2.2 The Geocentric Universe

The Greeks of antiquity, and undoubtedly civilizations before them, built models of the universe. The study of the workings of the universe on the largest scales is called cosmology. Today, cosmology entails looking at the universe on scales so large that even entire galaxies can be regarded as mere points of light scattered throughout space. To the Greeks, however, the universe was basically the solar system—namely, the Sun, Earth, Moon, and the planets known at that time. The stars beyond were surely part of the universe, but they were considered to be fixed, unchanging beacons on the celestial sphere. The Greeks did not consider the Sun, the Moon, and the planets to be part of this mammoth celestial dome, however. Those objects had patterns of behavior that set them apart.

Greek astronomers observed that over the course of a night, the stars slid smoothly across the sky. Over the course of a month, the Moon moved smoothly and steadily along its path on the sky relative to the stars, passing through its familiar cycle of phases. Over the course of a year, the Sun progressed along the ecliptic at an almost constant rate, varying little in brightness from day to day. In short, the behavior of both Sun and Moon seemed fairly simple and orderly. But ancient astronomers were also aware of five other bodies in the sky—the planets Mercury, Venus, Mars, Jupiter, and Saturn—whose behavior was not so easy to grasp. Their motions ultimately led to the downfall of an entire theory of the solar system and to a fundamental change in humankind’s view of the universe.

Planets do not behave in as regular and predictable a fashion as the Sun, Moon, and stars. They vary in brightness, and they don’t maintain a fixed position in the sky. Unlike the Sun and Moon, the planets seem to wander around the celestial sphere—indeed, the word planet derives from the Greek word planetes, meaning "wanderer." Planets never stray far from the ecliptic and generally traverse the celestial sphere from west to east, like the Sun. However, they seem to speed up and slow down during their journeys, and at times they even appear to loop back and forth relative to the stars, as shown in Figure 2.4. In other words, there are periods when a planet’s eastward motion (relative to the stars) stops, and the planet appears to move westward in the sky for a month or two before reversing direction again and continuing on its eastward journey. Motion in the eastward sense is usually referred to as direct, or prograde, motion; the backward (westward) loops are known as retrograde motion.

Figure 2.4 Planetary Motion Most of the time, planets move from west to east relative to the background stars. Occasionally—roughly once per year—however, they change direction and temporarily undergo retrograde motion before looping back. The main figure shows an actual retrograde loop in the motion of the planet Mars. The inset above depicts the movements of several planets over the course of several years, as reproduced on the inside dome of a planetarium. The motion of the planets relative to the stars (represented as unmoving points) produces continuous streaks on the planetarium "sky." (Museum of Science, Boston)

Like the Moon, the planets produce no light of their own; instead, they shine by reflected sunlight. Ancient astronomers correctly reasoned that the apparent brightness of a planet in the night sky is related to its distance from Earth—planets appear brightest when closest to us. However, the planets Mars, Jupiter, and Saturn are always brightest during the retrograde portions of their orbits. The challenge facing astronomers was to explain the observed motions of the planets and to relate those motions to the variations in planetary brightness.

The earliest models of the solar system followed the teachings of the Greek philosopher Aristotle (384–322 B.C.) and were geocentric, meaning that Earth lay at the center of the universe and all other bodies moved around it. (Figures 1.7 and 1.10a illustrate the basic geocentric view.) (Sec. 1.2) These models employed what Aristotle, and Plato before him, had taught was the perfect form: the circle. The simplest possible description—uniform motion around a circle with Earth at its center—provided a fairly good approximation to the orbits of the Sun and the Moon, but it could not account for the observed variations in planetary brightness or their retrograde motion. A more complex model was needed to describe the planets.

