| Chapter 1: | The New Astronomy |
values, they provided results that mimicked the observed motion of Ancient Planets.
Ptolemy succeeded in predicting and accounting for positions of the Ancient Planets (G) with tolerable accuracy and without violating the doctrine of circular and spherical perfection. He accounted for planetary motions by compounding the effects of small circular motions (epicycles) centered on a larger circle (the deferent), abetted by uniform angular displacements around points off center from the center of the deferent (eccentrics and equants) (see Mitton 138). Because nature herself gave no rules on how to select and manipulate this geometry, the Ptolemaic model was not an explanation of physical phenomena but more of an algorithm geared to “saving phenomena” (i.e., to finding ways to reproduce or account for them). Ptolemy's celestial geometry was ad hoc because it relied on the aesthetic and mathematical appeal of circles and spheres as well as the theological belief in the central importance of humankind, but it lacked a self-consistent pattern of physical causes upon which to base understanding of the very phenomena that it was geared to “save.” Nevertheless, the moderate success of the geocentric algorithm and the absence of an alternative led to its widespread adoption. In Toledo in 1080, scholars recalculated the ephemerides (i.e., tables of apparent directions in the sky for celestial objects at selected times), and the process repeated in 1252 under the supervision of Alfonso X (1221–1284), King of Castile and Leon. These became known as the Alfonsine Tables.
One product of geocentric theory was the capacity to determine the physical dimensions of the Universe as it was then conceived. In the first millennium AD, the size of the Earth was quite well known, and with the help of eclipses of the Sun and Moon, Ptolemy and his predecessors devised a way to estimate distances to the planets. Because the bounded geocentric model placed the sphere of the stars just beyond the distance of the outermost planet, Saturn, the belief was that the physical Universe ended at a distance of about 20,000 Earth radii from Earth (van Helden, Measuring 27). Ptolemaic values persisted into the sixteenth century with only minor modifications, but with the exception of the distance of