1) OPPOSITION OF THE MOON, OBSERVED FROM LAND AND FROM SEA
QUESTIONS: The Gemara relates that Rav Nachman gave advice to people who would be traveling at sea at Pesach time and would have no way of knowing when the new month was declared. Rav Nachman taught them a way to know when the time had arrived to get rid of their Chametz: when they see that the full moon sets at the same time that the sun rises, that is the day to get rid of their Chametz.
The Gemara asks that we observe the moon to set at the same time the sun rises on the fifteenth of the month. Chametz, however, must be destroyed on the fourteenth of the month! The Gemara answers that at sea the horizons are clearer and thus the moon can be seen setting at sunrise on the fourteenth of the month, one day earlier than people on land see the moon set at sunrise.
(a) Why do people on land see the moon set at sunrise one day later than people at sea?
(b) What day is considered the halfway point of the month? The average length of a month is slightly more than 29 1/2 days, and thus half of that amount is about 14 3/4 days. After 14 3/4 days have passed since the beginning of the month, the moon should be seen setting at the time the sun rises. However, Rav Nachman says that the moon can be seen setting at sunrise on the fourteenth day. At sunrise on the fourteenth day of the month, however, only 13 1/2 days have passed since the appearance of the new moon. Why does Rav Nachman give that day as the day on which Chametz must be destroyed?
(a) As discussed earlier (see Insights to Rosh Hashanah 20b), the moon is observed to travel around the earth slower than the sun. At the moment of the Molad, the moon and sun are at the same point in the sky. As the days pass, the moon lags farther and farther behind the sun (that is, each day it lags another 12 degrees towards the east). Halfway through the month the moon has lagged so far behind the sun that it is on the other side of the earth at the opposite horizon (or 180 degrees away from the sun). The next day it will be only 168 degrees away (when measured from the west of the sun), having moved another 12 degrees farther from the sun to the east. When the sun rises on that day, the moon will be higher up (12 degrees) in the western horizon than it was the day before at sunrise.
Rav Nachman says that at sunrise on the fourteenth day of the month, the moon is 180 degrees away from the sun, at the opposite horizon. The moon sets when the sun rises. The exact moment of opposition, however, can be witnessed accurately only by one at sea, where the horizons are unobstructed. On land, though, there are obstructions in both the eastern and western horizons. If the obstructions in each horizon are tall enough (about 6 degrees), one will see the moon set at the time the sun rises when they are actually closer together by 12 degrees, or only 168 degrees apart from each other. Thus, people on land will see the moon set at the time the sun rises one day later than actual opposition occurs, on the fifteenth of the month.
(b) In the times of Rav Nachman, the new month was still established by Beis Din according to the testimony of witnesses who saw the new moon. When the Molad occurred before midday, the new moon was visible for the first time only 6 hours after the Molad. When the Molad occurred after midday, the new moon was visible 18 hours after the Molad. Consequently, day 13 1/2 of the Hebrew month (that is, 13 1/2 days from the day that Beis Din declared as the start of the new month) actually occurs between day 14 and 14 1/2 from the time of the Molad of the new moon. Therefore, Rav Nachman was justified in instructing the people at sea to determine the day of Bi'ur Chametz, the fourteenth of Nisan, according to when they saw the moon set at the time of sunrise. (KUNTRUS DI SHEMAYA, Rav Alexander Schutz of Kiryat Sefer, Israel)