What is a year, but that by any other name 'twould be as long.

> Date:         Mon, 30 Aug 1999 13:13:23 +0200
> From: Christophe Grandsire <grandsir@...>
> Hese Kiel wrote:
> > need no exact year length just remember this:
> > year needs 365 days.
> > 4 years (=3Done section) need one extra day.
> > every 26th section (a 4 years) leave the extra day off.
>=20
>         I already know that. It's the Gregorian calendar, the one we alre=
ady
> use and the one that will cause the year 2000 not to be a bissextile
> year (problem that leads to a second Y2K bug on the 1st of March 2000,
> as many computers will think they are the 29th of February). What I need
> is the exact length of the year to build my own calendar which will be
> different. Thank you in advance.
Ummm... it's the other way around. 1900 wasn't a leap year, but 2000
is. So the bug will occur on February 29 2000, when a lot of programs
will think it's March 1.

Anyway, the current best estimate of the length of the tropical year,
measured in days of 24 hours, is 365.2421897 with a current decreasing
trend of 6.152e-6 such days per century.

However, for calendar purposes you want to express the length of the
year in terms of the number of sunrises that happen. The rotation of
the Earth is slower than this 24-hour day (about 1.3 seconds/year),
and it's slowing further (about .6 seconds/year/century); civilian
timekeeping is adjusted (using leap seconds) to keep the sun rising at
the appropriate time.

With this adjustment, we get something like 365.2421746 =B1 .000007
`solar days' in a tropical year, with a decreasing trend of 13e-6 such
days per century. It's illustrative to express this in terms of a 4000
year period, since this seems to be a popular period for calendar
construction:

        Days in CE years    1 to 4000, inclusive: 1460968.7 =B1 .1
        Days in CE years 4001 to 8000, inclusive: 1460966.6 =B1 .2

(I may even have underestimated the error term for the rotation of the
Earth, which is the main contributor to the overall error. The trend I
used is the estimate for tidal braking; there are medium-term (1000y)
fluctuations too, caused by unpredictable movements in the interior of
the planet; they may well contribute a random deviation of a day or
two during any 4000 year period).

The Gregorian calendar has 1460970 days in 4000 years; as can be seen,
the proposed adjustment of leaving out the leap day in years divisible
by 4000 will only be adequate the first time around; stronger measures
will be required later.

In other words: Earth cannot have a perpetual calendar.

Lars Mathiesen (U of Copenhagen CS Dep) <thorinn@...> (Humour NOT marke=
d)