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1. A Common Error And Its Origin
There is a common misconception that the first sighting of the new crescent Moon can generally take place on the evening after the calendric molad (=the simplified mean conjunction time of the Moon with the Sun, calculated according to the rules of the Hebrew calendar; see below), if this molad occurs before noon [otherwise the calendric molad is called a late (=zaqen) molad]. Others put the misconception about the first sighting differently: six hours after the calendric molad it is possible to sight the new crescent Moon. In reality the earliest naked eye sighting becomes feasible only 15 hours or more after the true molad (see below).
The origin of this error is in a misinterpretation of a well-known Talmudic passage (BT, Rosh Ha-Shana 20b):
We calculate (the time of) its (the Moon's) birth (molad). If it was born before midday, then we know it will become visible close to sunset. If it was not born before midday, then we know it will not become visible close to sunset.
Commenting on this text Rabbenu Hannan'el
(11th cent.) writes: "This matter was not sufficiently
clear to us, therefore we did not write its explanation".
On the other hand, Ibn Ezra (12th cent.) explains
the Talmudic text at length. His explanation seems especially
significant (see section 4, below). First let us examine the various
types of molad.
2. Three Types of Molad
The True Molad = True Conjunction = the time at which the Moon (during its monthly orbital motion around the Earth) is between the Earth and the Sun, close to (or at the time of a solar eclipse: on) a straight line between the Earth and the Sun. At this time the Moon is generally not visible from the Earth. Since the Earth and the Moon move in elliptical orbits, not circles, the time interval between two consecutive true moladot varies. In the twentieth and the twenty-first centuries the length of the true lunar month is between approximately 29 days 6.5 hours and 29 days 20 hours (MEEUS, Astronomical Algorithms, 1991, p. 324).
The Mean Molad = Mean Conjunction = the average time, from which the true molad can deviate up to approximately 14 hours in either direction. The deviation possible varies, depending on the location of Earth in its path around the Sun. In Nissan the true molad can occur from approximately 6 hours before the mean molad until near to 14 hours after it, and in Tishri the true molad can occur from about 14 hours before the mean molad until around 6 hours after it (see Ibn Ezra, Commentary on the Tora, Ex. 12 2). The time interval between two mean moladot is currently (near the year 2000 C.E.): 29 days, 12 hours 44 minutes, 2.9 seconds [expressed in standard SI (Systeme International) seconds, measured by atomic clocks; MEEUS, 1991, p. 319]. This interval grows longer by approximately 0.1 SI seconds in 500 years. The great astronomer, Rabbi Raphael Ha-Lewi of Hanover calls this molad the "correct molad" (Luhot Ha-Ibbur, part 1, 1756, title page).
The Calendric (or: Common) Molad = Molad Ha-Ibbur = the Calendric (Mean) Conjunction calculated by the rules of the Hebrew calendar. It was close to the mean molad in the times of our Sages (1st cent.). Near the year 2000 C.E. it occurs about 2 hours after the mean molad (assuming that the common calendric molad, announced in synagogues on the Sabbath before Rosh Hodesh, refers to Jerusalem Mean Time i.e., the Israel Standard Time plus 21 minutes). The time interval between two consecutive calendric moladot is fixed by halakha at a constant 29 days, 12 hours, 44 minutes and one heleq (=1 part = 3.33 seconds).
3. The Time Between the True Molad and the First Sighting of the Crescent Moon
According to an ancient dictum, quoted in Pirqe Rabbi Eliezer (chap. 7, 17b, compiled in the 8th century), the first sighting of the crescent Moon becomes possible after eight large hours (equivalent to 16 standard hours) from the time of the true molad.
According to Ibn Ezra (Sefer Ha-Ibbur, 11b, 1146 C.E.) the sighting in Tishri becomes possible only after more than 20 hours from the true molad.
According to Maimonides (Hilkhot Qiddush Ha-Hodesh - Sanctification of the New Moon, Chap. 1, halakha 3, 1170/78 C.E.) it becomes feasible "about a day after it (the Moon) adheres to the Sun" (=the true molad). But from his detailed calculations in chapter 17 (ibid), it becomes clear that 18 hours is the minimal time between the true molad and the first sighting of the Moon in the spring and 20 and one third hours in the autumn (Rabbi Raphael Ha-Lewi of Hanover, Tekhunat Ha-Shamayyim, section 91, which was copied into the common editions of the Code of Maimonides, at the end of Sefer Zemanim under the title: An Explanation of Maimonides' Words in Chapter 17 of the Treatise: Hilkhot Qiddush Ha-Hodesh).
Contemporary scientists present similar parameters concerning the age of the Moon when it is first visually perceivable. The earliest sightings for which we have full documentation (See: Schaefer, QJRAS 29, 1988, and also, Doggett and Schaefer, ICARUS 107, 1994, in the list of 252 sightings presented there, with comments of Loewinger, QJRAS 36, 1995 on them) are:
A telescopic sighting: 13.4 hours after the true molad (ibid. sighting 239).
Unaided sighting: 15.5 hours after the true molad (ibid. sighting 252).
(See some even younger recent sightings in Schaefer, QJRAS 37, 1996).
