JOHANNES KEPLER

Harmonices Mundi

Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world."[54] In Harmony, he attempted to explain the proportions of the natural world — particularly the astronomical and astrological aspects — in terms of music. The central set of "harmonies" was the musica universalis or "music of the spheres," which had been studied by Pythagoras, Ptolemy and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.

Kepler began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler's solids. From there, he extended his harmonic analysis to music, meteorology and astrology; harmony resulted from the tones made by the souls of heavenly bodies — and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler — with Tycho's data and his own astronomical theories — treated them much more precisely and attached
new physical significance to them.

Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He then tried many combinations until he discovered that (approximately) "The square of the periodic times are to each other as the cubes of the mean distances." However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. For when conjoined with Christian Huygens' newly discovered law of centrifugal force it enabled Isaac Newton, Edmund Halley and perhaps Christopher Wren and Robert Hooke to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them. This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall
is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.