Sacha Stern is widely regarded as the expert in the Jewish Calendar. He has aggregated an encyclopedia of sources pertaining to the Jewish Calendar in the period of second century BCE to tenth century CE. Yet his focus on his translation of the Exilarch's Letter of 835/6 CE as proof that a calculated calendar had yet to be implemented is flawed.
This quote is from page 184-5 of his book Calendar and Community.
"Of far greater importance, however, is a much later document from the Cairo Geniza: a letter of a Babylonian exilarch - one of the main leaders of the Rabbanite community - with detailed calendrical instructions for the year 835/6 CE. The letter reveals that Passover (15 Nisan) in that year was due to occur on a Tuesday; whilst according to the present-day rabbinic calendar, it should have occurred on Thursday. According to the exilarch, the setting of Passover on Tuesday was dictated by a concern to avoid visibility of the new moon before the first day of the month. This concern does not exist in the present-day rabbinic calendar.
Once discovered and published in 1922, the exilarch's letter proved beyond doubt that almost five hundred years after R.Yose and 'Hillel the Patriarch', then fixed calendar in its present-day form had still not been instituted."
Now let us examine the calendar facts and see how they affect understanding the exilarch's letter.
The Molad of Tishrei for 835 CE was Friday, August 27, at 22 hours and 660 parts (4:36 PM). The year 835CE was the seventeenth year of the cycle and thus a leap year. The Molad for Tishrei for 836 CE was Thursday, September 14, at 20 hours and 169 parts (2:09 PM). According to present rules both days are subject to the Dehiyya Molad Zaqen. The year 836 CE would then receive a further Dehiyya due to the rule Lo ADU Rosh. This would make 835 CE have a year length of 385 days starting on Saturday. Basic apportionment of days to months would be Tishrei 30, Cheshvan 30, Kislev 30, Tevet 29, Shvat 30, Adar I 30, Adar II 29, for a total of 208 days. Thus Rosh Chodesh Nisan would fall on Thursday, March 23, 0836 and Passover would also fall on Thursday.
The lunar conjunction for Tishrei was August 27, 20:40 in Israel. The Old Moon at sunrise on Erev Rosh HaShanah would be 38 hours and 43 minutes from the conjunction, a very visible Old Moon! We know from the Exilach's Letter that he was deferring to Israel in calendar matters. Question remains did not the people believe that the calendar was being based on witnesses. During the 9th Century the Karaites were in their ascendancy and constituted a significant threat to Rabbinical Judaism. at this time, believed that the Torah mandated witnesses to establish the new month, The Exilarch had good reason to be concerned as to how this would play out at Passover.
In Baghdad the lunar conjunction occurred Tuesday, Mar 21, 836 CE at 5:16. As this chart clearly shows the New Moon would not be visible in Baghdad nor in Israel on Tuesday. In Baghdad the New Moon would be first visible on Wednesday evening after the sun sets at 18:19, in Israel after the sun sets at 17:55.
The Molad for Nisan 836 CE was Tuesday, March 21, at 15 hours and 811 parts. However, the Molads of months other than Tishrei are not used in the Hebrew Calendar Calculation. None the less in this case Israel actually established the Nisan as starting Tuesday, Mar 21, 836 CE.
Sacha Stern tells us that this has something to do with a calendar rule of which we have no knowledge because the visibility of the New Moon before Rosh Chodesh. This "proved" that Israel was using a different system then we use today.
What I believeThe source of Sacha Stern's error is his misunderstanding of this moon that was sighted being the New Moon. Actually it was the Old Moon. His false assumption that this calendar court in Israel was using the dehiyyot. And his forgetting that the prominent issue of this period was the conflict of the Exilarch and rabbis in Bavel with the Karites.
Let is restart this analysis.
Neither the Dehiyya Molad Zaqen nor the Dehiyya Lo Adu Rosh (at least for yom Shlishi) were being implemented by the Calendrical Court in Israel. The Molad of Tishrei for 835 CE was Friday, August 27, at 22 hours and 660 parts (4:36 PM). The year 835CE was the seventeenth year of the cycle and thus a leap year. Rosh HaShanah 836 Ce would be Thursday, September 14, 0836. Basic apportionment of days to months would be Tishrei 30, Cheshvan 29, Kislev 30, Tevet 29, Shvat 30, Adar I 30, Adar II 29, for a total of 207 days. Thus Rosh Chodesh Nisan would fall on Tuesday, March 21, 0836, and Passover would also fall on Tuesday.
Erev Rosh HaShanah, in Israel, the Old Moon rose at 3:29 AM at 3.8% visibility and 41 hours and 45 minutes to the conjunction. This was clearly visible in the predawn sky. No doubt the Karites were able to capitalize on this apparent failure of the rabbinic calendar. They maintained that actual witnesses must be used. Surely in Bavel where the battle with the Karites was intense there was no joy with this reality. Bavel wanted Israel to adopt the dehiiyyot to bring the calculated calendar more in line with the appearance of the moon. Certainly they did not want the Old Moon to be seen on the morning when we would start the new month.
The Exilarch's concern was about a visible Old Moon, not the New Moon. The real problem was Monday morning March 20 when the Old Moon rose at 5:00 AM 38 minutes before sunrise. That evening Nisan would begin. This is the classic case of Rabbi Yohanan ben Nuri "if the old moon appears in the morning, the new moon doesn't appear in the evening". It was the possibility of sighting the Old Moon, not the New Moon, that concerned the Exilarch. Because such a sighting would aid the Karites in proving that the rabbis were not properly observing Passover at the correct time.
The Exilarch was in a major battle with the Karites at this time and a visible Old Moon was very helpful to the Karites against the Rabbis. No doubt Bavel wanted Israel to adopt the Molad Zaqen rule. As we will soon explore this was the motive of Saadia in his fight with Ben Meir.