1,316. Calculating the Moon's Actual Position Forever

Hilchos Kiddush HaChodesh 15:8

Based on everything we have said so far, if one wants to know the actual position of the moon for Friday night, 2 Iyar, in the (Rambam’s) current year, then the number of whole days that passed from the Rambam’s previously-established starting point until this date is 29. Calculate the average position of the sun for that night. This is 35 degrees, 38 minutes, 33 seconds (35, 38, 33). Next, calculate the average of the moon at the time of its sighting, which is 53 degrees, 36 minutes, 39 seconds (53, 36, 39). Then, calculate the moon’s average in its path for this time, which is 103 degrees, 21 minutes, 46 seconds (103, 21, 46). Subtract the average position of the sun from the moon’s average; this gives us 17 degrees, 58 minutes, 6 seconds. This is the distance, which we double to get a double distance of 35 degrees, 56 minutes, 12 seconds (35, 56, 12). (Because the double distance falls in between 32 and 38 degrees,) add five degrees to the course (refer back to halacha 15:3). The proper course will come out to be 108 degrees, 21 minutes. As with the sun, the minutes are irrelevant when calculating the course.

Hilchos Kiddush HaChodesh 15:9

The angle for a course of 108 is 5 degrees, 1 minute (refer back to halachos 15:6-7). Since the proper course is smaller than 180 degrees, subtract it from the moon’s average. This gives us 48 degrees, 35 minutes, 39 seconds. Round the seconds up to a minute. The result is that the moon’s actual position for the desired time is 18 degrees, 36 minutes in the 19th degree of Taurus (18,36). In this way, one can calculate the actual position of the moon at the time of its sighting for any date one likes, from the beginning of the year that was selected as the starting point until the end of the world.