137 - Arthur I. Miller [43]
Kepler’s third law
In 1611 Emperor Rudolf abdicated. To escape the dangerous political intrigues that followed, Kepler moved to Linz, the capital of Upper Austria, a charming city on the Danube. Before leaving Prague, however, his wife fell ill with typhus and died.
Kepler’s marriage had not been happy. Nevertheless, after her death he was lonely. He also had three young children to look after, two girls and a boy. He looked around for another wife in the same way he had discovered his two laws—by trial and error. He ended up with eleven choices, some of whom he had advertised for, others whom he had tried out, sometimes boarding his children with them to see if they all got along. One was attractive but too young, another fat, another was of poor health. Kepler finally settled on number five and she gave him the peace of mind to resume his scientific research.
His first two laws had been essentially geometrical—number was missing. Now he turned his attention to numbers. If the sun controlled the planets, he thought there had to be a relationship between the planets’ distances from the sun and their speeds.
Meanwhile Europe was heading for the Thirty Years’ War. Troops were on the move causing famine, havoc, and plague. Then one of his daughters died. In his grief he turned inward to “contemplation of the Harmony,” which he believed to exist in nature. Thinking of the musical harmonies explored by Pythagoras, he pondered the eternal reality of numbers, which revealed the very essence of the soul.
How did this numerical harmony relate to the planets in a sun-centered system? Kepler tried to find a way to work out whether harmonious ratios could be formed out of the planets’ periods of revolution, their volumes, their sizes, or their velocities when they were furthest from and closest to the sun. But he failed. Then he thought of examining the ratios of a planet’s angular velocities at its extremes from the sun, that is, its change in angle at any period as it moved across the sky. And finally the astral music of the Divine Composer began to emerge.
Little by little Kepler worked out the ratios that produced the melodies played by the planets as they moved in their elliptical orbits. It was a heavenly symphony “perceived by the intellect, not by the ear,” he wrote. But for Kepler it was much more. To him the planets sang in “imitation of God” in different voices—soprano, contralto, tenor, and bass. But on the earth there was only discord: “The Earth sings Mi-Fa-Mi, so we can gather even from this that Misery and Famine reign on our planet,” he wrote despondently.
Kepler’s third law asserts that the following two quantities are proportional: the time needed for the earth to go once around the sun, multiplied by itself (that is, squared); and the earth’s average distance from the sun, multiplied by itself three times (that is, cubed). It completed for him what had been the goal of Pythagoras: to explain the universe in terms of geometry and number. He scoured tables of numbers until he found the pattern but he never revealed precisely how he had discovered this capstone of his life’s work. He recorded the date: March 8, 1618. “At first I thought I was dreaming,” he wrote in the book he published the following year, Harmonices Mundi.
Sure that God had spoken through him,