How long is a year -- EXACTLY?

Date: Fri, 25 Oct 1996 19:35:46 -0700
From: Simon Cassidy <simoncas@PACBELL.NET>
Subject: Re: How long is a year -- EXACTLY?
Chris Carrier wrote:
>Actually, it depends on whether or not the March equinox is the most
>important marking-point of the year. I do not consider it so, and neither
>should most people unless the Easter setting date is paramount as it was
>with Gregory.
As I explained in my messages of 03Oct and 04Oct [both titled "Re: Misnamed months, (Amos asked)"] and in my message of 10Oct [titled "Thirty-three year calendars"], there is a NATURAL ASTRONOMICAL reason why the vernal equinox year is preferable to the other three natural regulating points. See herein, below, for a numerical demonstration, in Chris Carrier's terms, of the natural superiority of the spring eqinox as a calendar regulator.
Chris Carrier then attempted to estimate the four year-lengths by starting with the relevant instants in ephemeris time for 200 A.D., as follows:
>AD 200 March equinox: 21d 11h 06m 13s WRONG!
> June solstice: 23d 8h 01m 41s WRONG!
> Sept. equinox: 23d 22h 21m 28s WRONG!
> Dec. solstice: 21d 17h 03m 51s WRONG!
Unfortunately Chris has used the times (as given in Meeus 1983) for 201 A.D.! The times for 200 A.D. are actually as follows (in Meeus 1983):
AD 200 March equinox: 21d 5h 18m 41s
June solstice: 23d 2h 26m 06s
Sept. equinox: 23d 16h 43m 06s
Dec. solstice: 21d 11h 20m 09s
Chris continued with the ephemeris times expected for 3000 A.D. and the discrepancies from whole numbers of Gregorian Years based on his WRONG 200 A.D. times:
>AD 3000 March equinox: 20d 17h 33m 33s, 62980s earlier after 2800 years
> June solstice: 20d 16h 58m 49s, 226972s earlier after 2800 years
> Sept. equinox: 22d 14h 54m 14s, 113174s earlier after 2800 years
> Dec. solstice: 22d 5h 23m 17s, 44366s LATER after 2800 years
The above, 3000 A.D. table, thus needs to be ammended as follows:
AD 3000 March equinox: 20d 17h 33m 33s, 42308s earlier after 2800 years
June solstice: 20d 16h 58m 49s, 206837s earlier after 2800 years
Sept. equinox: 22d 14h 54m 14s, 92932s earlier after 2800 years
Dec. solstice: 22d 5h 23m 12s, 64983s LATER after 2800 years
Then continuing with Chris' procedure:
>So, using 365/05:49:12 as a Gregorian year, and dividing these variances
>from it by 2800, we get a year length of:
ACTUALLY
365d 5h 48m 56.89s for the March equinox. [or 365.242325 ephemeris days]
365d 5h 47m 58.13s for the June solstice. [or 365.241645 ephemeris days]
365d 5h 48m 38.81s for the September equinox. [365.242116 ephemeris days]
365d 5h 49m 35.21s for the December solstice. [365.242769 ephemeris days]
365d 5h 48m 47.26s for the average of four. [or 365.242214 epehmeris days]
NOT as Chris gives:
>365d 5h 48m 49.54s measured against the March equinox. WRONG!
>365d 5h 47m 50.94s measured against the June solstice. WRONG!
>365d 5h 48m 31.58s measured against the September equinox. WRONG!
>365d 5h 49m 27.85s measured against the December solstice. WRONG!
>
>365d 5h 48m 39.97s measured against the average of all four of them.WRONG! So in fact, the Exigian and the Soviet year are less accurate than Dee's year, against the vernal equinox, in Chris's 2800 year run, EVEN IN EPHEMERIS DAYS!
>Gregorian Year, 365+(97/400) days, 365/05:49:12.
>Khayyam's (and Dee's) Year, 365+(8/33) days, 365/05:49:05.454545....
>Soviet Year, 365.25-(7/900) days, 365/05:48:48.
>Exigius's (and my[Carrier]) Year, 365+(31/128) days, 365/05:48:45.
While Chris Carrier's conclusion still, APPARENTLY, holds:
>So the Exigian or Soviet year is more accurate, even against the vernal
>equinox, than the Gregorian year over a 2800 year run, which we are a
>little past the middle of.
this is only because he has centered his 2800 years on 1600 A.D. instead of the present century, and because he has ignored the Delta-T correction necessary to translate ephemeris days into REAL calendrical Universal days.
If we consult Meeus 1995, where he redoes his tables in the more accurate Dynamical Time of current astronomers, and gives (on page 7) appropriate Delta-T corrections for finding Universal time from the new Dynamical times, we obtain the following results, using Chris' method, for the same 2800 year period, ca. 1600AD, in real calendrical Universal days.
365d 5h 48m 59.2s for the March equinox. [or 365.242352 Universal days]
365d 5h 48m 0.5s for the June solstice. [or 365.241673 Universal days]
365d 5h 48m 41.2s for the September equinox. [ 365.242143 Universal days]
365d 5h 49m 37.5s for the December solstice. [ 365.242795 Universal days]
which demonstrates that even circa 1600 A.D. the V.E. year was 365.2424 days (Dee's year to the nearest ten-thousandth of a day) and that the Gregorian mean year was more accurate than the Exigian mean calendar year, on its own, Nicene, terms!
Furthermore if we compare these four values ca. 1600 AD with those for the 2000 year period, (1000 AD to 3000 AD), ca. 2000 AD, using the same method, we get:
365d 5h 48m 59.6s for the March equinox. [or 365.242357 Universal days] 365d 5h 47m 56.1s for the June solstice. [or 365.241621 Universal days] 365d 5h 48m 29.1s for the September equinox. [ 365.242003 Universal days] 365d 5h 49m 30.5s for the December solstice. [ 365.242714 Universal days]
which demonstrates that the Vernal Equinox year length is relatively constant compared to the other three values, and is thus to be preferred for regulating solar calendars that use a fixed mean calendar year-length!
The slow upward trend of the Vernal Equinox year-length (when averaged over a couple of millenia) will continue to make the Dee Calendar-Year ever more accurate in the centuries ahead, thus making it (the Stonehenge-Khayyam-Dee year-length) the preferable mean calendar year of all candidates proposed to date.
An average taken over a period of a few decades (rather than centuries or millenia) reveals a small perturbation of the year-length with a period of about 240 years and an amplitude of about 0.00002 days. This and the non-linearity of the function being averaged conspire to make the average Vernal Equinox year-length be 365.24237 Universal days, ca. 1923 AD. (when the Greek Orthodox church adopted the "Soviet" mean calendar year-length) thus vindicating my assertion that the Gregorian year-length is more accurate than the Soviet (Greek Orthodox) value on their own Nicene terms! The average length of the Vernal Equinox year is currently 365.24238 days (to the mearest one-hundred-thousandth of a day) and will probably only ever drop below the mean betwen the Gregorian and Orthodox value for a brief few decades after 2060 AD. The Dee value will, of course, continue to be superior to both these for the foreseeable future.
--
Dee's Yrs, Simon Cassidy, 1053 47th.St. Emeryville Ca.94608. ph.510-547-0684.