Kepler, elliptical orbits, and celestial circularity: A study in the persistece of metaphysical commitment

Summary

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains a discussion of how, for Kepler, the circle also functions in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology to select the basic aspects. In Part II, the discussion centres on the question of how the replacement of circular planetary orbits by elliptical orbits in the Astronomia Nova of 1609 affected Kepler's metaphysical commitment to celestial circularity that was made manifest in the derivation of planetary radii in the Mysterium Cosmographicum of 1596. The answer is found in the new and much more accurate derivation of both the planetary radii and their eccentricities in the Harmonice Mundi of 1619. It is the relationship of the diurnal movements of single planets at aphelion and perihelion to specific musical consonances that provides the first step. Then, in the second step, these ratios are ‘tempered’ so that all six planets can provide a heavenly choir. The third and final step employs the ‘mean period’, which is obtained directly from the tempered ratios given by musical theory and diurnal (not annual) motion, in the 3/2 power law to calculate the planetary radii and eccentricities with amazing accuracy. Thus the ellipse is necessary to supply the variation in angular velocities that contain the Creator's archetypal celestial circularity.