חכמת מנוח, which is among the commentaries in my Shas following masekhet Rosh Hashanah, pointed me to a book called
Yesod Olam, by Yitzhak ben Yosef Yisreli, whom the first edition of Encyclopedia Judaica calls "ISRAELI, ISAAC BEN JOSEPH". He was a medieval astronomer who wrote the book, at the request of the RoSH, to elucidate the astronomical basis of the Jewish calendar. Section 4 Chapter 8 presents his interpretation of the
sugya.
Unlike the medieval commentators in part I, he is not interested in a dateline. I presume that this is because, according to his understanding of geography, all of the inhabitable land surface of the Earth is in what we now would call the "eastern hemisphere", with the rest of the globe being covered by water. So as far as he is concerned, the dateline can be anywhere in the western hemisphere and it doesn't matter where.
Instead, his interpretation is based on three meridians. His prime meridian is about 59 degrees east of Greenwich, which he estimates to be in the middle of the inhabitable hemisphere. His other significant meridians are an east meridian 90 degrees east of the prime meridian, a west meridian 90 degrees west of the prime meridian, and the meridian of Jerusalem, 23.5 degrees west of the prime meridian.
Another factor that he introduces, and that was ignored by the commentators in part I, is that as a real astronomer, he knows that the
molad is just an average, and that the actual conjunction of the Sun and the Moon usually is different from the average conjunction by several hours. The modern explanation of this phenomenon is that the Moon's orbit is elliptical. The pre-modern explanation used epicycles. His estimate of the maximum deviation is 14 hours and 648
halakim (one hour = 1080
halakim).
His explanation of "Differentiate between when
the molad occurred before hatzot and when
the molad occurred after hatzot" is with reference to noon at the prime meridian, and on the assumptions that the new moon is visible starting 22.5 hours after the true conjunction and that such a thin crescent won't be visible until 20 minutes after sunset. If the
molad occurs before noon at the prime meridian, then, if this time the true conjunction was as early as it possibly can be relative to the
molad, then theoretically it is possible for witnesses to see the new moon at sunset in or near Jerusalem. If the molad occurs after noon at the prime meridian then it is physically impossible to see the new moon at sunset in or near Jerusalem and witnesses who claim to have done so are mistaken.
This is how he gets it:
6 hours from noon to sunset +
20 minutes = 360
halakim +
Jerusalem is 1 hour and 612
halakim later than the prime meridian (his estimate of the longitude of Jerusalem is 23.5 degrees west of the prime meridian) +
14 hours and 648 halakim is the most time by which the true conjunction can ever precede the
molad
= 22.5 hours.
His explanation of "
it is necessary that both
the night and the day be of the new month" is that that statement of Rabbi Zeira has nothing to do with whether the
molad is before or after
hatzot at the prime meridian. Instead, it is a rule of thumb to use in the diaspora to estimate when the Sanhedrin declares the new month. If the
molad is before local sunset then most likely the Sanhedrin will declare the new month one day later. Otherwise, most likely the Sanhedrin will declare the new month two days later.
In his first explanation of "
For us, in Babylonia, it is not visible for
six hours
of the old moon
and eighteen hours
of the new; for them, in Eretz Yisrael, it is not visible for
six hours
of the new moon
and eighteen hours
of the old" he posits, like the other Rishonim in
part I, that "
us" doesn't mean Babylonians, and, like some of the Rishonim (Tashbetz second explanation and Ra'avad), that "them" doesn't mean Israelis. Instead, "
us" means observers at the east meridian and "
them" means observers at the west meridian. He assumes that the Moon is invisible for 48 hours on the average, and gives an example of the true conjunction being at the start of Shabbat (at sunset) near the Fall equinox (for determining the day of Rosh HaShanah). The same time is midnight Shabbat for "
us" and noon Friday for "
them". The old Moon is invisible all of Friday and the new moon is invisible all of Shabbat at the prime meridian. For "
us", though, the first six hours of Shabbat are the last six hours of the old Moon's invisibility and the last 18 hours of Shabbat are the first 18 hours of the new Moon's invisibility. Similarly, for "
them", the first 18 hours of Friday are the last 18 hours of the old Moon's invisibility and the last six hours of Friday are the first six hours of the new Moon's invisibility.
I have two objections to Yitzhak ben Yosef Israeli's explanation of the
sugya. My first objection is that he disconnects Rabbi Zeira's first statement ("
it is necessary that both
the night and the day be of the new month") from the
baraita quoted by Abba the father of Rabbi Simlai. It is clear from the
sugya that Rabbi Zeira's first statement is intended as an explanation of the
baraita. My second objection is that the plain meaning of "
us" is Babylonians and the plain meaning of "
them" is Israelis. It should not be necessary to make "
us" mean observers in the extreme east and to make "
them" mean observers in the extreme west.
He also has a second explanation of "
For us, in Babylonia, it is not visible for
six hours
of the old moon
and eighteen hours
of the new; for them, in Eretz Yisrael, it is not visible for
six hours
of the new moon
and eighteen hours
of the old" that seems to be based on interpreting "
old" as meaning the old
month (Elul) and "
new" as meaning the new
month (Tishrei) but I was unable to make sense of it.
Finally, in
part I, my own explanation of "
For us, in Babylonia, it is not visible for
six hours
of the old moon
and eighteen hours
of the new; for them, in Eretz Yisrael, it is not visible for
six hours
of the new moon
and eighteen hours
of the old" was that it refers to a 24 hour discrepancy, between when Israelis see the new moon and when Babylonians see the new moon, that happens in about one out of every 36 months. I was assuming that the difference in longitude between Babylonia and Jerusalem is about 10 degrees. In Section 2 Chapter 3, Yitzhak ben Yosef Yisraeli gives a value for the longitude of Babylonia that places it 13.5 degrees east of Jerusalem, not 10 degrees east of Jerusalem. If I use that longitude difference in my calculation then I get a slightly larger discrepancy frequency of about three times every 80 months.
