Harmony Accommodates Experience

Harmony Accommodates Experience

Tycho Brahe’s 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 discomforting. But far from becoming morose, Johannes 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 could be there 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… 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 around 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 that 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.

The universe is stamped with the adornment of harmonic proportions, but harmonies must accommodate experience. Image: by © Megan Jorgensen (Elena)

In fact, Tycho has commented Mars to Kepler because the 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, place high in the heavens, away from earthly “corruption”, were also thought to be in some mystical sense “perfect”. Galileo, Tycho and Copernicus were all committed 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.

The difference between a circular orbit and the true orbit could be distinguished only by precise measurement and a courageous acceptance of the facts: “The universe is stamped with the adornment of harmonic proportions, but harmonies must accommodate experience”.