Harmonices Mundi (1619)

Harmonices Mundi (The Harmony of the World) is the 1619 book by Johannes Kepler in which he published his Third Law of Planetary Motion. It is a sprawling, ambitious work that attempts to find mathematical harmonies throughout nature—in geometry, music, astrology, and astronomy.

Kepler's Search for Harmony

Kepler believed deeply that the universe was designed according to mathematical principles. Harmonices Mundi explores this idea across five books. The first two deal with geometry and the properties of regular polygons. The third applies these ideas to music theory, attempting to derive musical harmonies from geometric ratios. The fourth covers astrology (which Kepler took seriously, though he reformulated it in his own way).

The fifth and final book applies these ideas to astronomy and contains the famous Third Law.

The Third Law

On March 8, 1618, Kepler discovered the relationship he had been seeking for years: the square of a planet's orbital period is proportional to the cube of its semi-major axis. In mathematical form:

This meant that if you knew how far a planet was from the Sun, you could calculate how long its year was, and vice versa. The law applied to all the known planets and provided a single, unifying relationship linking the entire solar system. For the full mathematical treatment, see the Third Law page.

Music of the Spheres

Kepler went further, assigning each planet a musical interval based on the ratio between its fastest and slowest orbital speeds. He believed the planets literally produced a kind of celestial music. While this aspect of the work is not taken literally today, the underlying idea—that the universe follows deeply mathematical patterns—has been vindicated many times over. See Music of the Spheres for more on this concept.