1 The Birth of Science - MSRI

72 3. Other Hellenistic Scientific Theories
the planets. Archimedes mentions in the Arenarius certain
(expositions or demonstrations of the phenomena) by Aristarchus.
98 These evidently consisted in showing that the complex planetarium
motions, with their stations and retrogressions, could be obtained
from the combination of two simple uniform circular motions around the
sun: the earth’s revolution and an analogous movement for the planets.
The “expositions” of Aristarchus could become particularly effective
if illustrated by a mechanical model of planetary motion. We know that
Archimedes did build such a model, a moving planetarium that reproduced
the apparent motion of the sun, the moon and the planets. The
question is often raised of how Archimedes contrived to do it, under the
presupposition that in his little model the sun and the planets moved
independently, their mechanisms hinged on a fixed “earth”. 99 A fixed- page 108
earth mechanism would indeed be extremely hard to build, but the idea
of building it would only occur to someone who did not know about
Aristarchus’ theory and its power to “save the phenomena”. Since this
theory came down to us precisely through the Arenarius, it is strange, to
say the least, to imagine that Archimedes made no use of it.
The idea that Archimedes built a “geocentric” planetarium probably
arises from the unanimity of the testimonia in saying that his device represented
the motion of the sun and the planets around the earth. It is
important to clarify this point. The aim of explaining planetary motions
as observed from the earth is not achieved by a machine that represents
only the motions of the planets around the sun. If one builds a mechanical
model where the earth and the planets revolve around the sun, it is necessary
to keep the earth fixed as the device operates in order to replicate
the motions actually seen in the sky. 100 What makes a planetarium heliocentric
is the (essential!) feature that the mechanical linkage between the
various planets and the earth is performed through a single hinge placed
in the sun, and this is sufficient to generate relative motions sometimes
in one direction and sometimes in the other. The conjecture that Archi-
98 Archimedes, Arenarius, 136, 1–2 (ed. Mugler, vol. II).
99 See, for example, [Neugebauer: HAMA], vol. 2, p. 652, note 7, which affirms that a planetarium
built on a spherical model cannot replicate even the main features of planetary motion: retrogressions
and stations.
100 Naturally, if one only wants to show “true” motion, with no concern for what is actually observed,
a “pure” heliocentric model is enough. But this attitude seems to me far removed from that
with which Aristarchus built a model that could preserve (explain) the phenomena — it is a much
more “modern” attitude. In fact, it’s typical of today’s teaching methods that a child is indoctrinated
from a tender age with the notion that the earth revolves around the sun (and indeed others,
such as that electrons revolve around the nucleus) without being aware of any phenomenon that
can be explained by such movement.
Revision: 1.13 Date: 2002/10/16 19:04:00