From this work on the shape and size of Earth, the next 2,000 years were marked by a struggle to come to grips with the spatial structure of the solar system. The search was an interesting one from the perspective of spatial thinking. Frequently, this search for an understanding of the structure of the solar system is described as a process of replacing the geocentric view of the universe with a heliocentric view. In a more fundamental spatial view, the search illustrates the power and implications of selecting an appropriate frame of reference.
From the time that individuals began to make systematic observations of the objects in the sky, and until the time of Copernicus, the crucial task of astronomers was predicting the position of the moving celestial bodies as a function of time. These predictions were essential for their primary functions of time keeping, eclipse prediction, and generating horoscopes. The Ptolemaic universe, the dominant geocentric cosmology for many centuries, is a spatialization of a method used to predict the position of various celestial objects, such as the Moon and the planets that appeared to move against the backdrop of the fixed stars. In general, the “fixed stars” tended to retain their positions with respect to one another on an imaginary “celestial sphere,” which appeared to turn slowly around Earth, making one circuit every 24 hours. In contrast, the planets (then taken to be the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn) appeared to move irregularly with respect to the stars. The Sun and Moon always moved in one direction with respect to the stars, while the other planets moved at different speeds and sometimes even moved backwards (retrograde motion). Furthermore, the planets Mercury and Venus were never seen far from the Sun. These features were well known even to the earliest observers, and any explanation of the structure of the solar system had to explain these motions.
The Ptolemaic system, set forth by Claudius Ptolemy in the Almagest around AD 150, was a refinement of earlier ideas. The major feature of the Ptolemaic system was the use of epicycles (Figure 3.3), or circles on circles, as a mathematical device to predict where a planet would be at any given time. The appropriate choice of epicycles could explain why Mercury and Venus were never seen too far from the Sun and could even explain the retrograde motion of the planets. The result was a remarkably good description of the relative motion of the objects in the solar system from the frame of reference of Earth.
The major feature of the Ptolemaic view was the use of epicycles (Figure 3.4) to explain the retrograde motion of the outer planets (Figure 3.5). In essence, however, the result is simply a description of the relative motion of the objects in the solar system from the frame of reference of Earth.
The Copernican cosmology can be viewed as a simple transformation of the motion of the same objects to the frame of reference of a fixed Sun. To the extent that the models of these respective universes are calibrated by observations, they have the same predictive power for a terrestrial observer interested in prediction. However, several steps, theology aside, led to the acceptance of the Copernican model. First, its elegant spatial simplicity was appealing. Next, the laws of planetary motion, derived from the model by Kepler, gave it some deeper appeal. Kepler’s laws were significant spatial generalizations about the relationships between the planets and the Sun. He not only inferred the elliptical nature of the orbits of the planets, but also provided a generalization that explained the orbits of all objects in terms of the period of rotation around the Sun and their distance from the Sun. By adopting elliptical orbits in a heliocentric system, Kepler was the first to be able to explain the retrograde orbit of the outer planets in modern terms (Figure 3.5). Finally, through the application of the theory of gravitation, Newton gave the Copernican system grounding in first principles, assigning primacy to the mass of the Sun as a referent for the entire solar system.