Ebook: The music of the heavens: Kepler's harmonic astronomy

Chapters 2-4 give pre-Keplerian background. Chapter 5 presents the polyhedral theory of planetary distances of Kepler's Mysterium cosmographicum of 1596. Chapter 7 discusses Kepler's reading of Ptolemy's work on celestial harmony. Chapter 8 gives an overview of Kepler's Harmonice mundi of 1619. Finally, half the book consists of chapter 9, which is a detailed analysis of book 5 of the Harmonice mundi.

Now, musical harmony consists in simple numerical relationships, namely 1:2, 3:5, 5:8, 2:3, 3:4, 4:5, 5:6. The twelve numbers given by the extreme angular velocities of the six planets as perceived from the sun exhibit many harmonic interrelations. This is the point of attack for Kepler in his attempt to unveil the divine design of the universe. His crowning achievement is the deduction of these harmonies from a set of axioms based on basic harmonic principles and the regular polyhedra. The angular velocities thus being determined, Kepler also deduces the eccentricities of the planetary orbits. Aside from this main argument the Harmonice mundi contains several interesting side topics, such as "Kepler's third law" and a classification of "universal harmonies" (i.e. possible states of the solar system where the angular velocities of the planets are all in harmony).