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קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 17
Sefer Zemanim · The chapter every earlier calculation was built for: the first longitude and first latitude that must be kept at hand, four corrections that turn them into the arc of sighting, and the five limits that decide whether the moon will be seen in Eretz Yisrael tonight
9
Degrees of first longitude ruling out a sighting, Capricorn through Gemini
24
Degrees above which sighting is certain in the other half of the sky
12
Sighting adjustments, one for each constellation
11°11'
The arc of sighting in his worked example, the second of Iyar
Part 1The two symbols, and the two halves of the sky
- Everything earlier was preparation for this. Calculate the true position of the sun, the true position of the moon and the position of the head of the orbit for the hour of the sighting, then subtract the sun's position from the moon's; the remainder is the first longitude. (17:1)
- Keep both starting figures at hand. From the head and the moon's position derive the moon's latitude and whether it is northerly or southerly, which is the first latitude; the Rambam warns explicitly to be careful with these two symbols and have them ready for the later calculations, and both are used again at the very end. (17:2)
- Two shortcuts that end the work early. A first longitude of nine degrees or less means the moon certainly cannot be sighted anywhere in Eretz Yisrael, and more than fifteen degrees means it certainly will be; only between nine and fifteen is further calculation required. (17:3)
- Those thresholds hold in only half the sky. They apply when the true position of the moon lies between the beginning of Capricorn and the end of Gemini; between the beginning of Cancer and the end of Sagittarius the figures are ten and twenty-four, so a first longitude of sixteen degrees demands full calculation there rather than a certain sighting. (17:4)
- The first correction, and why it exists. Subtract the sighting adjustment for the moon's constellation from the first longitude, from thirty-four minutes in Libra and Scorpio to a full degree in Taurus, giving the second longitude; the adjustment exists because the true position of the moon is not the place where the moon will actually be sighted. (17:5, 17:6)
RememberAlmost nothing in this chapter is simply true. Nearly every step is true given which half of the sky the moon is standing in.
Part 2Four corrections, and the arc they produce
- The latitude adjustment runs both ways. The longitude adjustment is always subtracted, but the latitude adjustment is subtracted when the moon's latitude is northerly and added when it is southerly; the values run from nine minutes in Aries to forty-six in Libra, and the result is the second latitude. (17:7, 17:8)
- The circuit of the moon is a fraction of that latitude. Because the moon fluctuates in its orbit, set aside a portion of the second latitude ranging from two fifths down to one twenty-fourth according to the moon's place in the zodiac, and nothing at all between the twenty-fifth degree of Gemini and the fifth of Cancer, where the moon does not fluctuate from its orbit. (17:10)
- Where the circuit goes reverses at the boundary. From Capricorn through Gemini a northerly latitude means the circuit is subtracted from the second longitude and a southerly latitude means it is added; from Cancer through Sagittarius the opposite is true, and the result is the third longitude, which equals the second wherever there was no fluctuation to set aside. (17:11)
- The fourth longitude, then the arc of sighting. Adjust the third longitude proportionally by constellation, adding a sixth, a fifth or a sixth again, leaving it as it stands, or subtracting a fifth or a third; then return to the first latitude, take two thirds of it as the correction for geographic latitude, add it if northerly and subtract it if southerly, and what remains is the arc of sighting. (17:12)
- The worked example, second of Iyar. Sun at 7°9' of Taurus, moon at 18°36' of Taurus, latitude 3°53' southerly; first longitude 11°27', second longitude 10°27', second latitude 4°3', circuit 1°1' added, third longitude 11°28', fourth longitude 13°46', less 2°35' for geographic latitude, giving an arc of sighting of 11°11'. (17:13, 17:14)
RememberWhere the moon truly is has been replaced, step by step, with where a person standing in Eretz Yisrael would see it from.
Part 3The limits, and the argument that closes the book
- The arc settles the extremes on its own. An arc of sighting of nine degrees or less makes sighting impossible anywhere in Eretz Yisrael, and an arc greater than fourteen degrees makes it impossible for the moon not to be seen and openly revealed throughout the land. (17:15)
- Between ten and fourteen the arc is read against the first longitude. The arc alone decides nothing in this range; it must be considered in relation to the first longitude, the raw figure taken before any correction was applied, and the resulting five pairings are called the sighting limits. (17:16)
- The five limits, in descending order. Arc between nine and ten requires a first longitude of thirteen degrees or more; between ten and eleven requires twelve; between eleven and twelve requires eleven; between twelve and thirteen requires ten; between thirteen and fourteen requires nine. Fall short on either figure and the moon will not be sighted. (17:17, 17:18, 17:19, 17:20, 17:21)
- The example resolved. With an arc of 11°11' on the second of Iyar the case falls between ten and fourteen degrees, so it is measured against the first longitude, which exceeds eleven degrees, and the moon is assured of being sighted that night. (17:22)
- Why the method is this complicated, and where it came from. The effort was spent to present a method that comes close without extremely complicated calculations, since the moon has major incongruities in its orbit, as the Sages said that the sun knows the time of its setting and the moon does not; the rationales belong to astronomy and geometry, and because they are proven, whether the author was a prophet or a gentile is of no concern. (17:23, 17:24)
RememberWe do not rely on the individual who made these statements, but on the proofs he presented and the reasons he made known.