Ptolemaic System

In his Dialogue Concerning the Two Chief World Systems, Ptolemaic and
Copernican of 1632, Galileo attacked the world system based on the cosmology of
Aristotle (384-322 BCE) and the technical astronomy of Ptolemy (ca. 150 CE).

In his books On the Heavens, and Physics, Aristotle put forward his notion of
an ordered universe or cosmos. It was governed by the concept of place , as
opposed to space, and was divided into two distinct parts, the earthly or
sublunary region, and the heavens. The former was the abode of change and
corruption, where things came into being, grew, matured, decayed, and died; the
latter was the region of perfection, where there was no change. In the
sublunary region, substances were made up of the four elements, earth, water,
air, and fire. Earth was the heaviest, and its natural place was the center of
the cosmos; for that reason the Earth was situated in the center of the cosmos.
The natural places of water, air, and fire, were concentric spherical shells
around the sphere of earth. Things were not arranged perfectly, and therefore
areas of land protruded above the water. Objects sought the natural place of
the element that predominated in them. Thus stones, in which earth
predominated, move down to the center of the cosmos, and fire moves straight
up. Natural motions were, then, radial, either down or up. The four elements
differed from each other only in their qualities. Thus, earth was cold and dry
while air was warm and moist. Changing one or both of its qualities, transmuted
one element into another. Such transmutations were going on constantly, adding
to the constant change in this sublunary region.

The heavens, on the other hand, were made up of an entirely different
substance, the aether [1] or quintessence (fifth element), an immutable
substance. Heavenly bodies were part of spherical shells of aether. These
spherical shells fit tightly around each other, without any spaces between
them, in the following order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn,
fixed stars. Each spherical shell (hereafter, simply, sphere) had its
particular rotation, that accounted for the motion of the heavenly body
contained in it. Outside the sphere of the fixed stars, there was the prime
mover (himself unmoved), who imparted motion from the outside inward. All
motions in the cosmos came ultimately from this prime mover. The natural
motions of heavenly bodies and their spheres was perfectly circular, that is,
circular and neither speeding up nor slowing down.

It is to be noted about this universe that everything had its natural place, a
privileged location for bodies with a particular makeup, and that the laws of
nature were not the same in the heavenly and the earthly regions. Further,
there were no empty places or vacua anywhere. Finally, it was finite: beyond
the sphere of the fixed stars and the prime mover, there was nothing, not even
space. The cosmos encompassed all existence.

[Image]  Christian Aristotelian Cosmos

Now, ingenious as this cosmology was, it turned out to be unsatisfactory for
astronomy. Heavenly bodies did, in fact, not move with perfect circular
motions: they speeded up, slowed down, and in the cases of the planets even
stopped and reversed their motions. Although Aristotle and his contemporaries
tried to account for these variations by splitting individual planetary spheres
into component spheres, each with a component of the composite motion, these
constructions were very complex and ultimately doomed to failure. Furthermore,
no matter how complex a system of spheres for an individual planet became,
these spheres were still centered on the Earth. The distance of a planet from
the Earth could therefore not be varied in this system, but planets vary in
brightness, a variation especially noticeable for Venus, Mars, and Jupiter.
Since in an unchangeable heaven variations in intrinsic brightness were ruled
out, and since spheres did not allow for a variation in planetary distances
from the Earth, variations in brightness could not be accounted for in this
system.

Thus, although Aristotle's spherical cosmology had a very long life,
mathematicians who wished to make geometrical models to account for the actual
motions of heavenly bodies began using different constructions within a century
of Aristotle's death. These constructions violated Aristotle's physical and
cosmological principles somewhat, but they were ultimately successful in
accounting for the motions of heavenly bodies. It is in the work of Claudius
Ptolemy, who lived in the second century CE, that we see the culmination of
these efforts. In his great astronomical work, Almagest, [2] Ptolemy presented
a complete system of mathematical constructions that accounted successfully for
the observed motion of each heavenly body.

Ptolemy used three basic constructions, the eccentric, the epicycle, and the
equant. An eccentric construction is one in which the Earth is placed outside
the center of the geometrical construction. Here, the Earth, E, is displaced
slightly from the center, C, of the path of the planet. Although this
construction violated the rule that the Earth was the center of the cosmos and
all planetary motions, the displacement was minimal and was considered a slight
bending of the rule rather than a violation. The eccentric in the figure below
is fixed; it could also be made movable. In this case the center of the large
circle was a point that rotated around the Earth in a small circle centered on
the Earth. In some constructions this little circle was not centered in the
Earth.

