PM 2Ring wrote:Brian-M wrote:The mean tropical year is measured at 365.24219 days, but is gradually getting smaller because the slowing of the earth's rotation is making the days longer. This means that in the long-run my system would be more accurate than either of those proposals.

In discussions like this one the mean Gregorian year length is often compared to the mean tropical year. However, that comparison may not be appropriate. The Gregorian calendar was created to stabilise the date of Easter, which is tied to the date of the (northern hemisphere) spring equinox. So rather than using the mean tropical year we should be using the vernal equinox year, which is (to 6 decimal places) 365.242374 days.

Astronomer

Duncan Steel has discussed this point in several publications, including his popular book

Marking Time: The Epic Quest to Invent the Perfect Calendar. Here's a short PDF that summarises his argument:

The proper length of a calendar year. There's also some interesting information in his story about the the non-implemented

33-year English Protestant Calendar; there are further details of this intriguing theory in

Marking Time.

Wikipedia

defines the tropical year as the vernal equinox year, and then proceeds to give the traditional 365.24219 figure. I am not exactly sure how is the 365.242374 supposed to work - are the March and September equinoxes getting closer to each other?

[EDIT: I've found the citation, also in Wikipedia; if those figures are correct, chances are it's probably a cyclical thing, and 365.24219 is what happens when we smooth those cycles away.]

In any case, true March equinox years

float by as much as 30 minutes (about 0.02 days), so any "mean year" definition would have to average it in a

very long period. I'm not sure whether a figure "to six decimal places" even makes sense - the length of a year in mean solar days (which would be equivalent to calendar days assuming continuing application of leap seconds) decreases by about a second (or 0.00001 days) per century.

I do somewhat like the idea of a 33-year calendar keeping the equinox on the same GMT-5 day. (Reminds me of the Sothic cycle and its relationship to the Julian calendar.)

But I still think that a 128-year cycle would be more convenient (especially on modern binary-based computers, where it corresponds to a year 16D.3E

_{16} days long), and it happens to be a lot closer to the modern mean tropical year (exact in SI days as of April 5, 2035, if I interpreted the Wikipedia formula correctly; not sure when, if ever, it was or will be exact in mean solar days).

[EDIT: fixed my hexadecimal math]

[EDIT 2: fixed it incorrectly, so fixed again]

[EDIT 3: added the edit notices]