tried by man on *div.six(6) with added KLWks* has remained under examination ever since, I joined Calndr-L list in mid-2002. The Mean Year =(365+31/128)=365.2421875 days =7*(52+159/896) days. The same is also obtained as: 7*[(52+1/6+29/2688)] days.The 834-year/148 LWks give Mean Year =7*[(52+1/6+9/834)] =365.242206235012 days.It may be worth noting that Mean Year=365.2421875 days is CLOSEST to the Mean Average Atomic Year Value, obtained as the average of Year values at FOUR cardinal points.
Irv replies:
Averaging the four cardinal points, which I assume Brij is referring to the mean lengths of the years measured at each equinox and solstice, will not equal the average value that you seek, because those points are not equally spaced. One can however average the longest and shortest year lengths and that will yield the average that you seek. The shortest is instantaneous mean solar year length at the ecliptic longitude of aphelion, and the longest is the instantaneous mean solar year length at the ecliptic longitude of perihelion. [These are not the same as the year length from aphelion to aphelion or from perihelion to perihelion, which is the appreciably longer solar anomalistic year.]
Anyhow, although it is true that 365+31/128 days is essentially equal to the long-term mean solar year length in terms of atomic days, that is of no relevance to any calendar.
Calendars need mean solar time, not atomic time. Don't be deceived by the small difference between atomic time and mean solar time in the present era, that is just because the atomic second currently happens to be nearly equal to the mean solar second. As the Earth rotation rate is progressively slowed by the tidal transfer of angular momentum to Moon the mean solar second will become progressively longer than the atomic second. Atomic time is essential for celestial mechanical calculations, but it is useless for calendrical calculations, except very near to the present era.
In terms of atomic time, each of the equinoctial and solstitial years take turns enjoying eras of stability in mean length, but those eras are much shorter than the correspondingly stable eras in terms of mean solar time:
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