Towards Renaissance Cosmology

The perfect crystalline spheres of Aristotle's unchanging Universe would persist, relatively unaltered, for the next 1700 years. This is likely the result of the tremendous appeal of the model in that it firmly establishes Humans as occupying a special place in the Cosmos. This positioning of Humans was, of course, consistent with some religion and philosophy of this time so there was little incentive to revise the model, even though there were clear observations in conflict with it. Among these observations are the following:

Transient phenomena such as comets, novae, and variable stars were observed. This indicates that the Universe does change but most of these phenomena were attributed to disturbances in the upper atmosphere of the Earth
The observed brightness of the planets were not always the same. In particular, the brightness of Venus was observed to vary considerably. If the distance between the earth and the planet is fixed, as in the Aristotelian model, then this variation in brightness could only be cause by something intrinsic to the planet.
The Aristotelian model makes the definite prediction that all the planets and stars should move in the same direction as the Crystalline Spheres upon which the planets and stars are fixed and therefore constrained to only rotate in one direction. However, at that time it was known that Mars would sometimes move in the opposite direction for a brief period of time (this is known as retrograde motion).

The retrograde motion of Mars was a serious challenge to the model and in fact, was sufficient to falsify it in favor of a simpler and more natural model. However, Ptolemy (circa 100-150 AD) provides us with an outstanding example of the human side of science in that he developed an elaborate model which would allow this retrograde motion to be explained in terms of the Aristotelian model. The central feature of this model, namely that the Earth is at the center of the Universe, was so appealing that the Ptolemaic model is an example of molding the data to fit the model, rather than abandoning the model because it was in conflict with the data. In fact, it would be more than 1000 years before this model would be abandoned by the Western World.

Key to the Ptolemaic model is the use of epicycles in explaining planetary motions. These epicycles make a full description of a planetary orbit quite complicated as many parameters are required. This is shown in Figure 1.2. In this figure the Earth is slightly offset from the center of the circle (C) 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 like the distance between the Earth and the Planet.

Figure 1.2 Schematic representation of the Ptolemaic System machinery required to explain planetary orbits. The major elements in this system are described in the text.

The use of these epicycles fully explains how a planet could appear to move backwards. If we refer to Figure 1.2 we see that the planet on the little wheel that rotates around point F oscillates between moving in the same direction as the big wheel (defined by the diameter AB ) and moving in the opposite direction. This would qualitatively explain why Mars would appear to move "backwards" at some times. Its not clear that this machinery correctly explains the duration over which Mars would behave in this way, but those observations were quite limited at the time. Of course, the real explanation for the retrograde motion of Mars (and all the other planets beyond Mars) is that the Earth is orbiting about the Sun faster than Mars and hence periodically overtakes it. As the Earth passes Mars, Mars appears to move backwards. This explanation, however, was not considered (because it would remove the Earth from being in a unique place in the Cosmos) so instead the very complicated set of machinery shown in Figure 1.2 to explain planetary motion was adopted.

The Ptolemaic model would remain unchallenged until the mid 16th century, when Copernicus (1473-1543) proposed a profound paradigm shift which swept away the previously accepted cosmology. The paradigm was a simple one: The Sun was at the center of the solar system. The Geocentric cosmology of the ancients was now supplanted by the much more natural Heliocentric Cosmology of Copernicus. In this new Cosmology, the uniqueness of the Earth is removed. However, Copernicus did retain the idea of perfection as he assumed the orbits of the planets around the Sun were perfectly circular. Although history rightly identifies Copernicus as starting the scientific revolution, many of its basic tenets were written down approximately 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 Aristotelian 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 Lucretius who, around 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.

Once the heliocentric model was documented, support for it came from a variety of other renaissance scientists. Galileo (1564-1642), with his newly made telescope, conducted many observations of the satellites of Jupiter. In so doing he directly observed small objects engaged in orbits around a larger object and in that sense was observing a mini solar system. To Galileo, this provided very strong confirmation of the Heliocentric model where the lesser bodies (the planets) orbit one primary body (the sun). Galileo also observed that Venus exhibited phases (which is why its brightness is so variable) and these phases could be naturally understood in terms of the Heliocentric model as a consequence of the changing Earth-Venus-Sun viewing angle.