Sara Smollett Sara Smollett
September 24, 2002
History of Science

Chief World Systems

We observe the heavenly bodies - the sun, moon, and planets - in motion. But what is the precise motion that we observe? Are these bodies actually in motion or do they merely appear to be in motion? How are the positions of these bodies related to the position of the Earth?

These are a few of the great open questions in astronomy. They are not open questions because they have not been seriously considered; instead, they are open questions because there are many different theories about the motions of the sun, moon, and planets. The challenge before us is to justify one of these theories to the exclusion of the others or, if none of these theories suffice, to justify a new theory to the exclusion of all of those considered before. If the astronomical sciences are not to be made a mockery, we must be able to disprove false theories and produce a single factual theory of the motions of the planets.

There are currently three competing chief world systems to understand and consider: the Ptolemaic (c. 150 AD), the Copernican (1543), and the Tychonic (1588). (There are actual more than three theories, but most of the theories can be categorized more generally as either Ptolemaic, Copernican, or Tychonic.) It is important to keep in mind that while these three models of the universal are conceptual very different, they are all compatible with our empirical observations and can be relied upon to yield predictions to a reasonable degree of accuracy. Though physically different, they are mathematically equivalent. What then, are the differences?

The primary difference between these three models can be put crudely as follows. The Ptolemaic model is geocentric and geostatic; the Earth is stationary and located at the center of the universe. The moon, sun, and planets revolve around the Earth in separate orbits. Under the Copernican system, the sun has replaced the Earth as the central body. The Earth, like the planets, is in motion (three kinds of motion, says Copernicus). The Earth revolves around the sun, somehow carrying us along with it. According to the Tychonic system, the sun and moon revolve around the Earth, while the planets all revolve around the sun.

These three systems yield different explanations for retrograde loops - the observation that the planets usually move eastward, but at times become brighter and move westward. The Ptolemaic system explains the motion of planets in retrograde loops by appeal to equants and epicycles (a curve involving the motion of a circle on another circle). Under the Copernican and Tychonic systems, there is no retrograde motion of the wandering stars and no need for major epicycles. Instead, the retrograde loops are merely an illusion which comes about as a result of the combined motion of the planet and the motion of the Earth. Under the Ptolemaic system, all observed motion is actual; in the Copernican and Tychonic, some observed motion is only apparent.

The above description may be enough to show that these three world systems are not the same, but it only begins to scratch the surface of the differences. These systems also differ with respect to actual versus apparent speed (Copernicus said that half of the observed speed was actual and half apparent), the question of solid spheres (which Tycho Brahe's discovery answers in the negative), whether to consider the tropical or sidereal year (the Ptolemaic system relies on the tropical year (equinoxes) while the Copernican relies on the siderial (positions of the stars)), and the determination of the distances between the Earth, sun, planets, and stars (the latter of which are much, much further away for Copernicus than for Ptolemy).

All three of these systems, then, cannot be correct. But which one is? How can we discern between them? We can appeal to scripture, aesthetics, or computational ease. The Copernican system is offensive to many who believe that the Earth is the center of the universe. And how are we to understand that we are perpetually in motion? But at the same time, many believe that the Copernican system is the simplest, that it makes more sense than the Ptolemaic system with its equants and epicycles or the Tychonic system which has nothing at all in the geographic center of the universe. We may decide to choose between theories by finding the one which provides us with the most believable and mathematically useful explanation.

But this will only helps us to predict behaviors; it will not lead us to the true nature of the universe and of our science. We have been given no authoritative manual of the motions of the universe, and we cannot simply guess. We must appeal to our own observations, however prone to error they may be (Mercury in particular is extremely difficult to observe and any observation may in general introduce some error). We make observations as precisely as we can, but that may not be precise enough to find some difference between these world systems.

But observations of what? Recall that these three systems are basically equivalent. They were developed from (roughly) the same observations. Furthermore, it seems that the Copernican and Tychonic systems are mathematically equivalent. The relative positions of the Earth, sun, and planets in the Copernican system are identical with those in the Tychonic. And, as we saw earlier, even though the Ptolemaic offers a different explanation for retrograde loops, the Ptolemaic system predicts the same appearance - the same latitudinal and longitudinal positions of the planets - as the Copernican and Ptolemaic.

I do not believe there is currently any decisive evidence which can discount any of these theories. And I fear that we may not be able to find any such evidence. Although it is possible that the Earth is not at the center of the universe, we make our observations from the Earth. It seems impossible, then, to determine whether the motion and speed we observe is actual or apparent. If only we could see more clearly with a keener vision, observe the Earth in motion, or look upon the Earth and stars from some point in the heavens. Then we might be able to understand, once and for all, the workings of our all-too-mysterious universe.

File translated from TEX by TTH, version 2.51.
On 31 Oct 2002, 12:06.