When the new moon first appears in the sky, that night (and the next day) is Rosh Chodesh - the first day of the new month. If the new moon appears on the thirtieth night (i.e. the night before the thirtieth day) then the old month is twenty-nine days long. If the new moon appears on the thirty-first night then the old month is thirty days long.
The Chachamim had remarkably accurate mathematical models to predict precisely when the new moon was due to appear each month. The Chachamim from the tribe of Issaschar were particularly renowned for being experts in astronomy15. However, the Beit Din decided what day was Rosh Chodesh based on witnesses who actually saw the new moon and came to to testify. Why then did the Chachamim need their mathematical models?
There are at least 3 reasons.
Firstly, in our time we do not have a Beit Din that is qualified to receive the testimony of witnesses. Therefore, we are forced to rely on a fixed calendar that is calculated based on those mathematical models. In fact, today we are still using the calendar that was calculated by Hillel II about 1600 years ago.
Secondly, the Beit Din would test the witnesses by asking them various questions16. Through using the mathematical models the Beit Din could calculate at what time the new moon would appear, where it would be located in the sky and which way the crescent would be facing. By asking each witness some basic questions about the moon’s appearance and location the Beit Din could establish the veracity of the witness.
Thirdly, as the Rambam explains17, the mathematical models were used to ensure that the calendar remained in sync with the actual phase of the moon. This is explained as follows. The phase of the moon is slightly more than twenty-nine and a half days long. A calendar month can only be twenty-nine or thirty days long. Slightly more than half of all months should have thirty days and slightly less than half should have twenty-nine days (thus averaging out to slightly more than twenty-nine and a half days per month i.e. the length of the phase of the moon).
If valid witnesses saw the new moon on the thirtieth night and they testified in time, the Beit Din would declare that day to be Rosh Chodesh and the old month would be a short month of twenty-nine days. If witnesses did not turn up in a particular month, then that month would automatically be a long month of thirty days. If witnesses did not turn up for a number of consecutive months (eg if the moon was not visible due to cloud coverage) then each of those months would by default be thirty days long and after a short while the calendar would no longer be synchronised with the phase of the moon. After a number of months a new moon might eventually be sighted on the twenty-fifth or twenty-sixth night of the month.
In order to avoid this outcome and to keep the calendar in sync with the moon, the Beit Din would sometimes designate short months of twenty-nine days even if witnesses did not turn up. This was done if the new moon was not sighted for a number of months in a row. These short months were inserted based on calculations using the mathematical models to ensure that if the new moon was sighted on the next month it would appear on the thirtieth or thirty-first night, but not earlier.
Given the accuracy of the mathematical models, it seems that the question that we posed at the beginning of this article could be asked the other way around. That is, instead of asking why the Beit Din needed the mathematical models, a better question might be - why was the Beit Din required to rely on witnesses who took the trouble of travelling to to testify? The journey could be dangerous18 and witnesses were even given permission to desecrate Shabbat in order to testify. Why couldn’t the Beit Din simply rely on their mathematical models to determine when Rosh Chodesh should be?
As was noted in the previous article, sanctifying the new moon allows the Jewish people to have a part in determining what day Yom Tov will be. We are literally partners with Hashem in bringing kedushah to the world. When the witnesses embarked on the journey to to testify they were actively participating in this partnership. Perhaps the lesson that we can learn is the importance of actions. Hashem wants us to be actively involved in carrying out His work in this world.
15 See Rashi to Bereshit 49:15
16 See Mishnah 6 of Perek 2
17 Hilchot Kiddush HaChodesh 18:5-9
18 As we see in Mishnah 9 of Perek 1
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