All this leads to the following:
The first possible sighting, even under exceptionally good conditions, can occur only after about 13 hours (with optical aid) or after about 15 hours (unaided vision) from the time of the true molad. A sighting earlier than this is extremely unlikely. More often, the sighting becomes possible when the Moon is around the age of 18 hours in the spring (Nissan, Iyyar, Siwan) and around the age of more than 20 hours in the autumn (Tishri, Marheshwan). The usual sighting takes place when the Moon's age is more than a day, measured from the true molad, but very often only at an age of 30 hours or more.
4. The Commentary of Ibn Ezra on the Talmudic Passage: "If It Was Born Before Midday"
See "Sefer Ha-Ibbur", 11b; (my amendments in brackets ):
We know already that at the molad of Tishri... at midday [when] the molad is before midday [there can be] fourteen hours and six hours till nightfall, thus twenty hours... the Moon is seen at [after] sunset, therefore if the molad was after midday it can not be seen at all.
This passage by Ibn Ezra can be explained as follows: when the mean molad in Tishri occurs even shortly before 12 a.m. (according to our clock), then the true molad could precede the mean molad by about 14 hours, at most (see section 2, above) and could have occured before 10 o'clock p.m., the night before the occurrence of the mean molad. We noted above (section 3) that in Tishri a sighting may be possible, if more than 20 hours pass from the true molad until the expected sighting time, shortly after sunset. So the sighting becomes feasible in this case approximately 6 hours after the mean molad, i.e. after sunset, which in Tishri occurs around 6 p.m.
On the other hand, if the mean molad occurs exactly at noon or thereafter (i.e. if the mean molad is a late (zaqen) molad) then there cannot possibly be a sighting shortly after sunset. For then, even if the true molad preceded the mean molad by its maximal value of 14 hours, there are not 20 hours and more, needed from the true molad until the expected sighting time shortly after sunset.
This, then, will be the explanation of the Talmudic passage in Rosh Ha-Shana 20b, according to Ibn Ezra (parentheses indicate his commentary inserted in the Talmudic text, in my rephrasing):
We calculate its birth (i.e. the mean molad in Tishri). If it was born before midday then we know it will (sometimes) become visible close to (after) sunset. If it was not born before midday, then we know it will not (under any circumstances - not even in Tishri) become visible, close to (after) su (because the time of more than 20 hours needed from the true molad until the time of sighting has not yet passed).
What is the (practical) outcome (of this rule)? (Consider, that from this rule of the late (zaqen) molad only a negative conclusion can be drawn, that no sighting is possible in the evening following the mean molad, if it is a late molad. However it is impossible to predict that the Moon can be seen on that evening, if the mean molad is not a late molad, because "if it was born before midday, then we know it will become visible" means: it might, sometimes, become visible).
Rav Ashi said (answering this question: the rule of the late (mean) molad helps us, indeed, only) to confute (false) witnesses (and cannot be used as a tool of confirming the testimony of true witnesses).
Despite the first impression from the Talmudic text in Tractate Rosh Ha-Shana and the explanations of several of the commentators on it, we must adhere to the following facts:
a. An unaided sighting of the new (crescent) Moon is impossible before the passage of 15 to 20 hours or more after the true molad (depending on the season of the year). Sometimes sighting becomes possible in Tishri, in the evening after the occurrence of the mean molad, if it is not a late (zaqen) molad. (A late calendric molad, nowadays, still enables a sighting on the evening after it, e.g. in Tishri 5761 (28.9.2000), when observed from southwestern areas of Erez Yisrael!)
b. A late (zaqen) mean molad in Tishri, and even moreso in the other months, is a sufficient basis for confuting witnesses claiming to have seen the new (crescent) Moon on the evening after that mean molad. Thus only the second of the two dicta: "If it was born before midday" and "If it was not born before midday" is practically relevant.
c. It is possible to see the new (crescent) Moon at the beginning of the month only after the passage of at least 29 days from its previous first sighting, and only at a relatively low altitude above the western horizon, at around 20 minutes after sunset. In Tishri the Moon will be south of the W (west) point of the horizon.
d. It is possible to see the old (crescent) Moon at the end of the month, only if there remain at sunrise more than approximately 15 to 20 hours until the true molad. The old Moon can then appear only at a relatively low altitude above the eastern horizon around 20 minutes before sunrise. In Tishri the Moon will be found directly above the E (east) point of the horizon. (Rashi's explanations in our printed editions of Rosh Ha-Shana 20b, and also the opinion of the Baal Ha-Maor commenting on Rabbi Yizhaq Alfassi, ibid., seem to contradict the above, requiring therefore serious examination).
For further study and bibliographies:
Loewinger Y., Luah Davar Beito, 5756-1995, Rabbi Mordekhay Gnut, ed., Bene Beraq, pp. 151-164.
Loewinger Y., Tehumin, 5754-1994, 14, pp. 473-500.
Loewinger Y., Sinai, 5756-1996, 118, pp.71-82.
Translated by: Phil Lerman, Qibbuz Beerot Yizhaq.
Proofreading by: Rabbi Dr. D. Mescheloff and the