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« Return to Thread: Part2, Joining list. Calendar reforms.
Re: Astronomical sidereal calendar (was: Part2, Joining list. Calendar reforms)
by Irv Bromberg
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On 2009 May 24, at 10:14 , Amos Shapir wrote:
A tropical calendar may be difficult, but this can be made simpler by defining the calendar along the sidereal year. A convenient cycle is 366 years with 95 leap (year Y is leap if (Y mod 27) mod 4 == 3); it can be started on apphelion or perihelion day, with 5 or 6 long months around the apphelion, the same way the Iranian calendar does.
Irv replies: A mean year of 365+95/366 = 365d 6h 13m 46.2s is quite a bit longer than the usually quoted length for the mean sidereal year of about 365.256363051 days = 365d 6h 9m 9.7676s, but nevertheless that excess should more closely approximate the advance of aphelion.
If a fixed cycle is going to be employed, doesn't the optimal year length have to be a good approximation to the mean anomalistic year, which is slightly longer?
365.259635864 days = 365d 6h 13min 52s = 365+701/2700 days is exact (for the given length, which I presume is in atomic time), or other close approximations are 365+182/701 days or 365+155/597 days. Also there is 365+27/104 days whose mean year is a tad short = 365d 6h 13m 50+10/13s but should be better than the 366-year cycle. Making it a tad short should prolong its useful duration of good accuracy, by better approximating mean solar time over future centuries.
To make it into a tropical calendar, just shift the starting day by 1 day every 57 years (that may change in the future), but keep month lengths the same as the overlapping sidereal months.
If astronomical algorithms are employed to determine the New Year Day, as is done for the modern Persian calendar, then the anomalistic year approximation cycle will only be used to determine which months have 31 days, although I'm not clear on what the criteria would be. If the criteria are defined then I see little advantage in using a fixed cycle for the aphelion approximation, assuming that astronomical algorithms (solar longitude) are being employed for the northward equinox anyway, because it would be simple enough to use a mean aphelion polynomial to find the target ecliptic longitude and then use the same solar longitude astronomical algorithms to find the moment when Sun reaches that target, then apply the defined 31-day month numbering criteria.
However, to avoid oscillations around leap years it will be necessary to pre-calculate switchover points, or have a complicated scheme that analyses a series of years and statistically decides what to do. If such a list is defined then there is no need to reckon the position of aphelion at all, except that the list would need re-verification from time-to-time as knowledge of celestial mechanics etc. advances sufficiently to justify re-evaluating the list.
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