Epicycles were mathematical modifications added to the geocentric theory to ensure that the model was consistent with astronomical observations. Geocentrism proposed that Earth was a stationary object at the center of the universe and that the planets, the Moon, the Sun, and the sphere of the fixed stars revolved about earth in a series of concentric orbits. This model implies that the planets always traverse the night sky in the same direction, from west to east with respect to the stars. Three planets visible to the naked eye (Mars, Jupiter, and Saturn) do not behave in this manner. Rather, their orbits exhibit the property of retrograde motion in which the planet appears to slow down in its eastward motion, stop, and briefly change its direction, traveling west with respect to the stars. It again stops and resumes its eastward journey. To explain this phenomenon, the astronomer Ptolemy proposed...