Figure 2.5 Geocentric Model In the geocentric model of the solar system, the observed motions of the planets made it impossible to assume that they moved on simple circular paths around Earth. Instead, each planet was thought to follow a small circular orbit (the epicycle) about an imaginary point that itself traveled in a large, circular orbit (the deferent) about Earth.
In the first step toward this new model, each planet was taken to move uniformly around a small circle, called an epicycle, whose center moved uniformly around Earth on a second and larger circle, known as the deferent (Figure 2.5). The motion was now composed of two separate circular orbits, creating the possibility that, at some times, the planet’s apparent motion could be retrograde. Also, the distance from the planet to Earth would vary, accounting for changes in brightness. By tinkering with the relative sizes of epicycle and deferent, with the planet’s speed on the epicycle, and with the epicycle’s speed along the deferent, early astronomers were able to bring this "epicyclic" motion into fairly good agreement with the observed paths of the planets in the sky. Moreover, this model had good predictive power, at least to the accuracy of observations at the time.

However, as the number and the quality of observations increased, it became clear that the simple epicyclic model was not perfect. Small corrections had to be introduced to bring it into line with new observations. The center of the deferents had to be shifted slightly from Earth’s center, and the motion of the epicycles had to be imagined uniform with respect to yet another point in space, not Earth. Around A.D. 140, a Greek astronomer named Ptolemy constructed perhaps the best geocentric model of all time. Illustrated in simplified form in Figure 2.6, it explained remarkably well the observed paths of the five planets then known, as well as the paths of the Sun and the Moon. However, to achieve its explanatory and predictive power, the full Ptolemaic model required a series of no fewer than 80 distinct circles. To account for the paths of the Sun, Moon, and all nine planets (and their moons) that we know today would require a vastly more complex set. Nevertheless, Ptolemy’s text on the topic, Syntaxis (better known today by its Arabic name Almagest—"the greatest"), provided the intellectual framework for all discussion of the universe for well over a thousand years.

Figure 2.6 Ptolemy’s Model The basic features, drawn roughly to scale, of the geocentric model of the inner solar system that enjoyed widespread popularity prior to the Renaissance. The planets’ deferents were considered to move on spheres lying within the celestial sphere that held the stars. The celestial sphere carried all interior spheres around with it, but the planetary (and solar) spheres had additional motions of their own, causing the Sun and planets to move relative to the stars. To avoid confusion, partial paths (dashed) of only two planets, Venus and Jupiter, are drawn here.
Today, our scientific training leads us to seek simplicity, because simplicity in the physical sciences has so often proved to be an indicator of truth.
We would regard the intricacy of a model as complicated as the Ptolemaic system as a clear sign of a fundamentally flawed theory. With the benefit of hindsight, we now recognize that the major error lay in the assumption of a geocentric universe. This was compounded by the insistence on uniform circular motion, whose basis was largely philosophical, rather than scientific, in nature.

Actually, history records that some ancient Greek astronomers reasoned differently about the motions of heavenly bodies. Foremost among them was Aristarchus of Samos (310–230 B.C.), who proposed that all the planets, including Earth, revolve around the Sun and, furthermore, that Earth rotates on its axis once each day. This, he argued, would create an apparent motion of the sky—a simple idea that is familiar to anyone who has ridden on a merry-go-round and watched the landscape appear to move past in the opposite direction. However, Aristarchus’s description of the heavens, though essentially correct, did not gain widespread acceptance during his lifetime. Aristotle’s influence was too strong, his followers too numerous, his writings too comprehensive. The geocentric model went largely unchallenged until the sixteenth century A.D.

The Aristotelian school did present some simple and (at the time) compelling arguments in favor of their views. First, of course, Earth doesn’t feel as if it’s moving. And if it were, wouldn’t there be a strong wind as we move at high speed around the Sun? Then again, considering that the vantage point from which we view the stars changes over the course of a year, why don’t we see stellar parallax? Nowadays we might be inclined to dismiss the first two points as merely naïve, but the third is a valid argument and the reasoning is essentially sound. We now know that there is stellar parallax as Earth orbits the Sun. However, because the stars are so distant, it amounts to less than 1", even for the closest stars. Early astronomers simply would not have noticed it. We will encounter many other instances in astronomy where correct reasoning has led to the wrong conclusions because it was based on inadequate data.