1) SOMETIMES THE MOON TRAVELS A SHORT WAY AND SOMETIMES A LONG WAY
OPINIONS: The Mishnah records a case in which witnesses testified that they saw the moon in the east in the morning and in the west in the evening. Rebbi Yochanan ben Nuri rejected their testimony. Raban Gamliel, however, accepted their testimony. Raban Gamliel reasoned, as the Beraisa records, that even though it is a most unusual occurrence for the moon to be seen in those two positions within such a short time, he had a tradition from his grandfather that "sometimes the moon travels a short distance and sometimes a long distance."
Why exactly did Rebbi Yochanan ben Nuri reject their testimony, and what was Raban Gamliel's response to Rebbi Yochanan's arguments?
(a) In his first explanation, RASHI (DH Edei Sheker) writes that the witnesses claim that they saw the old moon in the east in the morning before sunrise, as the Mishnah implies, and the new moon in the west in the evening after sunset. Rebbi Yochanan ben Nuri rejected their testimony because the moon is not visible for 24 hours around the time of the Molad. If they saw the old moon in the morning, then the Molad must have occurred after midday (at least six hours later), in which case the new moon could not have been visible in the evening, but only 18 hours later (the next morning). On the other hand, if they saw the new moon in the evening, then the Molad must have occurred before midday (at least six hours earlier), in which case the old moon could not have been visible in the morning because of its proximity to the luminous sun.
Rashi rejects this explanation because it fails to take into account Raban Gamliel's response. If the reason why Rebbi Yochanan ben Nuri rejected the testimony of the witnesses was because they could not have seen the new moon so soon after they saw the old moon due to the moon's proximity to the sun, then Raban Gamliel's response about the different speeds at which the moon travels is not relevant.
1. The BA'AL HA'ME'OR justifies Raban Gamliel's response. Raban Gamliel accepted the witnesses because he assumed that they made a mistake when they said that they saw the old moon in the morning. They probably saw a small cloud and thought that it was the moon. Since what the witnesses say they saw in the morning is not relevant to Beis Din's declaration of the new month, Beis Din may assume that the witnesses erred and ignore that part of their testimony.
The Ba'al ha'Me'or adds that since what the witnesses say they saw in the morning is not relevant to their testimony about the new moon, we apply the principle that a person does not pay close attention to something unimportant to him. Therefore, their mistaken testimony about what they saw in the morning does not invalidate their proper testimony about what they saw in the evening (which was important to them and to which they paid close attention because of its Halachic implications).
What did Raban Gamliel mean when he said that sometimes the moon travels faster, if the speed of the moon is entirely unrelated to his reason for accepting the witnesses? The Ba'al ha'Me'or answers that the Gemara is teaching an unrelated tradition that Raban Gamliel had received from his forebears, and it indeed is unrelated to the case in the Mishnah.
2. The RAMBAM (in PERUSH HA'RAMBAM to Rosh Hashanah) justifies Raban Gamliel's response differently. He explains that it indeed is possible for the moon to be seen at both sunrise and sunset on the same day. He explains that Raban Gamliel's answer to Rebbi Yochanan ben Nuri was that the only time the moon cannot be seen within 6 hours of the Molad is when the moon's orbit is neither to the north nor to the south of the ecliptic, but exactly on the ecliptic (see Insights to Rosh Hashanah 24:1:b). The moon can travel on a path off of the ecliptic by up to 5 degrees to the north or south, and when it does the earth has a better viewing angle of the new moon (since it is not directly between the sun and the earth but is off by a few degrees). During those times, the new moon can be seen in the evening even when the old moon was seen in the morning. (It is interesting to note that in Perush ha'Mishnayos, the Rambam ridicules this suggestion and asserts that anyone familiar with astronomy knows that the testimony described in the Mishnah is absolutely impossible. See (c) below.)
3. The BEN ARYEH (20b) gives another explanation for how the moon can be seen in the east at sunrise and in the west at sunset on the same day. When the Gemara says that the old moon cannot be seen at sunrise when the Molad occurs before midday, it refers to an equinoctial day -- when there are exactly six hours from sunrise to midday and six hours from midday to sunset. In contrast, at the summer solstice -- when the day is much longer than the night -- sunrise and sunset are more than six hours away from midday and thus there is no reason why the old moon should not be visible at sunrise and the new moon at sunset. This is what Raban Gamliel meant when he said that sometimes the moon travels a short distance and sometimes a long distance.
(This explanation is consistent only with the words of Rashi, who writes earlier that the new moon can be seen six hours after the Molad. According to the Rambam and others who maintain that the new moon cannot be seen until 18 hours after the Molad, even on a very long day the testimony described in the Mishnah remains an impossibility. See Insights to Rosh Hashanah 20:3:c for a discussion of whether Rashi indeed disagrees with the Rambam or not.)
(b) The RAMBAM (in Perush ha'Mishnayos; see also Hilchos Kidush ha'Chodesh 2:6) and the BARTENURA explain the dialogue between Rebbi Yochanan ben Nuri and Raban Gamliel in an entirely different manner. As the Ba'al ha'Me'or points out, the witnesses' statement that they saw the moon in the morning obviously is a mistake and may be ignored. That statement is unrelated to the disagreement between Rebbi Yochanan ben Nuri and Raban Gamliel because both agreed that what the witnesses saw in the morning was not the moon. They disagreed merely about a mathematical point -- whether it was possible for the witnesses to have seen the new moon in the evening. Rebbi Yochanan ben Nuri maintained that it was too early for the new moon to be seen. Raban Gamliel maintained that Rebbi Yochanan ben Nuri's calculations were incorrect because sometimes the moon travels faster, and thus sometimes it can be seen earlier, depending on its height from the horizon at the time of sunset. (See Hilchos Kidush ha'Chodesh 17:23 for a discussion of the factors involved in this calculation.)
