Sanhedrin 11b ~ The Tekufot

The Jewish leap year

The Jewish year usually contains twelve lunar months. In today's page of Talmud we learn the reasons that the rabbis may add an extra month to the Jewish calendar, and proclaim a thirteen month leap year:

סנהדרין יא, ב

תנו רבנן על שלשה דברים מעברין את השנה על האביב ועל פירות האילן ועל התקופה על שנים מהן מעברין ועל אחד מהן אין מעברין

The rabbis taught in a Baraisa. We may intercalate a month and declare a leap year on account of three things: On account of the grain's ripening after the month of Nissan, on account of the fruit ripening after Shavuot, and on account of a season [tekufah] that is scheduled to begin in the wrong calendar month. We intercalate the year if two of these reasons are present, but for just one of these reasons we do not intercalate.

Let's look at the last reason. If the season is scheduled to being in 'the wrong month', the rabbis adjust the length of the year to bring it back into line.  Pesach must always fall in the Spring, so if the 15th of Nissan is part of the season of winter, we add another lunar month to the previous year and so push Pesach into Spring. 

The Solar Year, according to Shmuel

Here is the thinking behind this.  The rabbis of the Talmud, led by Shmuel, believed that a solar year was 365.25 days long, or 365 days and 6 hours. No more and no less. (This is also the length of the Julian calendar, adopted by Rome and all of Europe, including the Catholic Church.  It was the prevailing calendar in Europe, so Shmuel was in good company. ) Shmuel also believed that each of the four seasons was precisely one quarter the length of the solar year, or 91 days and 7.5 hours. Jewish tradition taught that the Sun was created on what would have been a Tuesday at 6pm. This time was also considered by the rabbis to have been the vernal equinox and the start of  Spring in the first year of creation.  Summer would therefore have started 91 days and 7.5 hours later, and fall another 91 days and seven hours after that.  The cycle repeats itself every 4 years, at which time the start of Spring will once again be at precisely 6pm, though not on a Tuesday. (It takes 28 years for the start of Spring to once again fall on a Tuesday at 6pm - and the next day is when we celebrate the rare event of Birkat Hachama. But I digress.)

Two Problems with Shmuel's Jewish Calendar

The first problem is that the solar year is not exactly 365 days and 6 hours in length. In fact it is 365 days, 5 hours, 48 minutes and 46 seconds - or 11 minutes and 14 seconds shorter than the Julian/Talmudic year. That's a small difference to be sure, but it adds up to three days every 400 years.  As a result of this difference, Spring, as measured by the day of the equinox, kept falling behind. In the days of Julius Caesar it had started on March 21, but by 1582 it had fallen behind and coincided with March 11. To bring the calendar back on track, Pope Gregory XIII knocked ten days out of the calendar, declaring the day after October 4, 1582 to be October 15th.  He also instituted a leap year of one extra day every four years, (except for years divisible by 100).  Shmuel's calendar had no similar fix, and the start of Spring in that calendar is about two weeks away from the actual, measurable Spring equinox.  

Path of the sun as seen over the northern hemisphere. On June 21, the start of summer the sun is at its most northern position. On Dec 21, the start of winter, it is at its most southern position.    

Path of the sun as seen over the northern hemisphere. On June 21, the start of summer the sun is at its most northern position. On Dec 21, the start of winter, it is at its most southern position.    


A second problem with Shmuel's calculation of the four seasons is that he attributed the same length to each, when in fact the seasons are not of equal length. This is because the earth does not revolve around the sun in a perfect circle, but instead has an elliptical orbit.  When the earth is closer to the sun it speeds up, and when it is further away it slows down.  In fact not one of the four seasons are 91 days and 7.5 hours in length. Here are the actual lengths:

Spring - about 92 days

Summer  - about 93 days

Fall - about 90 days

Winter - about 89 days

Shmuel's orderly system has no astronomical basis, and his seasons do not follow an orderly and predictable pattern. If you were to ask, "what happens in the sky at the beginning of Spring according to Shmuel?"the correct answer is nothing.  If you were to ask the same question of the actual day and time on which Spring begins, the answer would be "on that day and at that precise moment, the tilt of the earth's axis is exactly perpendicular to the sun."

Here are the actual start days of the seasons for this year, and their start according to the calendar of Shmuel.  

Start of the Seasons
Season Astronomical Shmuel
Times are for Jerusalem
Spring March 20
6:29 A.M. EDT
April 7
Summer June 21
12:24 A.M. EDT
July 8
10.30 AM
Fall September 22
4:02 P.M. EDT
Oct 7
Winter Dec 21
11:28 A.M. EST
Jan 6

Shmuel's calendar is pretty accurate, but over time, small discrepancies become larger.  Pope Gregory instituted a fix, but we have yet to do so. By not tweaking our Jewish calendar, the average date of the first day of Pesach is one day later every 216 years compared to the Sun, and one day every 231 years compared to the Gregorian date. This may not seem like a problem now.  But around the year 15,000 CE [sic] the first day of Pesach will occur on June 22, which is clearly not in the Spring. But I guess by then it will be somebody else's problem to fix.

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