Rambam - 1 Chapter a Day

The concept of a renewal each month is relevant regarding lunar months, but not with regard to solar months. For the moon is not seen for a day or two each month, while the sun shines continually every day throughout the year.

Although the implication to a lunar month in this verse is not as obvious as in the former verse, there is an explicit teaching from our Sages indicating a connection, as the Rambam proceeds to explain.

Mechilta D’Rashbi on the above verse; see also Midrash Tanchumah, Shemini, sec. 8; Menachot 29a.

Sanhedrin 13b (cited by the Rambam, Chapter 4, Halachah 1) explains that this verse is a charge to arrange the calendar so that the vernal (spring) equinox always falls in the month of Nisan.

The Rambam speaks in more precise figures in Chapter 6. At present, he is speaking in general terms to give an outline of the how the Jewish calendar is structured.

Megillah 5a.

As will be explained in the notes to Ch. 11, when the sun, the moon, and the earth are aligned in a straight line in that order, the moon reflects the sun’s rays directly back to it, and no light can be seen from the earth. This is called the conjunction of the sun and the moon. Afterwards, the moon proceeds in its orbit away from the sun, and within approximately one day’s time it will have moved a sufficient distance for it to reflect a small crescent of light to the earth. This crescent will always be sighted first in the western portion of the sky, close to the horizon.

I.e., in contrast to the Sabbath, a person who thinks that he has sighted the moon may not begin counting the days of the new month on his own initiative. Rather, he must go to the Sanhedrin and present his testimony to them, and it is they who decide whether or not to begin the new month. (Note the Rambam’s comments in Sefer HaMitzvot, Positive Commandment 153, where he elaborates on this theme.)

I.e., the Sanhedrin, the High Court that held sessions in Jerusalem until the Temple’s destruction, and afterwards was located in various cities throughout Eretz Yisrael.

As explained in Rosh HaShanah 22a, this command was addressed to Moses and Aaron. The words “to you” are seemingly unnecessary. Thus, they are interpreted to mean that just as this command is being given to you, so too, the fulfillment of it in subsequent times will be the responsibility of men like you—i.e., the judges of Israel’s High Court. (See Chapter 2, Halachah 8, which mentions an application of this principle. See also Chapter 5, Halachah 1.)

Rav Kapach explains that the Rambam chose his wording exactly. The calculations of the High Court merely “resembled the calculations of the astronomers.” In truth, however, they operated under a different system. As the Rambam explains in Chapter 17, Halachah 24, the prophets and the descendants of the tribe of Issachar had a method of calculating the movement of the sun, the moon, and the stars, which had been transmitted to Moses on Mount Sinai. Although this method resembled the method of calculations employed by gentile scholars, it was unique and different. (See also the Rambam’s Commentary to the Mishnah, Rosh HaShanah 2:8.)
This method of calculation was lost to our people shortly after the composition of the Mishnah. Subsequent texts, including the Rambam’s own system of calculation, as explained from Chapter 11 onward, were based on Greek sources

Because the moon was covered with clouds or for other similar reasons. (See Chapter 18, Halachah 1.)

See Sefer HaMitzvot (Positive Commandment 153) and Sefer HaChinuch (Mitzvah 4), which consider this to be one of the Torah’s 613 mitzvot.

The Rambam mentions three activities imperative on the court in fulfillment of this mitzvah: the calculation of the time for the sighting of the moon, the examination of the witnesses, and the notification of the Jewish people.
It is interesting to note that the structure of Hilchot Kiddush HaChodesh represents somewhat of a departure from the Rambam’s usual style of presentation in the Mishneh Torah. He generally begins by citing a mitzvah and the proof-text from which it is derived, and afterwards he describes it. In this instance, the Rambam begins by describing the basic ground rules for the sighting of the moon, and afterwards he explains the mitzvah that is associated with this sighting.
Rav Kapach suggests that this approach could have been taken in reaction to the position of Rav Sa’adiah Gaon, who maintains that the fundamental aspect of determining the calendar was not the sighting of the moon, but rather the calculations of the Sages. See the Rambam’s Commentary to the Mishnah (Rosh HaShanah 2:6).

As stated in the conclusion of Chapter 2, this verse is an indication that the determination of the days on which the festivals are to be celebrated—and thus the establishment of the monthly calendar on which the former depends—was entrusted to the Jewish High Court

This verse refers to the Paschal sacrifice and teaches us that there is an obligation to “observe this statute,” bring the Paschal sacrifice, “at its appointed time”—i.e., in the spring. This alludes to the second dimension of this mitzvah, the establishment of leap years so that the holiday of Pesach will always fall in the spring.
Note the Ramban (Hasagot to Sefer HaMitzvot, Shoresh 1), who cites opinions that consider these two dimensions—the establishment of Rosh Chodesh and the decision whether to observe leap years—as two separate mitzvot.
The Rambam’s citation of this proof-text has attracted the attention of commentaries because of another difficulty. In Menachot 36b, the meaning of this verse is the subject of a difference of opinion between Rabbi Akiva and Rabbi Yosse HaG’lili. While the simple meaning of the phrase “this statute” is the Paschal sacrifice—and this is the interpretation of Rabbi Akiva—Rabbi Yosse HaG’lili interprets the phrase as referring to the mitzvah of wearing tefillin.
What is significant is that in the Mishneh Torah, the Rambam cites both the interpretations of Rabbi Akiva (in this halachah) and that of Rabbi Yosse HaG’lili (Hilchot Tefillin 4:10) as Torah law. The commentaries (see Radbaz, Vol. V, Responsum 1693) explain that this is indicative of a general pattern within the Mishneh Torah. The Rambam’s intent in composing the Mishneh Torah was to provide us with a text of Torah practice, not a source book explaining the derivation of Torah law. He refers to verses only when they are necessary as supports. Therefore, in each instance he cites the proof-text that has the most obvious connection to the law or principle he is referring to, although it is possible that there is another verse from which this law was actually derived.

See Sefer HaMitzvot, loc. cit., where the Rambam explains the connection of this mitzvah—and the Jewish people as a whole—to Eretz Yisrael in stirring terms.

The ordination conveyed upon the Sages from Sage to Sage, in a chain that began with Moses himself. (See Hilchot Sanhedrin, Chapter 4.)

Yevamot 122a relates that Rabbi Akiva journeyed to Neharde’a for this purpose, and from the narrative in Berachot 63a, it would appear that Chanina, Rabbi Yehoshua’s nephew, lived in Babylon and ordained the order of the calendar from there for several years.

Berachot, ibid., states that the Sages of Eretz Yisrael ordered Chanina to stop ordaining the calendar, because “the kids that you left behind have grown and become billy-goats with horns”—i.e., the Sages who were once on a lower level of understanding had matured and achieved a par with him.

The Rambam is speaking about the era when the beginning of the new month was determined through the testimony of witnesses. The use of the fixed calendar we follow at present is discussed in Chapter 5.