Planetary Orbits #3: Kepler's Wrong Paths

So Johann Kepler now had Tycho’s data. As Kitty Ferguson wrote in Tycho and Kepler, Kepler was very poor and a devout Protestant in a Catholic dominated society, both of which caused enormous problems throughout his life. Kepler described his nature thus:
“There was nothing I could state that I could not also contradict.”

Back then, mankind knew of 6 planets. Why 6, wondered Kepler? Why were the orbits at those distances, not others? Why did they have certain speeds and why did those change? As the author put it:
“Part of Kepler’s genius was that these questions nagged him.”
And:
“For him, the most fundamental attribute of nature was geometry.”
Sometimes, those very tendencies would led him down the wrong trail…

Kepler noticed that there are only 5 “perfect solids”: solids in which all the edges have the same length; and all the sides are of the same shape. Aha, he thought, the reason there were 6 planets was that there are only 5 perfect solids to dictate their relative distances.

Further, each perfect solid can be nested inside a sphere so that every corner of the solid touches the inside surface of the sphere; and a sphere can be nested inside any perfect solid such that the sphere touches the center of every face of the solid. Perhaps a planet was “allowed” to move anywhere within these 2 spheres; that would account for the non-circular orbits, thought Kepler.

Next, he thought that a cube (the first “perfect solid”) dictated the distance between the orbits of Jupiter and Saturn; and the next perfect solid would dictate the distance between the next pair of planets… and so on.

The data he found did seem to align with this… to some extent. He published all this in a book titled Mysterium. As Owen Gingerich said:
“Seldom in history has so wrong a book been so seminal in directing the future course of science.”
But this would be the very book that brought him to Tycho’s attention!

As he analyzed the data further, Kepler saw that it didn’t match his perfect solids model. He then checked if the ratios of the speed of successive planets would map to harmonious chords from the world of music. This, surprisingly, was a better fit than his perfect solids theory!

Was Kepler doomed to keep chasing false leads? A man who would forever be lured by the siren song of patterns, both geometric and musical? Was he too Greek in his way of thinking?

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