Rambam - 1 Chapter a Day

Which is also Rosh HaShanah.

The Rambam mentions the reason for postponing Rosh Chodesh in Halachah 7.

The first day of Rosh HaShanah is therefore celebrated frequently on Monday, Thursday, and the Sabbath, for the holiday is held on these days when the conjunction falls on the day itself or on the previous day. The first day of Rosh HaShanah is rarely celebrated on Tuesday, for the probability of the conjunction falling on that day is merely one out of seven, half that of the other days.

The principle mentioned in this halachah—and indeed, in the entire chapter—applies to Rosh Chodesh Tishrei alone, and not to the other months.

This condition is referred to as a molad zaken, literally, “an aged conjunction.” The rationale for postponing Rosh HaShanah in such a situation can be explained as follows: In principle, Rosh Chodesh is dependent on the sighting of the moon, not on the conjunction. As is explained in the subsequent chapters of the text, the new moon does not become visible until several hours after the conjunction between the moon and the sun. Thus, if the conjunction takes place after noon, it is impossible for the moon to be sighted on that day. Therefore, Rosh HaShanah is celebrated on the following day. (See Rosh HaShanah 20b and commentaries.) There is a slight difficulty in the Rambam’s statements, for based on Chapter 15, Halachah 2, it would appear that at certain times it is possible to sight the moon only five hours after conjunction.

I.e., after the eighteenth hour of the seventh day.

It should not be established on the Sabbath, because of the principle of molad zaken. Nor should it be established on Sunday, as stated in Halachah 1

I.e., the night between Monday and Tuesday.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the maximum length of a lunar year is 355 days. As mentioned previously, 4 days, 8 hours, and 876 units is the remainder of a normal year. To calculate the conjunction of Tishrei in the following year, this figure should be added to 3—9—204 (the day and the time mentioned by the Rambam above). The result is 12:00 noon on the Sabbath. As explained above, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Sunday, and Rosh HaShanah never begins on that day. Thus, the holiday would have to be celebrated on Monday. If Rosh HaShanah had been celebrated on Tuesday of the previous year, there would have been a six-day difference between the days on which the holiday was celebrated in these two successive years, producing a year of 356 days, one day longer than the maximum length of an ordinary year. To avoid this, Rosh HaShanah is not celebrated on Tuesday. Since it also is never celebrated on Wednesday, it is postponed until Thursday, producing a lunar year of 354 days (Tur, Orach Chayim 428).

For three hours after daybreak is 15 hours after the beginning of the day.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the minimum length of a lunar leap year is 383 days. As mentioned previously, the remainder of a leap year is five days, twenty-one hours, and 589 units. When, in an effort to calculate the time of the conjunction of the leap year, this figure is subtracted from 2—15—589 (the day and the time mentioned by the Rambam), the result is Tuesday at noon. As mentioned, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Wednesday, and Rosh HaShanah never begins on that day. Thus, in the leap year, Rosh HaShanah began on Thursday. If Rosh HaShanah were celebrated on Monday in the year after the leap year, this would produce only a four-day difference between the days on which the holiday was celebrated in these two successive years, causing the length of the year to be only 382 days. To avoid this, in the year following the leap year Rosh HaShanah is celebrated on Tuesday, rather than on Monday, causing the leap year to be 383 days long (Tur, Orach Chayim 428).

The Rambam’s statements have stirred the attention—and often the indignation—of the Ra’avad and other commentaries, because they appear to ignore the explanations given by Rosh HaShanah 20a why Rosh HaShanah never begins on these days. The Talmud states that if Rosh HaShanah falls on either Wednesday or Friday, Yom Kippur will fall on either Friday or Sunday, and thus there would be two consecutive days, Yom Kippur and the Sabbath, when it would be forbidden to bury the dead. In the Talmudic era, this could have caused a corpse to deteriorate, detracting from its honor and respect. Alternatively, the Sages state that if Rosh HaShanah fell on any of these three days, there would be two successive days when it would be forbidden to pick fresh vegetables, and the people would be unable to celebrate the festivals or the Sabbath properly. Sukkah 43a gives another reason why Rosh HaShanah is not held on Sunday: were this to be the case, Hoshana Rabbah, the seventh day of Sukkot, would fall on the Sabbath. In such an instance, restrictions were placed on the willow ritual in the Temple. (See Hilchot Shofar, Sukkah V’Lulav 7:21-22.) To avoid such an instance, the Sages structured the calendar so that Rosh HaShanah never falls on Sunday. In defense of the Rambam’s position, it must be noted that both earlier (Rabbenu Chanan’el) and subsequent (the P’nei Yehoshua) Talmudic commentaries understood the reasons given by the Talmud as being merely the external dimension of the rationale for the calendar’s adjustment, while the inner meaning is associated with the actual position of the sun and the moon in the heavenly sphere. Even according to this perspective, there is, however, a difficulty with the Rambam’s statements. Although it is correct that the true positions of the sun and the moon often differ from the position determined by calculating their mean movement, the concept of postponing the celebration of Rosh HaShanah on these three days appears arbitrary and without any obvious connection to the movement of these bodies in the celestial sphere. The commentaries note that explanations why Rosh HaShanah is not celebrated on these days are found in the Kabbalah.

The instance mentioned in Halachah 4.