Date: Thu, 9 Oct 1997

From: Simon Cassidy <scassidy@EARTHLINK.NET>

Subject: Re: lengths of "seasons"

To: Multiple recipients of list CALNDR-L <CALNDR-L@ECUVM1.BITNET>Alex LIVINGSTON wrote:

> Note that the lengths of four consecutive "seasons" sum to a figure not

> particularly close to the length of the average tropical year [Simon

> Cassidy please restrain yourself ;-) ], indicating that other factors are

> at work besides the eccentricity of the earth's orbit.Simon notes:

The "other factors" are, of course, short period perturbations which need to be averaged out over dozens of years to obtain a useful mean. The "mean tropical year" of the astronomers is conceptually** averaged over DOZENS OF THOUSANDS of years and is therefore not applicable to calendars regulated by the spring equinox. If anybody still does not believe me on this point, I can now (thanks to Duncan Steel) refer you all to a published article (Journal of the British Astronomical Association V102, #1, 1992, pp40-42) in which the authors state:

"It should be noted that the tropical year is not equal to the (mean) time interval between two successive spring equinoxes. In present-day astronomy, the tropical year is defined as the time interval needed for the mean tropical longitude of the Sun to increase by 360 degrees."

On the same page (42) is given the Mean time interval between two March equinoxes, as 365.242374 days, for the year 2000. This figure agrees with the figure I have given (365.2424), though there are two small perturbations of period ~200 years and ~1500 years which I take into account when quoting a more exact figure of 365.24238 days for the current value.

** The astronomers' tropical year is only conceptually an average over a number of years. It is not defined as such an average, but is defined as the period of an UNREAL object ("the mean tropical longitude of the Sun" from the quote above). IT IS CERTAINLY NOT THE YEAR LENGTH TO USE WHEN JUDGING THE ACCURACY OF OUR GREGORIAN CALENDAR OR THE PERSIAN (IRANIAN) CALENDAR; even if "experts" such as Stephen Jay Gould (heard giving the error in the Gregorian calendar as one day in two thousand years, on the radio yesterday) and Dr. Reingold (misrepresenting the distribution of the leap years in the Persian calendar, in his book "Calendrical Calculations"), continue to make the mistake of equating the vernal equinox year to the astronomer's tropical year of 365.2422 days.

I hope this is restrained enough :-).

Dee's Yr's Simon Cassidy email: scassidy@earthlink.net

Emeryville Ca. U.S.A.

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