Kepler's Explanation for Spacing of Planets

Conjecture


In the 16th century there were $6$ known planets.

It was also known that there were Five Platonic Solids.

reasoned that it was possible to fit the orbits of the planets around the sun into spheres such that:


 * $(1): \quad$ Between each sphere was a (real or imaginary) platonic solid
 * $(2): \quad$ The sphere of one planet was inscribed within the platonic solid between that and the next planet out
 * $(3): \quad$ The sphere of one planet was circumscribed around the platonic solid between that and the next planet in.

Thus:


 * Between the orbits of Mercury and Venus was an octahedron
 * Between the orbits of Venus and Earth was an icosahedron
 * Between the orbits of Earth and Mars was a dodecahedron
 * Between the orbits of Mars and Jupiter was a tetrahedron
 * Between the orbits of Jupiter and Saturn was a cube.