From: Jerome Fine [jhfine@idirect.com]
Sent: Wednesday, November 15, 2000 10:29 PM
To: Info-VAX@Mvb.Saic.Com
Subject: Forcasting the Tropical Year - the Laskar expression?

Considering the case sensitivity posts over the last few days,
these news groups seems like a reasonable place to pose
a question about the use of the Laskar (1986) expression which
http://astro.nmsu.edu/~lhuber/leaphist.html
http://www.treasure-troves.com/astro/TropicalYear.html
provides an estimate of how the Tropical Year will change
in the future.  In addition, the relatively new use of Leap
http://www.treasure-troves.com/astro/LeapSecond.html
Seconds starting about 27 years ago may also have a strong
influence in the future on the essential results of this inquiry.

More specifically, I am requesting help on evaluating just
how the decrease in the Tropical Year from its current value
of 365.242190 days or 365 days, 5 hours, 48 minutes,
45.2 seconds will affect the number of leap years needed
in the future.  In addition, the use of Leap Seconds may
also have a significant effect in future years in respect to
how many leap years are omitted form the current Common
Era (Gregorian) calendar.

Now, a quick simple calculation using the present difference
of 11 minutes and 14.8 seconds per year over 400 years
shows that 3.124 days are extra leap years in the Julian
calendar and the even with the Gregorian modification, there
are still 0.124 extra days for each 400 years or 0.62 days
in 2000 years.

Consequently,  there will probably be insufficient drift between
the present Common Era calendar and the actual Tropical
Year to require any additional leap years (beyond the 3 per
400 years that the Gregory modification stipulates) to be
omitted for about 2000 years until 4000 C.E., so we should
all realize that the whole topic is not going to have an overriding
impact on our present situation.

Do you know of anyone who has done an actual evaluation
of the leap year situation in the future?  My initial calculations
using the Laskar expression suggest that both 4000 C.E. and
6000 C.E. should not be leap years, but thereafter, I can see
where I have made some errors which may be quite substantial.

Plus, it really seems unlikely that the Laskar expression will
be accurate for such a long time into the future.  If it does,
a very rough calculation indicates that the Tropical Year
will reach a minimum value in about 8,900 years and start
to increase thereafter - around the year 10,900 C.E.

Still, the key question concerns the possibility of whether
Leap Seconds add to the drift or decrease the drift.  My
own intuition is inclined to assume that Leap Seconds
are a substitute for leap days and that the drift will increase,
unless some overly capable beings in this vicinity decide
that just for fun the solar day should again be exactly
86,400 seconds, hopefully by a non-destructive and
environmentally friendly method.

And finally, the actual goal of the exercise is to be able
to write some code which can be used for a long time
into the future, as opposed to calendars which still
assume a constant Tropical Year along with the inaccurate
Gregorian calendar.  Based on the above information,
I feel it should be possible, at the very least, to establish
a minimum and maximum bound for the number of extra
leap years to be omitted over a limited period of time
into the future, such as 32,000 years.  If the minimum
number over any 400 year cycle is -3 (i.e. all of the extra
leap years removed during the Gregorian modification
from the Julian calendar must be restored) and the maximum
number is +97 (i.e. all remaining leap years in the 400 year
cycle must be removed), then it should actually be relatively
straightforward to produce code which allows an accurate
date/time to be calculated based on a specified number of
elapsed seconds between any other date/time within the
target window of 32,000 years.  Obviously a table of
actual used Leap Seconds would be needed along with
a predicted set of Leap Seconds into the future.  In addition,
the same sort of table would be needed for leap years
that differ from the Common Era (Gregorian) calendar.
Naturally, the table for omitted leap years can only be
a predicted table at present.  AND, developers of code
which predicts date/time conversions would be required
to remind users that future date/time conversions will
depend on the accuracy of the values predicted in the
table that the user provides.

Any ideas would be appreciated.

Sincerely yours,

Jerome Fine