RABEINU BACHYE (Parshas Bo 12:2) cites a very interesting opinion in the
name of RABEINU CHANANEL, which is also cited in the name of RAV SA'ADYAH
GA'ON (see TORAH SHELEIMAH vol. 13, #293, and OTZAR HA'GE'ONIM to Beitzah,
p. 3), that Kidush ha'Chodesh actually has nothing to do with witnesses.
Rather, it is determined solely by the calculations of the Sod ha'Ibur given
to Moshe Rabeinu at Sinai, with which the Beis Din calculates the new month
every month. Witnesses did not affect the determination of the new month at
Rabeinu Chananel cites a number of proofs for this opinion. First, for the
forty years that the Jews sojourned in the Midbar, they were covered and
protected by the Ananei ha'Kavod, the Clouds of Glory. If so, it was
impossible to see the new moon, and thus it must not have been necessary to
see the new moon in order be Mekadesh the Chodesh!
Second, we find that in Shmuel I (20:5) David ha'Melech tells Yonasan that
on the next day there will be a Rosh Chodesh meal, and on the following day
there was a meal for the second day of Rosh Chodesh. How did they know that
the next day would be Rosh Chodesh if witnesses had not yet come? And if it
was Rosh Chodesh, why should there be a second day of Rosh Chodesh? It must
be that they worked only with calculations. (Both days were considered Rosh
Chodesh, since the calculations showed that the new month started towards
the end of the thirtieth day, as the Rambam writes, Hilchos Kidush
Third, the Mishnah (25a) states that Raban Gamliel was Mekadesh the Chodesh
even when the testimony of the witnesses was physically impossible to have
been correct. (See Insights to Daf 25.)
Fourth, the Mishnah (25b) states that when all of the Jewish people see the
new moon but there is not enough time to be Mekadesh the new month before
nightfall, the Beis Din is Mekadesh the next day instead. If the new month
depends on the testimony of witnesses, why does Beis Din not declare on the
next day that the previous day was Rosh Chodesh (retroactively)? It must be
that it has nothing to do with seeing the new moon, but rather it depends
solely on the calculations.
However, why do all of the Mishnayos discuss witnesses in the first place if
Kidush ha'Chodesh has nothing to do with witnesses, but with the
calculations? He answers that the Tzedukim did not accept the calculations
of Beis Din. They did not believe in the Mesorah of Sod ha'Ibur, and they
claimed that the month is determined by when the moon actually appears.
Based on mathematical calculations alone, they claimed that Beis Din could
not possibly know when exactly the new moon will appear every month. They
only accepted the testimony of witnesses who saw the new moon. Therefore, in
order to prove the Tzedukim wrong, the Beis Din said that they would
Mekadesh the Chodesh based on the testimony of witnesses, which would then
show that their mathematical calculations are always correct. Hence, it is a
Mitzvah d'Rabanan to be Mekadesh the Chodesh based on testimony of
witnesses. This is why Raban Gamliel had models of the moon -- it was in
order to discredit the Tzedukim ("Hedyotos"). Every month on the day before
the new moon appeared, he would show them where the new moon would be seen
*the next day*. When witnesses arrived in court the following day to testify
that the moon was actually seen where the court expected it, those who
attended proclaimed in unison "Mekudash, Mekudash!" -- the calculation of
Beis Din was correct!
Eventually the Tzedukim were won over, but the Beis Din kept the practice of
accepting witnesses of the new moon in order to remember how the Chachamim
overcame the Tzedukim.
According to this unique opinion that the new month depends solely on
calculations and not on witnesses, why are there two days of Yom Tov outside
of Eretz Yisrael (or two days of Rosh Hashanah even in Eretz Yisrael)? The
Ge'onim (OTZAR HA'GE'ONIM Beitzah p. 3) answered that keeping two days of
Yom Tov outside of Israel is a Halachah l'Moshe mi'Sinai!
(b) The RAMBAM (Perush ha'Mishnayos) strongly rejects this explanation, for
it contradicts many explicit statements in the Gemara. It is obvious that
they were Mekadesh the Chodesh based on witnesses, and only when there were
no witnesses did they do it based on calculations. The Rambam suggests that
perhaps Rabeinu Sa'adyah wrote this opinion because of the Karaites in his
time who were pestering him, saying that Kidush ha'Chodesh based on
calculations is unreliable. In response, Rav Sa'adyah said that not only is
Kidush ha'Chodesh based on calculations completely accurate, but Kidush
based on witnesses is not even mid'Oraisa.