1.1.3. Towards Renaissance Cosmology
The two sphere Universe of Aristotle was to persist, relatively unaltered, for about 1700 years. Possibly this was a consequence of the loss of distinction between cosmology, philosophy and religion; as all three were now unified under Aristotle's simple geocentric model. Such a model has a powerful allure and may explain why, instead of using unbiased observations to test and refine the model, cosmologists of the time forced the physical world to conform to this simple geocentric model. Chief among these early cosmologists was Ptolemy (circa 100-150 AD), who created a remarkably cumbersome model to account for the observed retrograde motion of the planets while keeping the earth the center of all planetary orbits. As Figure 1-2 attests, a large number of parameters are required to account for each orbit. Despite the fact that Ptolemy's model predicted that Mercury should be able to be seen at midnight (see Figure 1-2), belief in an Earth-centered universe was so strong that Ptolemy's model went unquestioned for centuries. The lack of challenges brought to the Ptolemaic model is an important historical reminder of the dangers of thinking that any particular cosmology - including ours today - is wholly correct.
Figure 1-2: Representation of the Ptolemaic System showing the three main elements of the eccentric, the epicycle and the equant. Here the Earth is slightly offset from the center of the circle (C) defined defined by diameter AB. The planet, in orbit about the earth, moves on an epicycle centered on F which is "affixed" to the larger circle defined by diameter AB. The planet's movement on the epicycle could qualitatively account for observed retrograde motion. The final element, the equant represents a fixed point (Q) in which the epicycle center (F) rotates about. Since Q is offset from C, the distance between F and Q varies slightly throughout one orbital cycle as one the distance between the Earth and the Planet.
In the mid 16th century, Copernicus (1473-1543) proposed a profound paradigm shift which swept away the previously accepted cosmology. With one idea, Copernicus removed the uniqueness of the Earth by placing the Sun at the center of the solar system. Although history rightly identifies Copernicus as starting this revolution, many of its basic tenets were written down 150 years earlier in the Essay On Learned Ignorance by Cardinal Nicholas de Cusa. In this essay it is postulated that:
All motion was relative
That no matter where one stood in the Universe the same pattern of stars would be "strewn out in front of them"
The earth may not be stationary (as demanded in the Two Sphere Universe)
Embodied in these postulates are the themes of relativity, homogeneity and the explicit concept that the Universe has no center. The Copernican notion of non-uniqueness would appear to be a subset of these grander ideas. As is usually the case in history, the original source of these grand ideas remains obscure. Cardinal Nicholas may have received much of his inspiration from the Roman poet Lucreutis who in 100 BC wrote about the infinite, atomist, non-deterministic Universe in his poem On the Nature of the Universe. This poem was lost for centuries until it was discovered in 1417 in an Italian monastery, approximately 100 years before Nicholas's essay.
Support of the Copernican revolution came from other other renaissance scientists. Galileo (1564-1642) upon observing that, in the case of Jupiter, small objects moved about the bigger object, embraced the Heliocentric Cosmology of Copernicus by analogy with the Jupiter-Galilean satellite system. Tycho Brahe (1546-1601) realized that it was possible to prove that the Earth did indeed revolve around the Sun, through direct measurement of stellar parallax. Stellar parallax is the reflection of the annual motion of the Earth around the Sun which cause a perceptible shift in the positions of nearby stars compared to more distant ones (see Figure 1-3). Tycho made very accurate naked eye measurements but failed to detect any positional shifts. Based his failure to detect parallax, Tycho concluded erroneously that the Heliocentric model must be incorrect. The alternative explanation, that the stars are too far away to allow for a naked eye determination of stellar parallax, was apparently never considered by Tycho. This is but one of numerous examples throughout the history of cosmology when scientific judgment was clouded by human ego or naivete; an experimenter who believes in the infallibility of their skills at detecting observational phenomena cannot be considered an impartial observer. In Tycho's case, the most scientifically plausible explanation for his non-detection of stellar parallax was simply that the effect was below the sensitivity of his experiment.
Figure 1-3: Schematic Representation of stellar Parallax. Distant stars act as a fixed background reference coordinate system (shown here as a ruler). Nearby stars, when observed 6 months apart, will show a small movement with respect to the background of fixed stars.
Still Tycho did one very important thing that accelerated the pace of cosmological model building - he published his data - in particular, his data on the position of Mars. These data were later used by Kepler (1571-1630) to empirically show that the orbits of the planets could not be perfect circles, as defined by Pythagoras and Aristotle and retained under the Copernican model. Armed with this improved positional data, Kepler was able to geometrically describe the orbits of the planets around the sun and, for the first time, to set the relative scale of the solar system. Kepler's second law of planetary motion, that planets sweep out equal areas in their elliptical orbits at equal times, of course demands that orbital speed is a function of distance from the sun. Hence, Kepler indirectly discovered the presence of a force acting upon the planets to change their velocity. However, Kepler's laws remained a set of empirical rules without a dynamical basis. The link between these laws and the physical world would be established about 50 years later by Isaac Newton (1642-1727).