Calendar – calculating length of year II

Equinox-90In a previous article, we discussed how the Pope was forced to strike ten days off the old calendar, established by Julius Caesar (the Julian calendar), because the 365¼-day year used until then was about eleven minutes too long. There was a danger that Easter, which is supposed to be commemorated the same time as Pesach, would start falling in the middle of summer and not in springtime. We also explained that, if one observes the position of the stars, it takes about 365¼ days for the earth to get back under the same star. This is called a sidereal (relating to the stars) year. But, “unfortunately,” since the world has a very slow “forward wobble” (it makes one wobble every 26,000 years), the world arrives under its star about eleven minutes early every year.

The year that is eleven minutes shorter than the sidereal year is known as the “tropical year.” The seasons go according to the tropical year and that is why anyone going according to the sidereal year will find the summer months slowly but surely moving back towards winter at the rate of one day every 128 years. This is why the Pope knocked ten days off the calendar a few centuries ago and introduced a new calendar with shorter, tropical years.

Every society on earth accepted the Pope’s new calendar with two exceptions – certain East Orthodox Christians who, on principle, refused to accept anything the Catholic Pope decreed even if it made sense, and the Jewish people who still cling to the old sidereal year of 365¼ days in connection with two well-known halachos.

One of these is Birkas HaChamah, the blessing we say every twenty-eight years at the end of the Machzor HaGadol (the Great Cycle) when the tekufah (season) of Nisan (spring) begins at the same hour and on the same day of the week (Tuesday 6 p.m.) that it began during the week of Creation. During Creation, the luach (the Jewish calendar) began at the moment when the sun and the moon were placed in the sky at the beginning of Wednesday, the first day of spring (Tekufas Nisan).

As the Gemara says: “Someone who sees the sun at the beginning of its cycle should say the blessing, ‘Blessed is the Maker of Creation.’ When does this happen? Abaye said, ‘Every twenty-eight years the cycle begins again and the Nisan equinox falls in Saturn, on the evening of Tuesday, the night before Wednesday’” (Berachos 59b).

This 28-year calculation is based on the sidereal year of 365¼ days since it takes twenty-eight years to even out all the ‘quarter days’ and get the beginning of the year back to Tuesday 6 p.m. This calculation would never work with a tropical year because its fractional days would take thousands of years to add up to exactly a week.

The second way we use the old Julian calendar is when we begin davening for rain in the Diaspora in accordance with the Gemara’s instruction (Taanis 10a) to begin saying Birkas Geshamim sixty days after the beginning of fall. We usually start doing this on the 5th or 6th of December, sixty days after the beginning of fall, around October 4. The trouble is that modern astronomy places the beginning of fall about twelve days earlier, on September 23. The discrepancy is caused by the fact that we are still going according to the old Julian calendar that is currently running twelve days later than the modern calendar instituted by the Pope.

Many people have written to Poskim and asked them: Why are we going according to a year that is eleven minutes out of sync? Why do we not bring things up to date?

The Chazon Ish (Orach Chaim 138:4) answers that the Torah is not always particular to use a precise measure and sometimes simplifies things so that uneducated people have no problem making the necessary calculation, and the same applies here. He adds that the decision to sometimes use the simpler year length is not arbitrary but from a tradition going back to Sinai.

For the past few centuries, people noticed an even bigger mystery. The day on which we say Birkas HaChamah every twentyeight years is the first day of tekufas Nisan (spring). This began on Rosh Chodesh Nisan at the time of Creation. But if so, why does Pesach, which starts on the fifteenth of Nisan, sometimes begin before we say Birkas HaChamah? How can this be if Birkas HaChamah is supposed to commemorate the first of Nisan?

Furthermore, unlike the Pope who was informed that Easter was drifting forwards towards summer, we, lehavdil, have no such problem. On the contrary, Pesach is slowly drifting backwards towards winter (although not fast enough to cause concern.) Why did we not end up with this headache as well?

Rav Avraham bar Chiya HaNasi, who lived shortly before the Rambam, discusses this problem in his Sefer HaIbur. He explains that we use two different kinds of solar years at the same time. As we discussed earlier, we use the simple Julian year of 365¼ days for Birkas HaChamah and Birkas Geshamim. This “revealed” year length was established by Shmuel (c. 3195/165- 4014/254).

However, the year length used to establish Pesach, which Rav Avraham calls the “hidden” Tekufas Rav Adda is almost identical in length to the modern tropical solar years of our time. So it turns out that we have been using the correct year all along. This “hidden” year was used by Hillel II when he created our static calendar. Until his time, the Nasi and Sanhedrin in Eretz Yisroel determined the months and leap years by physical observation of the moon and the seasons. In Hillel II’s time, however, the Jews rebelled against the Roman Emperor Gallus and his commander Ursicunus, which resulted in many Jewish communities, including Tzippori, Teveriah and Lud, being destroyed. Harsh new decrees were enacted to weaken the Jews’ internal authority and the observance of mitzvos and attempts were made to curtail the power of the Nasi and Sanhedrin.

Against this backdrop, Hillel II established a fixed calendar that would basically run itself until the Mashiach comes. Thus the Ramban writes in Sefer HaZechus (Gittin ch. 4): “From the time of Hillel… in the year 670 of the Seuclid era (4145/385), the Sanhedrin in Eretz Yisroel was terminated and ceased to have experts, and it was [Hillel II] who regulated the order of intercalation (leap years), reckoned the years, and fixed the months for generations to come.”

How has Hillel II’s calendar managed to keep the chagim on track so accurately for over 1,500 years? The chief element of his calendar is what is known as the Machzor HaKatan (the Metonic Cycle). As Rabban Gamliel tells us in Rosh Hashanah, the average month length is 29.53058 days. Interestingly, nineteen modern tropical years almost exactly equal 235 such average months. (The calculation is as follows: 29.53058 days x 235 months = 6,939.68 days; 365.24219 days x 19 years = 6,939.601days.) Thus, by having a nineteenyear cycle of 235 months (which equals nineteen lunar years of 12 or 13 months each), the chagim and solar years stay comfortably in sync, not quite ad infinitum but, at least, until the Mashiach comes and the Sanhedrin is reestablished.

Except for a one-time controversy in the time of Rav Saadya Gaon, this calendar has been running without a hitch for the past fifteen centuries.

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