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were no more supported by Tycho’s data than by Copernicus’. His “Cosmic Mystery” was disproved entirely by the much later discoveries of the planets Uranus, Neptune and Pluto—there are no additional platonic solids* that would determine their distances from the sun. The nested Pythagorean solids also made no allowance for the existence of the Earth’s moon, and Galileo’s discovery of the four large moons of Jupiter was also discomfiting. But far from becoming morose, Kepler wished to find additional satellites and wondered how many satellites each planet should have. He wrote to Galileo: “I immediately began to think how there could be any addition to the number of the planets without overturning my Mysterium Cosmographicum, according to which Euclid’s five regular solids do not allow more than six planets around the Sun … I am so far from disbelieving the existence of the four circumjovial planets that I long for a telescope, to anticipate you, if possible, in discovering two around Mars, as the proportion seems to require, six or eight round Saturn, and perhaps one each round Mercury and Venus.” Mars does have two small moons, and a major geological feature on the larger of them is today called the Kepler Ridge in honor of this guess. But he was entirely mistaken about Saturn, Mercury and Venus, and Jupiter has many more moons than Galileo discovered. We still do not really know why there are only nine planets, more or less, and why they have the relative distances from the Sun that they do. (See Chapter 8.)

Tycho’s observations of the apparent motion of Mars and other planets through the constellations were made over a period of many years. These data, from the last few decades before the telescope was invented, were the most accurate that had yet been obtained. Kepler worked with a passionate intensity to understand them: What real motion of the Earth and Mars about the Sun could explain, to the precision of measurement, the apparent motion of Mars in the sky, including its retrograde loops through the background constellations? Tycho had commended Mars to Kepler because its apparent motion seemed most anomalous, most difficult to reconcile with an orbit made of circles. (To the reader who might be bored by his many calculations, he later wrote: “If you are wearied by this tedious procedure, take pity on me who carried out at least seventy trials.”)

Pythagoras, in the sixth century B.C., Plato, Ptolemy and all the Christian astronomers before Kepler had assumed that the planets moved in circular paths. The circle was thought to be a “perfect” geometrical shape and the planets, placed high in the heavens, away from earthly “corruption,” were also thought to be in some mystical sense “perfect.” Galileo, Tycho and Copernicus were all commited to uniform circular planetary motion, the latter asserting that “the mind shudders” at the alternative, because “it would be unworthy to suppose such a thing in a Creation constituted in the best possible way.” So at first Kepler tried to explain the observations by imagining that the Earth and Mars moved in circular orbits about the Sun.

After three years of calculation, he believed he had found the correct values for a Martian circular orbit, which matched ten of Tycho’s observations within two minutes of arc. Now, there are 60 minutes of arc in an angular degree, and 90 degrees, a right angle, from the horizon to the zenith. So a few minutes of arc is a very small quantity to measure—especially without a telescope. It is one-fifteenth the angular diameter of the full Moon as seen from Earth. But Kepler’s replenishable ecstasy soon crumbled into gloom—because two of Tycho’s further observations were inconsistent with Kepler’s orbit, by as much as eight minutes of arc:

Divine Providence granted us such a diligent observer in Tycho Brahe that his observations convicted this … calculation of an error of eight minutes; it is only right that we should accept God’s gift with a grateful mind … If I had believed that we could ignore these eight minutes, I would have patched up my hypothesis