Deferents and Epicycles

Plato and Aristotle were fixated on the notion that circles were perfect, and that far away objects were more perfect than objects found close to, or on, the imperfect Earth. As a result, they insisted that planetary motion be circular, with the imperfect Earth at circle center.Still, astronomers of their times (and following, for almost 2000 years) struggled to explain planetary retrograde motion. (See this movie here.)To "explain" planetary retrograde motion while retaining "the perfection of circles", various astronomers, starting with Apollonius of Perga, suggested a "circle on circle" solution, called deferents and epicycles.The deferent is considered the main orbit of the planet, even though the planet is never on it. Instead, the center of a subsidiary orbit, the epicycle, advances on the deferent. Both the deferent and epicycle advance counterclockwise, as viewed from above (or north of) the Ecliptic Plane (the plane of Earth's true orbit, and the plane of the Sun's fictitious orbit around the Earth, the Ecliptic).In this animation, we make our own deferents and epicycles, varying them by orbital size and orbital speed. We view what the result looks like, both from above the Ecliptic Plane, and from a side view, relative to the background (or "fixed") stars. In the screenshot above, the large blue dot is the home star (for us, the Sun) of the planet (indicated here by the yellow dot). The little white dot is the center of the epicycle, which advances at an adjustable speed along an adjustably sized deferent (indicated by the blue orbit). The yellow orbit is the epicycle itself (its radius and orbital speed are adjustable too). The red path is the supposed orbital path that the planet sweeps out, in accordance with this model of planetary motion.ExperimentRun the animation, varying the radii and speeds of the deferent and epicycle. First view the animation as from above the Ecliptic Plane. Notice how bizarre the planetary path is, and how unnecessarily complicated (and without scientific merit) is the deferent-epicycle model.

Now run the animation again, but observe the side view (i.e., the boxed view). Pay no attention to the white dot (as it is not an actual celestial body), but watch the movement of the yellow dot (the planet) relative to the blue dot (the star). Does the planet's motion look like it adequately mimics true planetary motion?

For a movie of a planet undergoing retrograde motion, click here.

For a movie of multiple planets circling the Earth, click here.