The Universe of
Aristotle and Ptolemy and
the Role of Eratosthenes
Aristotle and Eratosthenes
Although Aristotle was not a scientist,
it is important to note that he did point out that
the Earth had to be sphere since its shadow was always
circular. This was in fact a key scientific insight.
It allowed Eratosthenes around 200 BC to calculate the
circumference of the Earth. The method was very clever for the time:
The southern Egyptian city of Syene had a well in which
sun-rays fell directly vertical during the summer solstice.
The sun was therefore at the Zenith there during this time.
However, during the same time in Alexandria,
the sun was 7 degrees south of the
Zenith (1/50 of the circumference of the sky).
Now since the Earth was spherical (from Aristotle)
the 7 degree angle subtended at the Earths surface divided by 360 degrees
equaled the distance between Alexandria and Syene divided by the
Earth's circumference. That is, by using
7 / 360 = distance / circumference
he could measure the distance (in units of stadia) and then
infer the circumference in stadia (about 40,000).
Hard to infer the actual distance in standard modern units
since stadia are of varying sizes, but the technique was
clever at the time and if one uses typical stadium lengths of the time
the estimate was only off by a number bewteen 4 and 14 percent.
Aristotle's Spheres
The celestial sphere that we introduced previously is a convenient "fiction" to
locate objects in the sky. However, the Greek philosopher
Aristotle
(many of
Aristotle's works are available at the
Internet Classics
Archive) proposed
that the heavens were literally
composed of 55 concentric, crystalline spheres to which
the celestial objects were attached and which rotated at different velocities
(but the angular velocity was constant for a given sphere),
with the Earth at the center. The following figure illustrates the ordering of
the spheres
to which the Sun, Moon, and visible planets were attached.
(The diagram is not to scale, and the
planets are aligned for convenience in illustration;
generally they were distributed around the spheres.)
There were additional "buffering" spheres that lay between the spheres
illustrated. The sphere of the stars lay beyond the ones shown here for the
planets; finally, in the Aristotelian conception there was an outermost
sphere that was the domain of the "Prime Mover". The Prime Mover caused the
outermost sphere to rotate at constant angular velocity, and this motion was
imparted from sphere to sphere, thus causing the whole thing to rotate.
By adjusting the velocities of these concentric spheres, many features of
planetary motion could be explained. However, the troubling observations of
varying planetary brightness and retrograde motion could not be accommodated:
the spheres moved with constant angular velocity, and the objects
attached to them were always the same distance from the earth because they
moved on spheres with the earth at the center.
Epicycles and Planetary Motion
The "solution" to these problems came in the form of a clever
proposal: planets were attached, not to the concentric spheres themselves, but
to circles attached to the concentric spheres, as illustrated in the adjacent
diagram. These circles were called "Epicycles", and the concentric spheres to
which they were attached were termed the "Deferents". Then, the centers of the
epicycles executed uniform circular motion as they went around the deferent at
uniform angular velocity, and at the same time the epicycles (to which the
planets were attached) executed their own uniform circular motion.
The net
effect was as illustrated in the following animation. As the center of the
epicycle moves around the deferent at constant angular velocity, the planet
moves around the epicycle, also at constant angular velocity. The apparent
position of the planet on the celestial sphere at each time is indicated by the
line drawn from the earth through the planet and projected onto the celestial
sphere. The resulting apparent path against the background stars is indicated
by the
blue line.
Now, in this tortured model one sees that it is possible to have retrograde
motion and varying brightness, since at times as viewed from the earth the
planet can appear to move "backward" on the celestial sphere. Obviously,
the distance
of the planet from the Earth also varies with time, which leads to variations
in brightness.
Thus, the idea of uniform
circular motion is saved (at least in some sense) by this scheme, and it allows
a description of retrograde motion and varying planetary brightness.
More Sophisticated Epicycles: The Ptolemaic Universe
In practice, even this was not enough to account for the detailed
motion of the planets on the celestial sphere. In more sophisticated epicycle
models further "refinements" were introduced:
- In some cases, epicycles were themselves placed on epicycles, as
illustrated in the adjacent figure.
- In actual models, the center of the epicycle moved with uniform circular
motion, not around the center of the deferent, but around a point that was
displaced by some distance from the center of the deferent.
That ancient astronomers could convince themselves that this elaborate scheme
still corresponded to "uniform circular motion" is testament to the power of
three ideas that we now know to be completely wrong, but that were so ingrained
in the astronomers of an earlier age that they were essentially never
questioned:
- All motion in the heavens is uniform circular motion.
- The objects in the heavens are made from perfect material, and cannot
change their intrinsic properties (e.g., their brightness).
- The Earth is at the center of the Universe.
These ideas concerning uniform circular motion and epicycles were cataloged by
Ptolemy in 150 A.D. His book was called the "Almagest" (literally, "The
Greatest"), and this picture of the structure of the Solar System has come to
be called the "Ptolemaic Universe".
Medieval Aristotelian Astronomy
By the Middle Ages, such ideas took on a
new power as the philosophy of Aristotle (newly rediscovered in Europe) was
wedded to Medieval theology in the great synthesis of Christianity and Reason
undertaken by philosopher-theologians such as Thomas Aquinas. The Prime Mover
of Aristotle's universe became the God of Christian theology, the outermost
sphere of the Prime Mover became identified with the Christian Heaven, and the
position of the Earth at the center of it all was understood in terms of the
concern that the Christian God had for the affairs of mankind.
Thus, the ideas largely
originating with pagan Greek philosophers were baptized into the
Catholic church and
eventually assumed the power of religious dogma: to challenge this view
of the Universe was not merely a scientific issue; it became a theological one
as well, and subjected dissenters to the considerable and not always benevolent
power of the Church.