The theory of vortical celestial mechanics, as presented in the Principles of Philosophy and The World, is the “engine room” of Descartes’ system of natural philosophy. Descartes starts his vortex theory with an “indefinitely” large chunk of divinely created matter or extension in which there are no void spaces whatsoever. When God injects motion into this extension, it is shattered into microparticles, and myriads of “circular” displacements ensue, forming gigantic whirlpools or vortices. This process eventually produces three species of corpuscle, or elements, along with the birth of stars and planets. The third element forms all solid and liquid bodies on all planets throughout the cosmos, including the earth. Interspersed in the pores of such planetary bodies are the spherical particles of the second element. The second element also makes up the bulk of every vortex, while the spaces between these spherical particles are filled by the first element, which also constitutes the stars, including our sun.

The key to Descartes’ celestial mechanics is his concept of the “massiveness” or “solidity” of a planet, meaning its aggregate volume to surface ratio, which is indicative of its ability to retain acquired motion or to resist the impact of other bodies. The particles of the second element making up a vortex also vary in volume to surface ratio with distance from the central star, as gathered from Descartes’ stipulations concerning the variation of the size (and speed) of the second-element particles with distance from the central star (Figure 32). Note also the important inflection point in the size and speed curves at radius K (Schuster 2005, 49). A planet is locked into an orbit at a radial distance at which its centrifugal tendency, related to its aggregate solidity, is balanced by the counter force arising from the centrifugal tendency of the second-element particles composing the vortex in the vicinity of the planet – that tendency similarly depending on the volume to surface ratio of the those particular particles.