1 The Birth of Science - MSRI

3.6 Aristarchus, Heliocentrism, and Relative Motion 71
of his scientific method and of the use of trigonometric methods, but it
is essentially a geometric work, unrelated to the fundamental problem of
astronomy: the description of the motion of heavenly bodies. Also barren
is Hipparchus’ commentary on the poem of Aratus, which merely furnishes
angular coordinates of fixed stars. In sum, the only contemporary
source of insight into early Hellenistic models for describing the motion
of planets is the passage in the Arenarius, and that’s just a brief digression,
a mention of an astronomical argument embedded in a different context.
The only important astronomical work that has come down to us from
antiquity was written in the imperial period by Claudius Ptolemy (second
century A.D.). Called Syntaxis mathematica (Mathematical treatise), it is
better known under the name the Arabs gave it, Almagest. 93
Two results of Hipparchus, recoverable from the Almagest, will suffice
to give an idea of the level astronomy had reached in his time in terms
of accuracy of measurements. Hipparchus discovered the precession of
the equinoxes, and he probably measured the mean distance to the moon,
finding it to be 59 earth radii. 94
The difficult problem of trying to reconstruct the fundamental ideas of page 107
astronomy in the third and second centuries B.C. will occupy us in Chapter
10. For now we make just a few observations about the heliocentrism
of Aristarchus. As related by Archimedes, 95 Plutarch 96 and Simplicius, 97
among others, Aristarchus formulated a theory according to which the
earth revolves yearly about the sun and rotates daily about an axis tilted
with respect to the plane of its orbit. The Plutarchan passage says that
by postulating these two earthly movements Aristarchus was trying to
, “save the phenomena” (i.e., explain the things seen, this
being the original meaning of “phenomena”). Since the description of the
apparent motion of sun, moon and fixed stars cannot be affected in any
way by heliocentrism, the phenomena in question must have concerned
93
The critical edition of the Almagest is Heiberg’s (Leipzig, 1898–1903), whose pagination we
follow. For a recent translation see [Ptolemy/Toomer].
94
Certainly Hipparchus made the observation (reported also in Plutarch, De facie quae in orbe
lunae apparet, 921D) that lunar parallax can be measured. The distance of 59 terrestrial radii is
obtained in the Almagest (V, xiii, 416) through a procedure marred by many errors that miraculously
cancel out. Toomer suggests that this was a value obtained by Hipparchus and known to Ptolemy
([Toomer: HDSM]). The mean distance between the centers of the two bodies is just over 60 earth
radii; thus the approximation reported by Ptolemy is very good, and indeed exceptionally good
if it refers to the distance between the surfaces, which is the datum that can be measured directly.
Aristarchus had taken the distance as measured “to the center of the moon from our eye” (On the
sizes and distances of the sun and moon, prop. 11), though there was no need for him to be specific,
since he assumed the radius of the earth to be negligible in comparison.
95
Archimedes, Arenarius, 135, 8–19 (ed. Mugler, vol. II).
96
Plutarch, De facie. . . , 923A.
97
Simplicius, In Aristotelis De Caelo commentaria, [CAG], vol. VII, p. 444.
Revision: 1.13 Date: 2002/10/16 19:04:00