One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 12
Sefer Zemanim · The sun's mean motion day by day, the slow rotation of its apogee, and the fixed starting point from which every later calculation is counted
59' 8"
The sun's mean travel in a single day
29
Days from one sighting of the moon to the next
70
Years for the apogee to move a single degree
4938
The year from creation at which all reckoning begins
Part 1The sun's mean motion, and the tables built from it
- One number, and everything else follows. The sun's mean travel in a day of twenty four hours is 59 minutes and 8 seconds; in ten days 9 degrees 51 minutes 23 seconds, in one hundred days 98 degrees 33 minutes 53 seconds. (12:1)
- Beyond a full circle, only the remainder counts. Over one thousand days, after all the multiples of 360 have been subtracted, the remainder is 265 degrees 38 minutes 50 seconds; over ten thousand days it is 136 degrees 28 minutes 20 seconds, and one may build the intermediate tables oneself. (12:1)
- Two figures worth preparing in advance. The mean distance for 29 days and for 354 days, the length of a regular lunar year, because there are 29 full days from the night the moon was sighted in one month to the night it may be sighted in the next, no more and no less. (12:1)
- The month and the year. The sun's mean travel in one month is 28 degrees 35 minutes 1 second, and over a regular lunar year 348 degrees 55 minutes 15 seconds; the whole apparatus exists because the sole desire in these calculations is to know when the moon will be sighted. (12:1)
RememberEvery table in this chapter is built from one daily rate, and aimed at one question: will it be seen tonight.
Part 2The apogee, and the starting point of all reckoning
- The furthest point, and it moves. Every one of the seven has a point in its orbit at which it stands furthest from the earth, called the apogee, and for the sun and the planets that point rotates in a uniform pattern, travelling about one degree in seventy years. (12:2)
- A table for a motion nobody can watch. The sun's apogee travels a second and thirty thirds in ten days, fifteen seconds in one hundred days, two minutes thirty seconds in one thousand days, twenty five minutes in ten thousand days, four seconds and a fraction in twenty nine days, and fifty three seconds in a regular year. (12:2)
- The fixed starting point. All calculation begins from the eve of Thursday, the third of Nisan, 4938 years after creation, when the sun's mean position stood at 7 degrees 3 minutes 32 seconds in Aries and its apogee at 26 degrees 45 minutes 8 seconds in Gemini. (12:2)
- The method itself. Count the days from the starting point to the day you want, take the mean distance travelled in those days from the tables, add the whole sum together while accumulating each unit of measure separately, and the result is the mean position on that day. (12:2)
RememberA rate that never varies, and an origin that had to be chosen. Only one of the two is fixed by nature.
Part 3The worked example, and the freedom at the end
- One hundred days out. Adding 98 degrees 33 minutes 53 seconds to the starting point of 7 degrees 3 minutes 32 seconds yields 105 degrees 37 minutes 25 seconds, placing the sun in Cancer, fifteen degrees complete and standing in the sixteenth. (12:2)
- An admitted hour of slack. The figure may hold at the beginning of the night, or an hour before sunset, or an hour after, and this is stated to be of no consequence for determining visibility, because the approximation is compensated when the mean position of the moon is calculated. (12:2)
- You may choose another starting point. The same procedure serves any date, even a thousand years ahead, and one may establish a different starting point instead, such as the beginning of a nineteen year cycle or of a new century, or a date in the past, since the path to it is well known. (12:2)
- Forward by adding, backward by subtracting. A year of full months runs one day longer than a regular year and a year of lacking months one day shorter, while a leap year runs thirty, thirty one or twenty nine days longer; add the accumulated distance to the starting point for a future date, subtract it for a past one, and the same holds for the moon and the other planets. (12:2)
RememberThe arithmetic runs in both directions. Any day you land on may become the day you count from.