[Image]  An eccentric

The second construction, the epicycle, is geometrically equivalent to the
simple movable eccentric. In this case, the planet moved on a little circle the
center of which rotated on the circumference of the large circle centered on
the on theEarth. When the directions and speeds of rotation of the epicycle and
large circle were chosen appropriately, the planet, as seen from the Earth,
would stop, reverse its course, and then move forward again. Thus the annual
retrograde motion of the planets (caused, in heliocentric terms by the addition
of the Earth's annual motion to the motion of the planet) could roughly be
accounted for.

[Image]  An epicycle

But these two constructions did not quite bring the resulting planetary motions
within close agreement with the observed motions. Ptolemy therefore added yet a
third construction, the equant. In this case, the center of construction of the
large circle was separated from the center of motion of a point on its
circumference, as shown below, where C is the geometrical center of the large
circle (usually called in these constructions the excentric circle) but the
motion of the center of the epicycle, O, is uniform about e, the equant point.

[Image]  An equant

Ptolemy combined all three constructions in the models of the planets, Sun, and
Moon. A typical construction might thus be as in the picture below, where E is
the Earth, C the geometric center of the eccentric circle, Q the equant point,
F the center of the epicycle, and P the planet. As mentioned before, the
eccentric was often not fixed but moved in a circle about the Earth or another
point between the Earth and the equant point.

[Image]  Ptolemy's system

With such combinations of constructions, Ptolemy was able to account for the
motions of heavenly bodies within the standards of observational accuracy of
his day. The idea was to break down the complex observed planetary motion into
components with perfect circular motions. In doing so, however, Ptolemy
violated the cosmological and physical rules of Aristotle. The excentric and
epicycle meant that planetary motions were not exactly centered on the Earth,
the center of the cosmos. This was, however, a "fudge" that few objected to.
The equant violated the stricture of perfect circular motion, and this
violation bothered thinkers a good deal more. Thus, in De Revolutionibus (see
Copernican System), Copernicus tells the reader that it was his aim to rid the
models of heavenly motions of this monstrous construction.

Aristotelian cosmology and Ptolemaic astronomy entered the West, in the twelfth
and thirteenth centuries, as distinct textual traditions. The former in
Aristotle's Physics and On the Heavens and the many commentaries on these
works; the latter in the Almagest and the technical astronomical literature
that had grown around it, especially the work of Islamic astronomers working in
the Ptolemaic paradigm. In the world of learning in the Christian West (settled
in the universities founded around 1200 CE), Aristotle's cosmology figured in
all questions concerned with the nature of the universe and impinged on many
philosophical and theological questions. Ptolemy's astronomy was taught as part
of the undergraduate mathematical curriculum only and impinged only on
technical questions of calendrics, positional predictions, and astrology.

Copernicus's innovations was therefore not only putting the Sun in the center
of the universe and working out a complete astronomical system on this basis of
this premise, but also trying to erase the disciplinary boundary between the
textual traditions of physical cosmology and technical astronomy.

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Sources

The Aristotelian cosmos is described in his Physics and On the Heavens, see The
Complete Works of Aristotle: The Revised Oxford Translation, ed. Jonathan
Barnes, 2 vols. (Princeton: Princeton University Press, 1984). On the
relationship between Greek cosmology and astronomy, see B. R. Goldstein and A.
C. Bowen, "A New View of Early Greek Astronomy," Isis 74 (1983):330-40. The
best translation of the Almagest is Ptolemy's Almagest, tr. G. J. Toomer
(London: Duckworth; New York: Springer Verlag, 1984). On Medieval cosmology and
astronomy, see Edward Grant, "Cosmology," in Science in the Middle Ages, ed.
David C. Lindberg (Chicago: University of Chicago Press, 1984), pp. 265-302;
and Olaf Pedersen, "Astronomy," ibid, pp. 303-37. For an account of
Aristotelian cosmology and Ptolemaic astronomy in the period leading up to
Galileo's discoveries, see James M. Lattis, Between Copernicus and Galileo:
Christoph Clavius and the Collapse of Ptolemaic Cosmology (Chicago: University
of Chicago Press, 1994).

Images:
Christian Aristotelian Cosmos: Taken from Peter Apian, Cosmographia (1524) is
out of copyright.
Diagrams of excentric, epicycle, equant, and Ptolemy's system: No current
references.

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[1] I use the traditional English spelling here to distinguish Aristotle's
heavenly substance from the modern chemical substance, ether. [2] The title is
one given to this book by Islamic translators in the ninth century. Its
original Greek title is Mathematical Syntaxis.
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Copyright ©1995 Albert Van Helden