The Moon

Besides its annual motion, as previously mentioned, the Moon appears to move through four distinct motions. First, it completes monthly revolutions around the Earth’s center in its deferent orbit, following the order of the zodiac signs. This deferent also carries what is called the epicycle of the first inequality (or “of the argument”), which we refer to as the greater epicycle. Additionally, there is a second epicycle attached to it, which moves opposite to the reflex motion of the deferent orbit at a slightly slower pace than the monthly motion.

The Moon, suspended within this system, completes two revolutions per month in the opposite direction of the greater epicycle. Whenever the center of the greater epicycle aligns with a straight line drawn from the center of the large orbital sphere through the Earth’s center (which we call the diameter of the great orbit), the Moon is at its closest point to the center of the greater epicycle. This occurs around the time of the new and full moon. Conversely, during the first and last quarters, it is at its furthest from this center.

The radius of the greater epicycle is one-tenth of the radius of the deferent orbit, plus a fraction of one unit. The radius of the smaller epicycle, in contrast, is five times less one-fourth of this same value. Because of this, the Moon appears to speed up, slow down, rise, and fall, producing variations in its motion due to the smaller epicycle. This epicycle draws the Moon away from uniformity, creating a maximum variation of 17 degrees and one-quarter of a degree in its orbit. Additionally, the center of the greater epicycle alternately pulls the Moon away or draws it closer, depending on the radius of this epicycle.

As a result, since the Moon traces unequal paths around the center of the greater epicycle, the first inequality undergoes multiple variations. This is why, during conjunctions and oppositions to the Sun, the maximum variation does not exceed 4 degrees and 56 minutes, whereas in quadratures, it extends to 6 degrees and 36 minutes. Those who have attempted to explain this motion using an eccentric orbit have made two clear errors, besides introducing an illogical inequality in the circular motion itself. Mathematically, this would imply that in quadratures, when the Moon is at the lowest part of its epicycle, it would appear four times larger than when it is new or full—unless one recklessly claims that the Moon’s physical size changes, which is absurd.

Additionally, the apparent size of the Moon is affected by the notable size of the Earth relative to its distance. This effect becomes particularly pronounced near quadratures. However, careful observation reveals that the apparent size of the Moon in quadratures differs very little from what is observed at the new and full moon, confirming the validity of this model.

Along with these three longitudinal motions, the Moon also follows a latitudinal motion through nodal points. The axes of the epicycles remain parallel to the axis of the deferent, meaning the Moon does not deviate from its general orbital plane.

However, the Moon’s orbit is tilted with respect to the axis of the great orbit (the ecliptic), causing the Moon to deviate from the ecliptic plane. This inclination corresponds to an angle subtended by five degrees on the orbital circumference, and its poles move along a path parallel to the axis of the ecliptic—similar to what was previously described for the Earth’s axial tilt. However, this motion occurs in the opposite direction of the zodiacal signs and at a much slower rate, taking 19 years to complete a full revolution. Many scholars believe this motion occurs in a more elevated orbital sphere, whose poles undergo movement in this manner.

Thus, this appears to be the structure of the Moon’s motions.