Chapter 13, 14 & 15: The Ptolemaic System and the Copernican System

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Worldviews, by Richard Dewitt

Chapter 13, 14 & 15: The Ptolemaic System and the Copernican System

Uniform and Circular Motion Redux
We saw in the previous chapters that, besides the various empirical data that any model of planetary and celestial motion must account for, there are some basic conceptual facts that it must accommodate as well. The two most important of these are Uniform Motion and Circular Motion.
In a sense, it is peculiar to think of these as conceptual facts, since whether an object is moving at a uniform speed or in a circular pattern would seem to be just as empirical as what point of the night sky a planet is located at any given time. This certainly would be the case if we were attempting to describe the motion of a ball on a string from an external vantage point. But, given the fact that scientists were constrained to make all their observations from earth, there is a very important sense in which uniform and circular motions play a more conceptual role. From the point of view of earth, any apparently complete, closed pattern of orbit at all is consistent with the observable data. There is no strictly logical reason to prefer a circle, to a heart to a 16 point star. That’s because from the vantage point of earth any line of sight to an orbiting planet will pass through three distinct but indistinguishable points on the corresponding orbit-shapes.

So, circular and uniform motion were conceptual in the sense that they were not observable, and in the sense that they established a framework, or model, for interpreting the empirical data. Of course, it is easy to understand the ancient and medieval attachment to both of these assumptions. Both are simple and familiar properties of moving bodies observed here on earth. Roughly circular and linear motion are much easier for us to generate than rapidly oscillating heart or star shaped motions. Of course, these two assumptions, while intuitively simple, are what ultimately complicated both the Ptolemaic and the Copernican Systems.

The Ptolemaic System
Epicyclic orbit
Ptolemy’s system respected the overwhelmingly empirical fact that the earth does not move. Given this assumption, the available data required that all celestial bodies be in motion around the earth. Simple circular motion was simply incompatible with the available data, specifically, the observed retrograde motion, and Ptolemy’s contribution was to show that epicyclic motion could model retrograde motion. Let’s revisit these concepts briefly:

  • The Ptolemaic System

Ptolemy’s system required major epicycles to deal with the retrograde motion, but it also required minor epicycles to deal with other more minor observed irregularities. Minor epicycles were epicycles on top of epicycles. (The cute phrase “piling on the epicycles” basically means a desperate resort to ad hoc hypotheses, but it’s important to understand that these do preserve circular motion, and the kinds of patterns you can create with a few moving circles is, in fact, pretty astounding. (Kenner, the toy manufacturer made a lot of money on Ptolemy’s insight with a toy called Spirograph )

Deferent vs. Eccentric Orbits
However, plain old epicyclic motion wasn’t enough to preserve the data, and it proved impossible to preserve a third, highly desirable conceptual truth, viz., that the earth, being the center of the universe, would also be the center of the planet’s orbit. Ptolemy had to sacrifice this assumption and content himself with showing that planet was in fact in circular orbit around something, just not the center of the universe.
Circular orbits around the center of the universe (earth) were called deferent - they deferred to the centrality of the earth - and circular orbits around something else were called eccentric, presumably because center of these orbits didn’t make any real sense. The stars on the celestial sphere moved deferentially, but the planets all moved eccentrically in Ptolemy’s system.
Equant Points
Epicycles and eccentric circles were sufficient to preserve the circular motion assumption, but it was not sufficient to preserve uniform motion. In other words a Ptolemaic system consisting only of epicycles and deferent points would still require the planets to be moving non uniformly in order to accurately predict the observed positions of the planets.
The equant point was the final expedient. Ptolemy was able to show that even though the planets did not move in uniform epicyclic motion around either the earth or an eccentric point, there did exist another distinct from whose vantage point the earth was moving uniformly, and this is what he called the equant point. However, it was not the speed of the object itself that was uniform, but the angle it swept out, using the equant point as a reference, between any two points in time.
Both the equant point and the eccentric point seem arbitrary from an explanatory perspective. It is perfectly reasonable to ask why planetary motion is circular with respect to one point, uniform with respect to another, with neither of these points being earth, the actual center of the universe.
Still, it was pretty amazing to discover that these points really existed, and one can partly counter such questions by asking how the existence of such points could turn out to be totally coincidental.
(So, if you look back at figure 13.1 on page 117, you will see all of the above concepts embedded in Ptolemy’s model for the orbit of Mars around the earth.)
The Copernican System
Copernicus basically hated the arbitrariness of equant points and he dedicated his career to showing that they could be dispensed with. He succeeded in this, but only by developing a totally insane model that conflicted with the most obvious fact in the world, namely that the earth was stationary. Copernicus’ achieved this result by putting the sun at the center of universe.
On this model the motion of earth and the planets could be represented as uniform, and it also provided a strikingly different account of retrograde motion. (See Figure 14.2) or

Copernican Retrograde.
You can see a demonstration of the mathematical equivalence of the Copernican and Ptolemaic systems here, as well as a review of all the basic concepts we’ve been studying here at Craig McConnell’s astronomy website.
Copernicus system did not eliminate the need for epicycles, or eccentrics, and it did not in any normal sense provide a conceptually simpler model of planetary motion than Ptolemy’s geocentric system. In order to make it work, Copernicus required a system in which the deferent of the epicycle of Mars itself revolved in a circle around the eccentric of the earth, with the eccentric of the earth revolving around another point which revolved around the sun. (See Figure 14.1 )

Copernicus’ Motivation
As your author points out toward the end of this chapter, Copernicus system did do a better job with the empirical data, specifically it gave a very nice explanation for why Mars, Jupiter and Saturn were brighter during retrograde (the earth was closer to them) and why Venus and Mercury were always seen near the sun (they are always nearest the sun).
However, these were relatively minor successes given its violation of the stationary earth fact. Besides his dislike of equant points Copernicus may have been motivated by a quasi religious attitude toward the sun. (Your author notes the influence of Plato’s allegory of the cave on Neoplatonism, in which the sun represents Plato’s form of the Good, which is the end toward which all things aspire (around which all things revolve?) in Plato’s system.) This is all pretty speculative, but it’s interesting to consider the possibility that what we now consider to be one of the great intellectual leaps forward in terms of our understanding of the cosmos was actually inspired by a weak and misguided analogy.
The Tychonic System
Tycho Brahe, who was born shortly after the death of Copernicus actually produced a system that was, given the available data, was better than the Ptolemaic and the Copernican system, as it borrowed the best aspects of each.
The Tychonic system preserved the stationary earth, with the moon, sun and the celestial sphere revolving around it. The rest of the planets orbit the earth as well, but the center of their orbit is the sun, so the planets orbit the earth because the sun is orbiting the earth. (Figure 15.1)
Ultimately, though, Tycho Brahe’s main contribution was to produce the most accurate astronomical observations to date, and it was these observations that made it possible for Johannes Kepler to break the grip of the past.
(As your author notes, there are still peole in the world who advocate something like the Tychonic System. There are various websites providing arguments in favor of it. )

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