On Shemini Atzeret, we begin reciting in the Amida "mashib ha-ruach umorid ha-geshem" praising HaShem for creating and directing the mechanism of precipitation (=rain). But we still refrain from asking haShem to give us rain for our plants.
In Israel, because although, after Shemini Atzeret it is a time for rain, we postpone the prayer for rain until the travelers who had made the pilgrimage to Jerusalem to celebrate Sukkot and Shemini Atzeret, are finally back home. For them rain is not going to be a blessing.
In Israel, therefore, even in our days, Jews start praying for rain two weeks after Shemini Atzeret, on the evening of the seventh of Cheshvan.
In Babylonia, at the time this disposition was established, the Jews who lived there did not need the rain so early, so the Rabbis ruled that in Babylonia the Jews would begin praying for rain on the 60th day of the season of (tequfat) Tishri, or the "Hebrew calendar autumn".
The Rabbis gave an easy round number for determining the beginning of each Hebrew calendar season. A season consists of exactly 91 days 7 hours and 30 minutes. This makes each year exactly 365 days and 6 hours long, about 11 minutes longer than the actual astronomical calculation of a solar year.
Jews who live outside of Israel, follow the practice of the Jews of Babylonia. Therefore, it has become tradition for all Jews who live in the Diaspora to start asking for rain in their prayers as the Babylonian Jews did.
Based on this calculation, this year, 2011, we will switch to 'Barekh Alenu' tonight, December 5th, in our Arbit prayer.
(Thanks to Mr. Mehran Etessami --our community expert in Hebrew calendar calculations-- for his help with this HOTD)
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