Halachah 1 – The Moon Has Two Mean Motions
The moon has two separate average movements. First, the moon itself travels around a smaller orbit, and that motion is called the mean anomaly or emtza ha-maslul. Second, that smaller orbit itself travels around a larger orbit surrounding the world, and that movement is called the mean moon or emtza ha-yare’ach. The moon’s average daily movement in this larger orbit is 13 degrees, 10 minutes, and 35 seconds.
Halachah 2 – The Moon’s Mean Movement Over Different Periods
The Rambam gives prepared values for the moon’s average movement over larger blocks of time, so the calculation will be easier. For example, in ten days the moon moves 131 degrees, 45 minutes, and 50 seconds, and in one hundred days it moves 237 degrees, 38 minutes, and 23 seconds. He also gives the remainders for one thousand days, ten thousand days, twenty-nine days, and a standard lunar year. These values allow a person to calculate the moon’s average position for any desired date.
Halachah 3 – The Mean Motion of the Moon’s Anomaly
The Rambam now gives the daily movement of the moon in its smaller orbit, called the mean anomaly. Its daily movement is 13 degrees, 3 minutes, and 54 seconds. He then provides shortcut values for ten days, one hundred days, one thousand days, ten thousand days, and twenty-nine days, so that one can calculate the moon’s anomaly without multiplying from scratch every time.
Halachah 4 – The Starting Positions for the Moon’s Calculations
The Rambam gives the starting point for the moon’s calculations at the established reference time. At that point, the moon’s mean position was 1 degree, 14 minutes, and 43 seconds in Taurus, and the moon’s mean anomaly was 84 degrees, 28 minutes, and 42 seconds. Once these starting values and the moon’s average motions are known, one can calculate the moon’s mean position for any desired night, just as the sun’s mean position was calculated earlier.
Halachah 5 – Adjusting the Moon’s Mean Position According to the Sun’s Location
After calculating the moon’s mean position, one looks at the sun’s position in the zodiac and adjusts the moon’s mean position accordingly. Depending on where the sun is, one either leaves the moon’s mean position unchanged, adds 15 or 30 minutes, or subtracts 15 or 30 minutes. This adjustment prepares the moon’s position for the specific time of visibility after sunset.
Halachah 6 – The Moon’s Mean Position at the Time of Visibility
After making the adjustment based on the sun’s location, the resulting value is considered the moon’s mean position approximately one third of an hour after sunset. This is called the mean moon for the time of visibility, because the purpose of these calculations is to determine whether the new moon could actually be seen in the evening sky.