Consonâncias planetárias: apresentação e fundamentação da terceira lei do movimento planetário no livro V do Harmonices Mundi (1619) de Johannes Kepler (1571 1630)

Abstract

One of the meanings of the word consonant is harmony. Harmony, in a mathematical context, refers to proportion, order and symmetry. In a musical context, harmony indicates a logical succession of the sounds. In a spiritual context, it denotes an approach to the divine, peace. Johannes Kepler´s work Harmonices mundi (1619) presents a harmonious composition of these three contexts set in the astronomical scene of the seventeenth century. In this book Kepler shows the existing mathematical relation between the planets periods of revolution and their respective distances from the Sun or as we know at the present time, the third law of the planetary motion, harmonic law, or Kepler s third law. Based on his own previous conclusions, essentially the ones published in Mysterium Cosmographicum (1596), and on the hypothesis of a relationship between the musical note frequency and the velocities of the planets in its orbits, Kepler made use of a theoretical structure typical of his period, which includes the Pythagoras mystics, the Platonic philosophy, the Euclidian geometry, the Ptolemaic music theory, and the Copernican heliocentricism. The aim of this dissertation is to examine the theoretical and epistemological basis used by Kepler on the development of the harmonic law , and to discuss its significance in the keplerian cosmology and for the astronomy of the period