1,317. The Head and Tail of the Moon's Orbit

Hilchos Kiddush HaChodesh 16:1

The orbit of the moon crosses the orbit of the sun at an angle with the result that part of the moon’s orbit is to the north of the sun’s orbit and part is to the south of it. These two intersect at two opposing points. When the moon is located at one of these points, it is in the same plane as the sun. When it leaves these points, it heads either north or south of the sun. The point of the moon's orbit where it starts to head north is called the head and the point where it starts to head south is called the tail. The head moves at a uniform rate of speed from Pisces to Aquarius without deviation.

Hilchos Kiddush HaChodesh 16:2

The average motion of the head in one day is 3 minutes, 11 seconds. Therefore, over ten days it moves 31 minutes, 47 seconds; in 100 days it moves 5 degrees, 17 minutes, 43 seconds (5, 17, 43); in 1,000 days it moves 52 degrees, 57 minutes, 10 seconds (52, 57, 10). The remainder over 10,000 days (after removing multiples of 360) is 169 degrees, 31 minutes, 40 seconds (169, 31, 40). Over 29 days it moves one degree, 32 minutes, 9 seconds (1, 32, 9). In a regular year, it moves 18 degrees, 44 minutes, 42 seconds (18, 44, 42). The average position of the head on the night that the Rambam established as his starting point is 180 degrees, 57 minutes, 28 seconds (180, 57, 28).