1 The Birth of Science - MSRI

10.5 A Passage of Seneca 255
The sling argument mentioned by Plutarch, which in modern language
we might phrase as the cancellation between gravity and centrifugal force,
can explain quite easily the motion of the moon around the earth, at least
if, as suggested in the Plutarchan passage, we just want an approximate
description involving circular orbits. But the extension of this argument
to planets runs tinto a serious obstacle: How it is that at the moment of a
planetary station, when presumably there should be no centrifugal force,
the planet does not start to fall on the earth? This is the reason for the
interest in planetary stations conveyed by Seneca and the gist of his question:
how is it that some planets seem sometimes to reverse their motion,
if heavenly bodies cannot stop or turn back without starting to fall upon
one another?
Seneca explains retrogressions by alluding to combinations of several
circular motions (natura viarum circolorumque sic positorum. . . ). The retrograde
motion of planets, arising for a while from such combinations, is but
a deception (ut certo tempore intuentes fallant); in their real motion, planets
never turn backwards. page 318
Possibly, Seneca’s source explained that the apparent motion of planets
(their motion relative to the earth) results from the combination of two
circular orbits, both centered at the sun and traveled respectively by the
earth and the planet, while the “real” motion of the planet happens on the
second of these orbits. This explanation accounts well for the occurrence
of retrogressions, and, having been proposed by Aristarchus of Samos,
at the time of Seneca’s source it would have been known to Hellenistic
astronomers for about two centuries. Of course, Seneca’s words about
“paths and circles” by themselves might admit other interpretations, and
might indeed suggest an epicycle-based geocentric theory. But I think that
the heliocentrism of Seneca’s source can be discerned clearly enough from
the following considerations.
First, heliocentrism is able to solve the dynamical problem mentioned
by Seneca: the sling argument can be applied to planetary motion exactly
as to lunar motion, by just interpreting the center as the sun rather than the
earth, whereas it is hard to see what the solution would be in a geocentric
framework.
Secondly, a Ptolemaic-type epicycle theory would explain the motion
of the planets without any reference to the sun, whereas the words solis
occursus in our passage show that the sun played a role in the explanation
given by Seneca’s source.
Thirdly, Seneca’s statement that planetary stations are just an illusion
and the ship analogy imply that what is regarded as the true motion (in
which the planets do not retrogress) is not the motion with respect to the
earth. Indeed, the ship topos is used to illustrate the relativity of motion
Revision: 1.11 Date: 2003/01/06 02:20:46