English 233:  Introduction to Western Humanities -- Baroque & Enlightenment

Complication in the Aristotelian-Ptolemaic model of the universe.

A model of the universe is a complex hypothesis about how objects really stand in space such that they present the appearances they do to an observer placed at a particular spot within the overall imagined system (e.g., to an astronomer on earth).

Let's review some of these appearances and then see how Ptolemy and his followers proposed to explain them. Since it is vitally important that we keep distinct in our minds the observed look of things that we are trying to explain and the imagined look of things that we postulate "behind experiences" to explain them, I will put descriptions of appearances (to a human observer, on the Earth) in green type, descriptions of Ptolemaic hypothetical machinery in purple type, and descriptions of Copernican machinery in red type.  It is the job of both the Ptolemaic and the Copernican theoretic models to explain the same appearances.

Here are the positions that the planet Mars takes on successive nights in the late Spring.  (The dash represents the path of the sun through the same region during the same season, as registered (for instance) at the moment just after sunset when the stars become visible).

 

Below, in (a), is the kind of epicycle/deferent system that astronomers working in the Ptolemaic framework postulated as the real relative motion of an "superior" planet in space, with respect to the Earth and the sphere of fixed stars.  (An "superior" planet in Ptolemy's scheme is one whose orbit around the Earth lies beyond that of the sun; these are Mars, Jupiter, and Saturn).  Such a motion would produce the appearances (above) for observers on Earth, whose surface Ptolemy supposed as concentric with both the sphere of fixed stars (rotating daily) and the deferent, whose period of rotation must differ slightly so as to make the planet advance.in general through the fixed stars (from April 1 to June 1 and from October 1 to October 15 in the picture above).  The job of the epicycle, when carried sideways (deferred by the deferent on which it is mounted), is to make the planet trace some such actual path through space as indicated in (b).  This motion in actual space would show up to an observer located on Earth as the kind of path drawn in (c), which corresponds to the sort of observed path recorded in the previous diagram.

 

And here is the sort of arrangement in actual space hypothesized by Copernicus to account for the same apparent retrograde motion, in this case of an "superior" planet -- Mars, Jupiter or Saturn -- whose orbits Copernicus places successively further out from the sun than that of Earth.

The Earth moves on its orbit from E1 to E7.  During the same time, the superior planet (e.g., Mars) moves more slowly in its orbit from P1 to P7.  The planet's apparent position against the fixed stars on the stellar sphere (which Copernicus postulates as motionless) slides eastward from position 1 to 7, but as Earth catches up and passes the more distant planet there will show up against the constellations a brief westward retrogression from 3 to 5.  This corresponds to the kind of path observed for Mars in the record summarized in the first diagram.

 

Ptolemaic astronomy had to postulate epicycle/deferent systems for all the inferior and superior planets (i.e., for all the theoretical planets except the Sun and the Moon).  And indeed, it was necessary to postulate epicycles on epicycles, and to resort to other complications (eccentrics and equants, which we will not discuss here).

The resulting complicated system (necessary to account for the observed data within the Ptolemaic geocentric framework) struck Copernicus as too senselessly complicated to be imagined as the work of a perfect Creator.

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      Contents copyright © 1998 by Lyman A. Baker. 

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      This page last updated 11 October 2000.