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Although often associated with the Winter Solstice, Tekufas Teves is an independent date. How is Tekufas Teves, or the other Tekufos (?) determined?

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Who said it's an independent date? – Double AA♦ Dec 27 '11 at 5:48
Well, for one the winter solstice is passed and we are only now entering Teves. – Yirmeyahu Dec 27 '11 at 6:02
Maybe our calculation of the solstice has drifted. – Double AA♦ Dec 27 '11 at 6:03

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Tekufot are the solar equinoxes and solstices. To calculate the tekufa, you must know that the sun was created at 6 pm on Tuesday of year 1 of creation (ie the beginning of the fourth day). The, add 91 days 7.5 hours to get the next tekufah and so on. This number is considered one fourth of a solar year of length 365.25 days. Since a solar year is actually 365.242581 days, our calculated tekufa shifts forward ever so slightly every time.

Sources: here and here

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+1. But should be 91 days and 7.5 hours. – Alex Dec 27 '11 at 16:03
@Alex Yes thank you, my bad. Corrected! – Double AA♦ Dec 27 '11 at 16:06
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There are actually two different calculations used in Jewish literature for the tekufos. (They are described in Rambam's Hilchos Kiddush Hachodesh, chs. 9 and 10.)

The one that DoubleAA described is called Shmuel's tekufah, and it is the one used for most halachic purposes, including the date when we start saying "vesein tal umatar" outside of Israel, and the date of Birkas Hachammah. Its starting point is indeed Tuesday night at 6 PM, but actually the date is 22 Adar of the year 1, which is not the time of the sun's creation. (Shmuel agrees with the opinion of R. Eliezer, that the world was created in Tishrei - i.e., beginning on 25 Elul and ending with Adam's creation on 1 Tishrei; on that assumption the sun would have been created on 28 Elul, a Wednesday, and that tekufah would have occurred at 9 AM. Calculating backwards two tekufos, 182 days and 15 hours, gets us back to 22 Adar at 6 PM.)

There is also Rav Adda's tekufah, which assumes that a solar year is exactly 1/19 of a machzor katan (19 Jewish years, containing 235 lunar months). This comes out to 365.246822 days - which is somewhat more accurate than Shmuel's value, but still gains about 4.5 days per millennium, which is why the dates of the Yamim Tovim slowly move later in the secular year. The first tekufah for this calculation is also Tuesday at 6 PM, but a week later than Shmuel's - on 29 Adar (because he holds with R. Yehoshua that the world was created in Nissan). Because R. Adda's year is shorter than Shmuel's, nowadays his tekufah is about 11 days earlier.

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Indeed. But is there any Halachik significance to the date of R Ada's tekufa? It seems we "paskin" like Shmuel for all matters relating to tekufot. – Double AA♦ Dec 27 '11 at 19:31
@DoubleAA, there is one big one: we use R. Adda's tekufah to determine when a leap year is and isn't needed. (Shmuel's tekufas Nissan can be almost at the end of Nissan nowadays, whereas R. Adda's is never later than the second day of Pesach.) – Alex Dec 27 '11 at 23:34
I think that logic is backwards. Are you suggesting that Shmuel had different leap years than R Ada? Rather, there was an existing leap year cycle of 19 years because it was a round number. R Ada said to use that calculation for other matters relating to tekufot, while Shmuel said to use the simplified 91.25 to make the remaining calculations more accessible to all Jews. See also Igrot Moshe OC 4:17 – Double AA♦ Dec 28 '11 at 2:23
@DoubleAA, I hear you. But why indeed shouldn't Shmuel's layout of leap years be different than R. Adda's? Both of them lived at a time when the fixed calendar wasn't yet in use. Had Shmuel been around a century later, when Hillel Hanassi was putting together our calendar, he might well have said that the arrangement of 7 leap months in every 19 years is generally fine, but that every so often it needs an adjustment. – Alex Dec 28 '11 at 15:55

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