One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 11
Sefer Zemanim · The mathematics behind the court's reckoning: the units of the sphere, the rules for adding and subtracting them, and the difference between a body's mean and true motion
360
Degrees in the heavenly sphere
30
Degrees in each of the twelve constellations
60
Minutes to a degree, seconds to a minute
32
Degrees north, the latitude all reckoning assumes
Part 1Why the Rambam teaches this at all
- The court calculated before it ever listened. As established earlier, the court made precise calculations and knew in advance whether the moon would be visible, so anyone who desires words of wisdom and probes to grasp the mysteries will want to know how it was done. (11:1)
- Great wise men blundered here. The sages of the nations who studied astronomy and mathematics in earlier eras disagreed sharply about these methods, doubts arose among them, and some calculated endlessly without finding the correct approach. (11:2)
- Do not regard these calculations lightly. They are deep and abstract matters, the mystery of the intercalation, conveyed only to ordained and perceptive sages; the fixed calendar used when no court hears witnesses is by contrast simple enough for schoolchildren in three or four days. (11:4)
- The approximations are deliberate. Where the method is imprecise, it is because the computation proved that the imprecision does not affect the determination of visibility, and where a step looks inadequate it buys a correct result without lengthy work. (11:5, 11:6)
RememberHe teaches a retired method on purpose, and warns you not to skip it because it is no longer needed.
Part 2The units and the arithmetic
- The sphere, divided. 360 degrees and twelve constellations beginning from Aries, thirty degrees each, sixty minutes to a degree, sixty seconds to a minute, sixty thirds to a second, and further if you wish. (11:7)
- Reading a position off the number. A star at 70 degrees, 30 minutes, 40 seconds sits in Gemini in the middle of its eleventh degree; a star at 320 degrees sits in Aquarius in its twentieth degree. (11:8, 11:9)
- Carry upward, and cast off the circle. Add like to like; sixty seconds become a minute, sixty minutes become a degree, and degrees are gathered in sets of 360, where only the remainder after 360 is of consequence. (11:10)
- A worked subtraction on the page. He takes 200 degrees 50 minutes 40 seconds from 100 degrees 20 minutes 30 seconds, converting a minute into sixty seconds and a degree into sixty minutes, and arrives at 259 degrees 29 minutes 50 seconds. (11:12)
RememberEverything in this chapter counts in sixties, and the circle keeps no memory of how many times you went around it.
Part 3Mean motion, true motion, and a starting point
- Uniform speed, off center orbits. The sun, the moon and the other five each proceed at a uniform speed in their own orbits, never inclining to heaviness or lightness, and although those orbits encircle the earth, the earth is not at their center. (11:13)
- Mean motion against true motion. Measured against the sphere of the constellations, where the earth is the center, the rate appears to change from day to day; the uniform rate is called mean motion and the apparent rate is called true motion, and the true motion gives the true position. (11:14, 11:15)
- One fixed epoch for every calculation. All reckoning begins from the eve of Thursday, the third of Nisan, the seventeenth year of the 260th cycle, the year 4938 from creation, 1489 with regard to contracts, and 1109 years after the destruction of the Second Temple. (11:16)
- Centered on Jerusalem. Since sighting matters only in Eretz Yisrael, the calculations assume Jerusalem and locations within six or seven days' journey, about 32 degrees north of the equator with a band from 29 to 35, and about 24 degrees west of the center of the populated area with a band from 21 to 27. (11:17)
RememberNothing up there ever changes speed. The unevenness you measure comes from standing somewhere that is not the center.