One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 14
Sefer Zemanim · The moon's two mean rates and why the geometry requires two, the multiples and the epoch positions for each, and the seasonal emendation that is keyed not to the moon but to the sun
2
Mean rates of progress for the moon
6' 41"
Daily gap between the moon's two mean rates
8
Solar bands governing the emendation
20
Minutes after sunset the emended mean describes
Part 1Why the moon needs two means
- A small orbit inside a large one. The moon revolves in a small orbit that does not encompass the earth, and that small orbit itself rotates within a larger orbit that does encompass the earth. (14:1)
- Two names for two motions. The moon's mean progress within the small orbit is called the mean within its path; the mean progress of the small orbit within the large one is called the moon's mean. (14:1)
- The moon's mean, per day. Thirteen degrees, ten minutes and thirty-five seconds, the figure from which the ten day, hundred day, thousand day, ten thousand day, twenty-nine day and yearly totals are built. (14:1, 14:2)
- The mean within its path, per day. Thirteen degrees, three minutes and fifty-four seconds, six minutes and forty-one seconds of arc slower, with its own parallel table of multiples. (14:3)
RememberTwo ladders of numbers, side by side, at almost the same pitch. Nothing on the page stops you taking the wrong one.
Part 2The tables and the starting point
- The moon's mean, multiplied out. Ten days give 131 degrees, 45 minutes, 50 seconds; a hundred days leave 237 degrees, 38 minutes, 23 seconds; twenty-nine days leave 22 degrees, 6 minutes, 56 seconds; a regular year leaves 344 degrees, 26 minutes, 43 seconds. (14:2)
- The mean within its path, multiplied out. Ten days give 130 degrees and 39 minutes exactly; a hundred days leave 226 degrees, 29 minutes, 53 seconds; twenty-nine days leave 18 degrees, 53 minutes, 4 seconds. (14:3)
- Two positions at one instant. On the night the calculations begin, Wednesday night, the third of Nisan, 4938, the moon's mean stood at 1 degree, 14 minutes, 43 seconds in Taurus, and the mean within its path stood at 84 degrees, 28 minutes, 42 seconds. (14:4)
- Then look at the sun. Knowing the rate and the epoch position lets you compute the moon's mean for any night, exactly as with the sun; after that, the next step is to determine which constellation the sun will be in at that time. (14:4)
RememberA known place, a known speed, and a count of days. No observation enters the calculation anywhere.
Part 3The emendation, and what it leaves you holding
- Left alone twice a year. Sun between midway in Pisces and midway in Aries, or between midway in Virgo and midway in Libra, and the moon's mean takes no emendation at all. (14:5)
- Added through the first half. Sun between midway in Aries and the beginning of Gemini, add 15 minutes; between the beginning of Gemini and the beginning of Leo, add 30; between the beginning of Leo and midway in Virgo, add 15. (14:5)
- Subtracted through the second half. Sun between midway in Libra and the beginning of Sagittarius, subtract 15 minutes; between the beginning of Sagittarius and the beginning of Aquarius, subtract 30; between the beginning of Aquarius and midway in Pisces, subtract 15. (14:5)
- What the emended figure is. The result, whether raised, lowered or left alone, is the mean of the moon approximately twenty minutes after the setting of the sun, and the Rambam names it the mean of the moon at the time of the sighting. (14:6)
RememberEvery band is defined by where the sun stands, not the moon. The number you correct and the number that tells you how belong to different bodies.