Planetary Motion
visualization science

There’s a piece of artwork in my house that frequently provokes curiosity from guests. The artwork in question depicts three early theoretical models for the motion of the classic planets (Figure 1). When I first acquired the artwork, I needed to brush up on my astronomy in order to adequately explain it to inquiring visitors. I took numerous physics courses in college, but regrettably, never any astronomy. This post is a short treatise I wrote for myself so that I could better explain the artwork to visitors and the underlying early history that gave rise to our understanding of planetary motion.

Figure 1. Three early models of planetary motion—the Ptolemaic model (left), Copernican model (center), and Tychonic model (right).

Early observers of the night sky largely believed that the cosmos was geocentric. The Greeks thought that the planets orbited around the Earth in perfect celestial paths, sometimes called crystalline spheres. Many theologians and philosophers, including Aristotle and his contemporaries, were proponents of geocentricism based on several lines of reasoning. The Earth was thought to be at the center of the universe because it did not appear to be in motion nor did distant stars exhibit parallax. Celestial bodies were observed rotating around the Earth, rising and falling in the sky, suggesting that the stars revolved around the Earth. The empirical evidence for geocentricism was further bolstered by religious ideals. Placing Earth at the center of the solar system supported the accepted notion of a perfect world created by God(s) and the importance of humanity in the universe.

Many of the early geocentric models required alarming complexity to explain the observations seen in the night sky. For example, Aristotle’s geocentric model consisted of more than 40 spheres and the unmoved mover, which he hypothesized controlled the daily motion of the planets. A fundamental problem with the early models was that they could not explain retrograde motion. Over many nights, planets were seen to travel in loops, moving west to east, then briefly east to west, before resuming their westward traverse across the night sky. Geocentric models which placed the planets on perfect circular orbits could not explain this looping phenomena.

Around 100 A.D., Ptolemy extended the ideas of Aristotle, Heraclides, and others by developing a geocentric model to account for retrograde motion. Using a system of deferents and epicycles, Ptolemy placed each planet on an orbit (the epicycle) around another orbit (the deferent). An illustration of his model can be seen in the lower left corner of my artwork in Figure 1. I’ve also constructed a dynamic version of the model below to better illustrate the salient features of the model:1

Figure 2. Visualization of the Ptolemaic model

In Ptolemy’s time, only 5 planets were known to exist. Each planet, as well as the Sun and the Moon, were thought to orbit the Earth on perfect circular paths.2 I’ve illustrated the deferents with dashed strokes and the epicycles with solid strokes. The looping phenomena produced by retrograde motion is depicted trailing Mars. Ptolemy claimed that celestial bodies orbited with uniform circular motion, but he needed to integrate numerous complexities into his model in order to account for the variable speed that the planets seemed to exhibit from Earth. Ptolemy suggested that the center of each epicycle moved at a constant distance from the center of the cosmos, but at a constant angular speed about another point called the equant.

Ptolemy’s model was fairly good at predicting the locations of the planets, but it was not entirely accurate. Over a thousand years later, Copernicus, motivated by these inaccuracies, devised an alternate model for planetary motion. Copernicus was troubled by the complexity of Ptolemy’s model and the need for the equant to explain planetary motion. He thought that modeling the planets as spheres rotating uniformly about an off center point was an indication that Ptolemy’s model was incorrect. To avoid the equant, Copernicus posited that the Sun, not the Earth, was at the center of the cosmos and that the speed of Earth’s orbit relative to the other planets was responsible for retrograde motion.3

Like Ptolemy, Copernicus adhered to the Aristotelian notion that planets rotated on perfect circular paths. He realized that certain planets were farther from the Sun and that this feature could account for retrograde motion. With different orbital periods, a planet closer to the sun would at certain points appear to pass more distant planets and this would manifest as retrograde motion for an observer on Earth. Here’s a visualization of the salient features of the Copernican system, also shown in the top center inset of the artwork in Figure 1:

Figure 3. Visualization of the Copernican model

As with the Ptolemaic model, Copernicus only knew of the classic planets, so Mercury, Venus, Earth, Mars, Jupiter, and Saturn are depicted in Figure 3. The salmon-colored lines passing from Earth though Mars and into the cosmos shows how one planet moves with respect to another planet as Copernicus envisaged it for an observer from Earth. When Earth passes Mars in its orbit around the Sun, retrograde motion can be seen in the visualization; Mars appears to move backwards for a brief period before resuming its westward motion.

Shortly after Copernicus published his heliocentric theory in De revolutionibus orbium coelestium, a colorful Danish nobleman named Tycho Brahe proposed the final model in my artwork (bottom right corner of Figure 1). Brahe modeled planetary motion as a chimera of the Ptolemaic and Copernican systems. His model borrowed geocentricism from Ptolemy with the Moon and the Sun in orbit around the Earth; however, it differed from the Ptolemaic system in that he placed all the planets except Earth in orbit around the Sun. Brahe’s model is sometime called the geoheliocentric model:

Figure 4. Illustration of the Tychonic system. Image courtesy History of Science Collections, University of Oklahoma Libraries.

Prior to Brahe’s death in 1601, he asked his apprentice, Johannes Kepler to elucidate the orbit of Mars. Using years of empirical data collected by Brahe, Kepler formulated his three laws of planetary motion, which began to overturn the idea that planets traveled in perfect circular orbits. Kepler realized that the data fit an ellipse, not a circle, and this work, along with the earlier models of Ptolemy, Copernicus, and Brahe, laid the foundation for Newton’s Law of Motion and a more complete understanding of planetary motion.

  1. Ptolemy did not know the distances, sizes, or velocities of the objects in the night sky; Kepler’s Laws had not yet been discovered. For these reasons, I’ve taken artistic license in my visualizations, as was done in the artwork. Nothing is to scale. Using an accurate scale of the cosmos was not practical given the extremity of distance, speed, and mass of the different celestial objects. 

  2. It’s unclear whether Ptolemy thought that the Moon and the Sun also revolved on epicycles along with the planets. I’ve seen the model described in both ways. 

  3. The Copernican system also used epicycles to refine the retrograde motion of the planets, but they were only a minor feature of the model.