1,308. Calculating the Sun's Actual Position for a Given Date

Hilchos Kiddush HaChodesh 13:9

Let’s say you wanted to know the actual position of the sun at the start of Friday night, 14 Tammuz for the (Rambam’s) current year. First, calculate the average position of the sun for that time, which, as explained in halacha 12:2, is 105, 37, 25. Next, calculate the sun’s apogee for this time, which is 86, 45, 23. Subtract the apogee from the average position and you get 18 degrees, 52 minutes, 2 seconds (18, 52, 2). When it comes to the sun’s course, the minutes are not important; if there are fewer than 30 minutes, just ignore them. If there are more than 30 minutes, convert them to a degree and add them to the total number of degrees. Therefore, in this example, it’s as if there are 19 degrees in the sun’s course. Using the process described, the angle for this course can be calculated as 38 minutes.

Hilchos Kiddush HaChodesh 13:10

Because the course is smaller than 180 degrees, this angle of 38 minutes is subtracted from the sun’s average position, which leaves us with 104 degrees, 59 minutes, 25 seconds (104, 59, 25). Therefore, the sun’s actual position at the desired time is 15 degrees minus 35 seconds in Cancer. In these calculations, one need not be at all concerned with the seconds – not for the sun’s position, nor that of the moon, nor in any other calculation. When the number of seconds reaches 30, simply convert them to a minute and add them to the total number of minutes.