Plan Childhood Kepler's opinions

Kepler's first cosmological model (1596)

Instead of the seven planets in standard geocentric astronomy the Copernican system had only six, the Moon having become a body of kind previously unknown to astronomy, which Kepler was later to call a 'satellite' (a name he coined in 1610 to describe the moons that Galileo had discovered were orbiting Jupiter, literally meaning 'attendant'). Why six planets?

Moreover, in geocentric astronomy there was no way of using observations to find the relative sizes of the planetary orbs; they were simply assumed to be in contact. This seemed to require no explanation, since it fitted nicely with natural philosophers' belief that the whole system was turned from the movement of the outermost sphere, one (or maybe two) beyond the sphere of the 'fixed' stars (the ones whose pattern made the constellations), beyond the sphere of Saturn. In the Copernican system, the fact that the annual component of each planetary motion was a reflection of the annual motion of the Earth allowed one to use observations to calculate the size of each planet's path, and it turned out that there were huge spaces between the planets. Why these particular spaces?



Kepler's answer to these questions, described in his Mysterium cosmographicum Ⓣ, Tübingen, 1596, looks bizarre to twentieth-century readers (see the figure on the right). He suggested that if a sphere were drawn to touch the inside of the path of Saturn, and a cube were inscribed in the sphere, then the sphere inscribed in that cube would be the sphere circumscribing the path of Jupiter. Then if a regular tetrahedron were drawn in the sphere inscribing the path of Jupiter, the insphere of the tetrahedron would be the sphere circumscribing the path of Mars, and so inwards, putting the regular dodecahedron between Mars and Earth, the regular icosahedron between Earth and Venus, and the regular octahedron between Venus and Mercury. This explains the number of planets perfectly: there are only five convex regular solids (as is proved in Euclid's Elements , Book 13). It also gives a convincing fit with the sizes of the paths as deduced by Copernicus, the greatest error being less than 10% (which is spectacularly good for a cosmological model even now). Kepler did not express himself in terms of percentage errors, and his is in fact the first mathematical cosmological model, but it is easy to see why he believed that the observational evidence supported his theory.


Kepler saw his cosmological theory as providing evidence for the Copernican theory. Before presenting his own theory he gave arguments to establish the plausibility of the Copernican theory itself. Kepler asserts that its advantages over the geocentric theory are in its greater explanatory power. For instance, the Copernican theory can explain why Venus and Mercury are never seen very far from the Sun (they lie between Earth and the Sun) whereas in the geocentric theory there is no explanation of this fact. Kepler lists nine such questions in the first chapter of the Mysterium cosmographicum Ⓣ.

Kepler carried out this work while he was teaching in Graz, but the book was seen through the press in Tübingen by Mästlin. The agreement with values deduced from observation was not exact, and Kepler hoped that better observations would improve the agreement, so he sent a copy of the Mysterium cosmographicum to one of the foremost observational astronomers of the time, Tycho Brahe (1546 - 1601). Tycho, then working in Prague (at that time the capital of the Holy Roman Empire), had in fact already written to Mästlin in search of a mathematical assistant. Kepler got the job.