More Discussions for this daf
1. The date of the equinox which we follow for Halachic matters 2. Adding a day to the year every 100 years 3. Shmuel's Tekufah
4. Tekufas Shmuel, Tal u'Matar 5. Avudraham 6. Learning while Walking
7. Southern Hemisphere 8. Rav in Eretz Yisrael
DAF DISCUSSIONS - TA'ANIS 10

Aaron Gal asked:

Harav, Shalom

I read that in the period of Abudaraham, they used the Julian Calendar; and the Abudaraham mentioned when to start asking for Rain based on this Calendar (I think he said Nov 22). My question is, what about the period of the Amoraim? How did they know when the tekufa is. Did they use the Julian Calendar as well?

Todah,

Aaron Gal, Fair Lawn, NJ, USA

The Kollel replies:

Chazal had their own calculation of the solar year and did not need to rely on anyone else for their calendar. The Rambam in Hilchos Kidush ha'Chodesh (Perek 10) explains how to calculate the Tekufah. Here is a brief step by step guide:

(1) There are four Tekufos in a solar year (called Tekufas Nisan, Tekufas Tamuz, Tekufas Tishrei and Tekufas Teves).

(2) Each solar year has a duration of three hundred and sixty five days, five hours, nine hundred and ninety seven Chalakim (parts of 1080 in an hour) and forty eight seconds (a second being one seventy sixth of a Chelek).

(3) Each Tekufah is exactly a quarter of the solar year: ninety one days, seven hours, five hundred and nineteen Chalakim and thirty one seconds. (The start of each Tekufah can be observed visually according to the position of the sun in relation to the relevant signs of the zodiac [see Rambam ibid. 9:3].)

(4) Each regular lunar year has three hundred and fifty four days, eight hours and eight hundred and seventy six Chalakim. A lunar leap year has three hundred and eighty three days, twenty one hours and five hundred and eighty nine Chalakim.

(5) Each cycle of nineteen lunar years is composed of twelve regular years and seven leap years, making a total of six thousand nine hundred and thirty nine days, sixteen hours and five hundred and ninety five Chalakim.

(6) Each solar cycle of nineteen years will have exactly the same duration.

(7) The first Tekufah, Nisan in the year of creation, fell nine hours and six hundred and forty two Chalakim before the Molad of that Nissan.

(8) Therefore, at the start of every nineteen year cycle the Tekufah falls at the same time stated in (7).

(9) If one wishes to know the time of the start of a Tekufah in a given year after creation, one must calculate how many of the nineteen years have passed in the Machzor, and add the required number of Tekufos and one will arrive at the correct date and time (hopefully!).

For example, this year (5767) is the tenth year in the three hundred and fourth cycle (5767/19 = 303.526, and 0.52631*19 = 10). So one must add ten times four (Tekufos in a year), times the length of each Tekufah, and add this to the date when the Machzor started (nine hours and the remainder before the Molad of Nisan ten years ago).

Dov Freedman