[Avodah] Interval between Tal and Geshem

[Micha Berger]

On Tue, Mar 13, 2018 at 06:06:22PM -0500, hankman via Avodah wrote:
: Tephilas Tal is done on the 1st day of Pessach while Geshem is done
: on Shmini Atzeret...                  I wonder if there may also be an
: astronomical reason as well. Since the earth's orbit is elliptical and
: the velocity of the planet varies with the season. The result is that
: the "half year" from spring equinox through summer to the fall equinox,
: is about 7-8 days longer than the "half year" from the fall equinox
: through the winter back to the spring equinox...

Brilliant!

A problem is, our tefillos aren't even as precise as our years. We use
Tequfas Shemu'el for davening (at least for Birkhas haShanim in chu"l
and for Birkhs haChamah), and Tequfas R' Adda for calendar calculations.
You are assuming more precision than we see evidenced as a goal for chazal.

OTOH, if the precision doesn't add to the complexity of implementation,
why not? We generally use Tequfas Shemi'el for davening because a simple
365-1/4 day year can be implemented by the masses. Whereas we only need
the Sanhedrin (or their proxy, but still not everyone) to be capable
of making the calendar. This rule, based on Jewish calendar dates,
is easy to implement AND more accurate. So perhaps.

Well, more accurate on average. We're talking about 7-8 days
in contrast to the 11 day average slippage of a regular year,
or the 22+ days of a me'uberes.

http://farside.ph.utexas.edu/Books/Syntaxis/Almagest/node36.html
spells out your application of Keppler's Law and concludes:
> ... Thus, the length of spring is 92.8 days, the length of summer 93.6
> days, and the length of autumn 89.9 days. Finally, the length of winter is
> the length of the tropical year (i.e., the time period between successive
> vernal equinoxes), which is 360/0.98564735 = 325.24 days, minus the
> sum of the lengths of the other three seasons. This gives 88.9 days.

Adding Spring and Summer, we get 186.4 days for the dry season, and
similar addition yields 178.8 days for the rainy one. A difference of
7.6 days, as stated.

However, Mar 21 to Sep 21 is only 3 more days than Sep 21 to Mar 21. Which
is why I was looking at the math.


Tir'u baTov!
-Micha

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Micha Berger             When one truly looks at everyone's good side,
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