Let
O be the center of the Earth and the center of the lunar deferent GAE.
Let A be the 7, center of the first (larger) epicycle BF . . ., and B the
center of the second (smaller) epicycle CD . . . which carries the Moon.
Copernicus postulated that A, the center of the first epicycle, moved from
A to E with the velocity of the Moon's mean sidereal motion.
If we then subtract from that the mean sidereal motion of the apparent
Sun, the difference is the rate at which A actually travels toward that
is, its mean synodic motion. Thus the first epicycle returns to point A
in one mean synodic month.
The
center B of the second epicycle (which is at the apogee of the first epicycle)
is carried toward F at a rate equal to the Moon's mean motion in anomaly,
while the Moon itself travels on the circumference of the second epicycle--beginning
at perigee C and traveling toward D--at a rate which is double the
rate at which A is traveling toward E. Thus he supposed that he had
accounted for both the first and second lunar inequalities. |