137 - Arthur I. Miller [42]
Johannes Kepler.
Tycho Brahe.
Tycho set Kepler to work to improve his observations of Mars, the most difficult of the planets due to its pronounced retrograde motion. Astronomers described the orbit of Mars as having a large “eccentricity”—the distance that the sun had to be moved from the center of Mars’s orbit to improve agreement with Tycho’s data of the complicated system of circles rolling on circles. This displacement was a mathematical device used in every model of the universe—in Ptolemy’s it was the earth whose position was displaced from the center of the universe. In reality, of course, in Copernicus’s system, the sun was at the center of the universe. The models of Ptolemy, Copernicus, and Tycho could not deal adequately with Mars’s eccentricity. Kepler bet his colleagues that he could straighten it out in eight days. In fact it took him eight years.
In October 1601 Tycho suddenly died at the age of fifty-five and Kepler was appointed imperial mathematician. He inherited all of Tycho’s data and more important, no longer had to waste time fiddling with Tycho’s model of the universe.
To start with, Kepler analyzed Tycho’s data on the orbit of Mars, trying to preserve the old model of the universe by explaining the orbits of the planets in terms of circles. Taking Tycho’s best data for Mars, he used the mathematical device of displacing the sun from the center of Mars’s orbit by a certain distance to allow for eccentricity. Then, by adroit mathematics, he moved himself from the earth to Mars and found that the earth also moved in an orbit similar to Mars’s, with varying speeds.
Supposing the orbit of Mars was not a circle but an oval? Kepler spent 1604 struggling with the mathematics of an oval. That year was full of problems. Both he and his wife fell ill; when he became short of money his wealthy wife refused to dip into her funds; and she also gave birth to yet another child whom Kepler saw as yet another problem. And an ominous new star appeared in the sky—the nova of 1604.
Then he tried replacing the oval with an ellipse. An ellipse is a circle that has been squashed at its north and south poles. It has two centers, or focii, neither of which is in the middle. When the two centers are moved together the ellipse becomes a circle. This worked perfectly. The curve went through all of Tycho’s data points for the orbit of Mars and also fitted Mars’s measured eccentricity. Kepler had discovered his first law of planetary motion: that every planet moves in an ellipse with the sun at one of its centers. The sun is no longer at the center of the universe but at one of the ellipse’s foci.
Soon after, he discovered his second law: that a line drawn from the sun to a planet sweeps out equal areas in equal times. This meant that a planet’s speed varied as it traveled in an ellipse around the sun: the planet sped up as it neared the sun and slowed down as it moved away.
Kepler had overthrown the two-thousand-year-old assumptions that the complicated orbits of planets could only be explained by adding circles moving on circles in uniform circular motion and that the planets move with a uniform speed. He published his new laws of astronomy in his 1609 Astronomia nova (The New Astronomy).
But what kept the planets from escaping altogether and flying off into the void? Perhaps there were tentacles emanating from the sun, grasping a planet and whipping it around in its orbit. Kepler imagined the attraction to be magnetism. Newton would later discover that it was gravity. Kepler, however, could only conceive of it as some sort of vital or living force.
As Pauli points out, Kepler was caught between two worlds. His laws of planetary motion were an accurate description of the paths of the planets around the sun, but they emerged from mathematical