Like the *Mysterium Cosmographicum*, the *Harmonice
Mundi* relied on a theory that was absolutely wrong. But
hidden within Kepler's lyrical ravings about having finally deciphered
God's plan is the final piece of his planetary puzzle: Kepler's
third law.

Kepler had fixated on trying to find a pattern or structure
for the spacing of the planets. By this point, he had realized
that his perfect solids universe was mathematically unfeasible.
But Kepler had a new vision, one that encompassed math, astronomy,
music, and God. Kepler argued that the same harmonies we find in
music were embedded in the geometrical proportions of the universe.

Kepler searched for any consistency that he might interpret
as a harmonic pattern. He finally found a relationship that worked:
the speed of the planets around their orbits versus their distance
from the sun. Kepler's third law states that the distance a planet
is from the sun, cubed, is directly proportional to the time it
takes to complete the orbit, squared. More simply, Kepler found
that the distance a planet was located from the sun directly determined
the time it took that planet to revolve around the sun. This was
the first time anyone had discovered the exact relationship between
these two quantities – in fact, this was the first time anyone
had even thought to wonder about the relationship.

Kepler was pleased to have discovered such a relationship
– but he was ecstatic to have found the final piece in his harmonic
puzzle. The harmonic universe, he believed, would truly be the
greatest achievement of his life. In 1618, he published his vision
in the *Harmonice Mundi.* Much like his earlier *Mysterium
Cosmographicum* Kepler went on and on, joyfully extolling
the divine basis of his theory. In the preface to his fifth book,
he admitted this himself: "Yes, I give myself up to holy raving."
To Kepler, the relationships he had discovered seemed so beautiful
that they must have come directly from God. He congratulated himself
for having the wisdom to finally understand God's plan: "I have
robbed the golden vessels of the Egyptians to make out of them
a tabernacle for my God, far from the frontiers of Egypt[my book]
may wait a hundred years for a reader, since God has also waited
six thousand years for a witness." This passage appears in the
same book as one of the most important scientific discoveries of
the seventeenth century.

Kepler still considered himself to be a modern scientist.
Even with his mysticism and his religious devotion, Kepler was
at the forefront of modern science. Yes, he was still rooted in
the past. But his work in the *Harmonice Mundi* confirms
that he was looking toward the future, asking the questions that
none of his colleagues had thought to ask, and forging mathematical
relationships where none had existed before.

Of course, Kepler realized none of this. He was proud
of the achievement of his harmonic universe – but he spared no
pride for his formation of the third law. Neither Kepler nor his
peers understood the importance of the equation, which would prove
integral to Newton's later discovery of universal gravitation.
Until Newton's work made sense of it, the third law was nothing
more than an interesting relationship between numbers, with no
physical basis. Only from a distance is it easily recognizable
as one of the most crucial pieces for solving the mysteries of
universal motion.