(c) In his second explanation, RASHI says that on the thirtieth day of the preceding month the witnesses saw the new moon in the morning after sunrise (rising behind the sun), because enough time had passed since the Molad to see it at that time (and it was not blocked by the luminosity of the sun). Later on the same day, before sunset, they again saw the new moon behind the sun. They came to Beis Din before sunset to testify.
According to this explanation, what was wrong with their testimony? The new moon certainly becomes more visible as the new month progresses. Why did Rebbi Yochanan ben Nuri reject their testimony?
Rashi answers that he maintained that the moon cannot travel across the entire firmament, from the east to the west, in only twelve hours. Raban Gamliel replied that sometimes it is possible.
The BA'AL HA'ME'OR asks that this explanation of Rashi is much more difficult to understand than the first explanation which Rashi rejects, because all celestial bodies travel from the eastern horizon to the western horizon in twelve hours.
Perhaps Rashi means that the witnesses testified that they saw the moon the same distance from the sun in both the morning and in the evening. Rebbi Yochanan ben Nuri rejected their testimony because the moon travels slower than the sun and cannot be the same distance from the sun in the evening as it was in the morning (rather, the moon lags 6 degrees every 12 hours). Raban Gamliel accepted their testimony because sometimes the moon indeed moves faster than usual (such as during perigee, when the moon is closer to the earth in its orbit and the gravitational pull of the earth on the moon is stronger).
2) THE MISSING MOON
OPINIONS: The Mishnah records a second case in which witnesses testified that they saw the new moon on the thirtieth day of the month, and on the next day (the thirty-first of the month) the moon was not visible despite clear skies. Raban Gamliel accepted their testimony. Rebbi Dosa ben Hurkenos said that the testimony of the witnesses cannot be valid if, the next day, no moon was visible.
Why did Raban Gamliel accept the witnesses?
(a) The RAMBAM (in Perush ha'Mishnayos, and Hilchos Kidush ha'Chodesh 2:6) writes that the moon obviously does not regress, and thus if the moon was not visible the next day it must have been covered by a cloud. Even though the sky seemed to be clear that day, Raban Gamliel determined based on his calculations (independent of the testimony of the witnesses) that the moon should have been visible and thus it must have been hidden by a cloud. The testimony about the missing moon on the second day is ignored since the witnesses were obviously mistaken in that regard.
(b) The BA'AL HA'ME'OR says that by the time Beis Din realized that the moon was not visible on the thirty-first day, the new moon had already been declared "Mekudash" based on the witnesses' testimony. Even though the moon was not visible on the following day and it became evident that the witnesses had erred, Raban Gamliel accepted the declaration of the new month because of the principle that the declaration of Beis Din is binding even when in error ("'Atem,' Afilu Muta'im," 25a). This is why Rebbi Akiva comforted Rebbi Yehoshua with the Derashah of "'Atem,' Afilu Muta'im."
3) AGADAH: THE MOON AND DAVID HA'MELECH
QUESTION: The Gemara relates that Rebbi told Rebbi Chiya that when he sanctifies the new month, he should send Rebbi a message saying, "David Melech Yisrael Chai v'Kayam." RASHI explains that the verse (Tehilim 89:37) compares the Davidic dynasty to the moon.
Why is Malchus Beis David compared to the moon?
(a) This analogy can be understood based on the words of the Midrash (Shemos Rabah 15; see also RABEINU BACHYE to Bereishis 38:30, cited by SHULCHAN ARUCH OC 426:2). The Midrash teaches that just as the moon waxes and wanes over a thirty-day period, so, too, the power of the kingdom of Yisrael "waxed and waned" over a period of thirty generations. For fifteen generations it grew until it was full -- from Avraham Avinu until Shlomo ha'Melech, and for the next fifteen generations it waned, coming to its end at the reign of Tzidkiyahu ha'Melech whose eyes were blinded by the enemy at the time of the destruction of the Beis ha'Mikdash (Yirmeyahu 52:11). The blinding of Tzidkiyahu, like the complete loss of the light of the moon, was a sign that the Davidic dynasty had ended. The return of the moon's light after the Molad is a sign that the dynasty of David ha'Melech will return to its former glory.
For this reason Rebbi established that Malchus Beis David be mentioned as a sign that the new month was declared. The MAHARATZ CHAYOS adds, based on the Yerushalmi in Sanhedrin, that it indeed was the common practice to announce the new month with the phrase "David Melech Yisrael..." The Chachamim viewed the new moon as a sign of hope and anticipation for the restoration of the autonomy of the Jewish people and the Davidic dynasty. This is also the source for the present-day custom to mention this phrase during Birkas ha'Levanah.
(The MENACHEM MESHIV NEFESH cites the SHA'AR EFRA'IM (10:36) who adds in the name of the BRIS KEHUNAS OLAM that the Gematriya of "David Melech Yisrael Chai v'Kayam" is 819, the same value as the Gematriya of "Rosh Chodesh" spelled Malei, with a Vav.) (See Insights to Sanhedrin 42:2.)
(b) RAV ELIE MUNK (in "Olam ha'Tefilos," "The World of Prayer," p. 94-99) discusses the connection between David ha'Melech and the new month. Aside from the above-mentioned sources, he mentions that some explain that the method for calculating the new month (Sod ha'Ibur) had been handed down by the House of David (from which Rebbi was descended).