REAL PLANETARY MODELS
THE MIDDLE AGES
antiquity, the task of the astronomer was 'to invent hypotheses by which
the phenomena will be saved (that is, accounted for).' The principal
examples in antiquity of attempts to transcend this limitation and produce
physically real astronomical systems were the adaptation of Eudoxus's system
of homocentric spheres by Aristotle, and the Planetary Hypothesis
nested system of 55 concentric spheres accounted, in a qualitative way,
for the major planetary phenomena, but failed to predict accurately either
the variation in the length of the retrograde motion or the observed variation
in the size and brightness of the planets. A system which would predict
these phenomena was that of Ptolemy's Almagest.
Ptolemaic system relied on the A geometrical mechanisms of deferent, epicycle,
equant to transform uniform circular motion into the irregular motions
of the planets.
variations in celestial latitude, one may describe the motions of most
of the planets
accurately by the diagram in Figure 1. The planet P revolves around the
at a constant velocity, while the center of the epicycle C revolves around
CAN with a constant angular velocity with respect to the equant point E
the center of the deferent G or the earth 0.
this system to a physical model was not difficult. Such a model consists
spherical surfaces forming the boundaries between three regions. The surfaces
have the center of the universe, that is, the center of the earth O for
T and T' have the center of the deferent circle G as their center.
planet P is embedded in a small sphere which is finally embedded in the
bounded by the surfaces T and T', which in its turn is embedded in the
S and S'. The sphere between S and S' shares the westward diurnal rotation
of the starry
The sphere between T and T' moves in an irregular manner so that C moves
angular velocity around E and the small sphere moves with the velocity
to the epicycle.
Ptolemaic system in this form is accurate, but it is less satisfying than
Aristotle's system of homocentric spheres as each planet is moved by many
spheres having diverse motions around diverse centers. A further attempt
to establish a system of homocentric spheres was undertaken in the 12th
century by a number of Spanish Arab philosophers and most fully elaborated
model of al-Bitruji, like that of Aristotle, N produces the complex motions
of the planets
nested series of concentric spheres. The M poles of these three spheres
are inclined at
angles to trace out the path of each planet. The outermost sphere shares
diurnal motion of the stellar sphere, rotating once daily around its axis
NS which passes
the poles of the earth and perpendicular to the equator WBE. This sphere
carries around C with it the axis MR of the second sphere, which is inclined
approximately 23° to the poles, a value constant for all the planets
and equal to the obliquity of the ecliptic ABC. The
sphere rotates at a varying rate, approximately equal to the mean daily
the planet through the zodiac and carries around with it the pole of the
axis LQ of the third sphere, which carries the planet P, is inclined to
the second at an
equal to the greatest deviation in latitude of the planet from the plane
of the ecliptic.
sphere, like the second, rotates at a varying velocity so computed that
the rotation of
second and third spheres together produce the observed proper motion of
the planet from
to East through the zodiac, while the rotation of the third sphere produces
motion in celestial latitude.
an astronomical point of view, al-Bitruji's model had little to offer.
It was incapable of yielding astronomical predictions without the introduction
of a complex computation of the nonuniform motions of the second and third
spheres. In fact, no known astronomical tables were based on this attempt
at a physically real planetary system.