My question is,
Below I quote a section of your explanation of Rashi on how the 18-6 hour split works for the people in Israel and how it differs for the people in Bavel. But if I recall my astronomy correctly, one can only see the last bit of the "old moon" in the morning prior to sunrise, and can only see the first bit of the "new moon" just after sunset.
Thus when you state (for people in Israel) "The old moon will only be visible before sunset the evening before the Molad, when it is approximately 18 hours (9 degrees) away from the Molad." This is not possible as the "old moon" is only visible in the mornings just before sunrise.
Similarly, when you state (for the people of Bavel), "The first time the people in Bavel will be able to see the new moon after the Molad is approximately 18 hours after the Molad, that is, when it rises again the morning after the Molad." This too is not possible, since the "new moon" is only visible in the evening, just after sunset!
The quote from your explanation of the daf follows:
Since in Bavel the Molad is half an hour after Chatzos, the moon will not be visible that evening (six hours will not have passed from the Molad before moonset, which is approximately 6:12 that evening, about twelve minutes after sunset). However, the Molad did occur more than six hours from sunrise that morning. Therefore, that morning the old moon was visible in the east, right before sunrise (i.e. to the immediate east of the sun), when the moon is three degrees away from the sun. The first time the people in Bavel will be able to see the new moon after the Molad is approximately 18 hours after the Molad, that is, when it rises again the morning after the Molad. This is what the Gemara means when it says that "for us [in Bavel], the old moon is covered for 6 hours, and the new moon is covered for 18 hours."
In contrast, in Eretz Yisrael, since the Molad occurred just before noon, the new moon will be visible just before sunset, 6 hours later (and it will remain visible until it sets, a few minutes after the sun). However, the old moon will not be visible in the morning, since it is within 6 hours of the Molad. The old moon will only be visible before sunset the evening before the Molad, when it is approximately 18 hours (9 degrees) away from the Molad. (The old moon will set before the sun, approximately 36 minutes before sunset). This is what the Gemara means when it says that "for them [in Eretz Yisrael], the old moon is covered for 18 hours and the new moon is covered for 6 hours."
All of the words of Rashi throughout the Sugya are easily understood based on this brilliant explanation.
Chaim Manaster, Montreal, Canada
The moon is always visible from any point on earth for 12 hours, just like the sun. If it can be seen a certain amount of time before or after sunset, it can also be seen that amount of time before or after sunrise. The only additional factor influencing its visibility that does not affect the sun is its luminosity. Since it is much less luminous, when it is both new and close to the sun (i.e. it is less than 18 degrees from the sun) it cannot be seen since the sun outshines it.
Go out and look for the moon now; you should see it if you look for it, anytime from about four hours after sunrise (until four hours after sunset).