הלכה על ראש השנה 49:2

All astronomers agree that the lunar month begins at the moment when the moon and the sun are in conjunction in the same longitude. This is what our Rabbis called the “molad ” (birth, i.e., new moon). Our scholars calculated it for the mean orbit,³ This figure is given in the Talmud: 29 days, 12 hours, and 793 halaqim (Rosh haShana 25a), or 29 days, 12 hours, 44 minutes, and 3 and ⅓ seconds, approximately 29.5306 days. Such a month is known as a “synodic month” and is defined as the mean time between new moons. The current approximation for a synodic month is 29 days, 12 hours, 44 minutes, and 2.7 seconds, or 29.5306 days. and all astronomers did the same. Then they adjusted it.⁴ “Mean conjunction” is conjunction of the sun and the moon relative to their individual spheres. However, since the moon’s sphere, the sun’s sphere, and the earth are not concentric, conjunction relative to the zodiacal sphere may differ from conjunction relative to the individual spheres. Conjunction relative to the zodiacal sphere is called “true conjunction.” Thus our Rabbis, their memory should be a blessing, said: “Sometimes it comes by a long path and sometimes it comes by a short path” (Rosh haShanah 25a). Since conjunction involves two bodies, we must know with regard to each one when it is a long path or a short path. Sometimes both are long, or both short, or the sun long and the moon short, or vice versa. Also, sometimes the length or shortness is small, sometimes large, to the extent that the length or the shortness may be as much as thirteen hours. Thus at times there is a difference between our calculation of conjunction and true conjunction of these many hours, either earlier or later.

All astronomers agree that the lunar month begins at the moment when the moon and the sun are in conjunction in the same longitude. This is what our Rabbis called the “molad ” (birth, i.e., new moon). Our scholars calculated it for the mean orbit,³ This figure is given in the Talmud: 29 days, 12 hours, and 793 halaqim (Rosh haShana 25a), or 29 days, 12 hours, 44 minutes, and 3 and ⅓ seconds, approximately 29.5306 days. Such a month is known as a “synodic month” and is defined as the mean time between new moons. The current approximation for a synodic month is 29 days, 12 hours, 44 minutes, and 2.7 seconds, or 29.5306 days. and all astronomers did the same. Then they adjusted it.⁴ “Mean conjunction” is conjunction of the sun and the moon relative to their individual spheres. However, since the moon’s sphere, the sun’s sphere, and the earth are not concentric, conjunction relative to the zodiacal sphere may differ from conjunction relative to the individual spheres. Conjunction relative to the zodiacal sphere is called “true conjunction.” Thus our Rabbis, their memory should be a blessing, said: “Sometimes it comes by a long path and sometimes it comes by a short path” (Rosh haShanah 25a). Since conjunction involves two bodies, we must know with regard to each one when it is a long path or a short path. Sometimes both are long, or both short, or the sun long and the moon short, or vice versa. Also, sometimes the length or shortness is small, sometimes large, to the extent that the length or the shortness may be as much as thirteen hours. Thus at times there is a difference between our calculation of conjunction and true conjunction of these many hours, either earlier or later.

That is that He commanded us to sanctify (proclaim) the months (in other versions, and to calculate the months) and years. And that is the commandment of sanctifying the month. And that is His, may He be exalted, saying, "This month shall mark for you the beginning of the months" (Exodus 12:2). And the explanation (Rosh Hashanah 22a) comes [and tells us] that "this testimony is given over to them" - meaning that this commandment is not given over to each and every individual, like the Shabbat of creation, towards which every individual counts six days and rests on the seventh. [Here, it is not] that when each and every individual sees the [new] moon, he determines that today is Rosh Chodesh (the first of the month), or that he should count some Torah matter and establish the new month or look into the lateness of the Spring - or something else that is fitting to observe - and add a month. Rather, this commandment is always only done by the High Court, and only in the Land of Israel. And the sighting [of the new moon] has therefore been annulled for us today with the absence of the High Court, just like the offering of sacrifices has been annulled with the absence of the Temple. And the heretics called Karaites have referred to this and erred about it. And this is a principle that even some of the rabbis did not concede and followed them into the darkness and the shade. You should know that the calculation that we count with today, through which we know Rosh Chodesh and the holidays, is impossible to do outside of the Land. However in the absence of sages in the Land of Israel, it is possible for a court that was ordained in the Land of Israel to intercalate years and determine months outside of the Land, like Rabbi Akiva did - as is explained in the Talmud (Berakhot 63a) - yet there is a great and strong question about this. And it is known that the Great Court, however, was in the Land of Israel; and that they were the ones that determined the months and intercalated the years in ways that were passed on to them, [doing so] in their gathering together. And this is one of the great principles of the faith - only those that have a deeper knowledge know it and see it in its place. And that is that that which we count today outside of the Land with the work of intercalation that is in our hands - and say that this day is Rosh Chodesh and that day is a holiday - is not because we have determined the holiday from our [own] calculation in any way. Rather, it is because the Great Court in the Land of Israel had already determined that this day is Rosh Chodesh or a holiday. And since they said that today is Rosh Chodesh or a holiday, it is [actually] Rosh Chodesh or a holiday - whether this action of theirs was through calculation or sighting - as appears in the explanation (Rosh Hashanah 25a), "'These are the set times of the Lord [...] which you shall proclaim as sacred occasions' (Leviticus 23:4); I have no other set times besides these" - meaning to say, the ones that they say are the sacred times, even under duress, even in error, even inadvertently - as it appears in the tradition. And we indeed consider the day determined by them - meaning the inhabitants of the Land of Israel - to be Rosh Chodesh. As it is upon [their] work itself that we count and determine [it] - not upon sighting; and it is upon their calculation that we rely, and not upon our [own] calculation. Rather our calculation is just an exposition of the matter. And understand this. And I will explain to you further. If we were to assume, by way of illustration, that the [Jewish] residents of the Land of Israel disappeared from the Land of Israel - God forbid that God would do this, since He promised that He would not erase the traces of the nation [there] totally - and that there would not be a court there, nor a court outside the Land of Israel that was ordained there. [In such a case,] this calculation of ours would surely not help us at all in any way. For we may only calculate months and intercalate years outside the Land of Israel according to the conditions mentioned, as we have explained - 'for out of Zion comes forth Torah.' And when someone with a complete intellect examines the [related] statements of the Talmud with this approach, everything that we said will become clear, without a doubt. And note that there were hints that appear in Scripture that indicate the principles of this work upon which we should rely to know Rosh Chodesh and the intercalation of years. Among them is His saying, "You shall keep this ordinance at its set time from year to year" (Exodus 13:10). They said (Mekhilta DeRabbi Shimon Bar Yochai 13:9), "It teaches that we only intercalate the year during the period that is proximate to the sacred occasion (Pesach)." And they said [further], "From where [do we know] that we only sanctify the month during the day? [Hence] we learn to say, 'from year to year (literally, from day to day).'" And they [also] said (Megillah 5a), "You calculate months for years, but you do not calculate days for years." This indeed indicates that the addition in this is in fact a full month. And they said [further], "'A month of days' - you count the days of a month, and you do not count the hours of a day." And His saying, "Observe the month of Spring" (Deuteronomy 16:1), indicates that it is fitting that we preserve the seasons of the year in our years, and that is why it is [also] solar. And the regulations of this commandment have already all been completely explained in the first chapter of Sanhedrin, in Tractate Rosh Hashanah and in Berakhot. (See Parashat Bo; Mishneh Torah, Sanctification of the New Month 1.)