Halachah 1 – The Moon’s Orbit Is Tilted from the Sun’s Path
The moon travels on a circular path that is tilted relative to the sun’s path. Half of the moon’s path leans north of the sun’s path, and half leans south of it. These two paths cross at two opposite points. When the moon is at one of these crossing points, it is exactly aligned with the sun’s path and has no northern or southern latitude. When it moves away from those points, it begins to move either north or south of the sun’s path.
Halachah 2 – The Head and Tail of the Moon’s Path
The point where the moon begins moving north of the sun’s path is called the Rosh, the “Head.” The opposite point, where the moon begins moving south, is called the Zanav, the “Tail.” The Head moves at a steady rate, but it moves backward through the zodiac, from Aries toward Pisces, Aquarius, and so on.
Halachah 3 – The Average Motion of the Head
The Rambam gives the average movement of the Head. In one day, it moves 3 minutes and 11 seconds backward. He also provides useful values for longer periods: ten days, one hundred days, one thousand days, ten thousand days, twenty-nine days, and a standard lunar year. These values allow one to calculate the position of the Head for any desired time.
Halachah 4 – The Starting Position of the Head
At the reference starting point used in these calculations, the average position of the Head was 180 degrees, 57 minutes, and 28 seconds. Since the Head moves backward through the zodiac, calculating its actual position requires first finding its average movement and then subtracting that from 360 degrees.
Halachah 5 – How to Calculate the Position of the Head
To find the Head’s position at any time, one calculates its average movement for that time just as one calculates the sun’s and moon’s average positions. Then one subtracts that value from 360 degrees. The remaining value is the position of the Head. The Tail is always exactly opposite the Head.
Halachah 6 – Example of Finding the Head and Tail
The Rambam gives an example for the beginning of Thursday night, the second of Iyar in the reference year. After adding the Head’s movement for twenty-nine days to the original value and subtracting from 360 degrees, the Head is found to be in Virgo, at about 27 degrees and 30 minutes. The Tail, being opposite it, is in Pisces, also at about 27 degrees and 30 minutes.
Halachah 7 – Determining Whether the Moon Is North or South
Once one knows the position of the Head, the Tail, and the true position of the moon, one can determine the moon’s direction. If the moon is at the Head or Tail, it has no latitude. If it has passed the Head and is moving toward the Tail, it is north of the sun’s path. If it has passed the Tail and is moving toward the Head, it is south of the sun’s path.
Halachah 8 – The Meaning of Lunar Latitude
The moon’s distance north or south of the sun’s path is called the latitude of the moon. If the moon is north of the sun’s path, it is called northern latitude. If it is south, it is called southern latitude. When the moon is exactly at the Head or Tail, it has no latitude at all.
Halachah 9 – The Moon’s Maximum Latitude
The moon’s latitude never exceeds five degrees, whether north or south. It begins at zero at the Head, increases gradually until it reaches five degrees, then decreases again until it reaches zero at the Tail. It then repeats the same pattern on the southern side until it returns to the Head.
Halachah 10 – How to Calculate the Moon’s Latitude
To calculate the moon’s latitude, one first finds the position of the Head and the moon’s true position. Then one subtracts the Head from the moon’s true position. The result is called the maslul harochav, the path of latitude. If this value is between 1 and 180 degrees, the moon’s latitude is north. If it is greater than 180 degrees, the moon’s latitude is south. If it is exactly 180 or 360 degrees, the moon has no latitude.
Halachah 11 – The Latitude Correction Table
The Rambam gives a table for finding how many degrees of latitude correspond to the path of latitude. For example:
- 10 degrees gives a latitude of 52 minutes.
- 20 degrees gives 1 degree and 43 minutes.
- 30 degrees gives 2 degrees and 30 minutes.
- 60 degrees gives 4 degrees and 20 minutes.
- 80 degrees gives 4 degrees and 55 minutes.
- 90 degrees gives the maximum of 5 degrees.
This table shows how far north or south the moon is from the sun’s path.
Halachah 12 – Estimating Between Listed Values
If the path of latitude falls between two values listed in the table, one estimates proportionally. For example, if the path is 53 degrees, it lies between 50 and 60 degrees. The difference between their latitude values is divided across the ten degrees, allowing one to estimate the correct value for 53 degrees.
Halachah 13 – Values Between 90 and 180 Degrees
Once the values up to 90 degrees are known, the values from 90 to 180 degrees can be found by subtraction. If the path of latitude is greater than 90 but less than 180, subtract it from 180, and use the latitude value of the remainder.
Halachah 14 – Values Between 180 and 270 Degrees
If the path of latitude is greater than 180 and less than 270, subtract 180 from it, and use the latitude value of the remainder. Since the path is now beyond 180 degrees, the latitude is on the southern side.
Halachah 15 – Values Between 270 and 360 Degrees
If the path of latitude is greater than 270 and up to 360, subtract it from 360, and use the latitude value of the remainder. This also gives the proper latitude amount, according to the same table.
Halachah 16 – Example: A Path of 150 Degrees
If the path of latitude is 150 degrees, subtract it from 180, leaving 30 degrees. The table teaches that 30 degrees corresponds to 2 degrees and 30 minutes, so that is the moon’s latitude.
Halachah 17 – Example: A Path of 200 Degrees
If the path of latitude is 200 degrees, subtract 180, leaving 20 degrees. Since 20 degrees corresponds to 1 degree and 43 minutes, that is the latitude. Since the original path was greater than 180, the latitude is southern.
Halachah 18 – Example: A Path of 300 Degrees
If the path of latitude is 300 degrees, subtract it from 360, leaving 60 degrees. Since 60 degrees corresponds to 4 degrees and 20 minutes, that is the moon’s latitude. The same method applies to all other values.
Halachah 19 – Complete Example of Calculating Lunar Latitude
The Rambam completes the example from the previous chapters. On the beginning of Thursday night, the second of Iyar in the reference year, the moon’s true position was in Taurus at about 18 degrees and 40 minutes, while the Head was in Virgo at about 27 degrees and 30 minutes. Subtracting the Head from the moon gives a path of latitude of about 231 degrees and 10 minutes. Since this is greater than 180 degrees, the latitude is southern. Using the table, the latitude is approximately 3 degrees and 53 minutes south.