The two body problem is the question of how two objects – say the Sun and the Earth – move under their mutual gravitational attraction. The problem is, happily, fully solvable and the purpose of this chapter is to fully solve it. We will understand how Keplers laws of planetary motion arise from the more fundamental Newtonian law of gravity. Because the electrostatic force has exactly the same form as the force of gravity, we can also use our solutions to understand how electrons scatter off atoms, a famous experiment performed by Rutherford that led to an understanding of the structure of matter.

This chapter discusses the sections of finite and absolute mechanics of Hegel’s Philosophy of Nature which are predicated upon his theory of space and time. It starts with the emergent notions of matter and movement before giving the details of the mechanical analysis in a close reading. Giving a foundation for Kepler’s laws is not only a touchstone of Hegel’s theory but is an integral rung in a system of steps building natural science from space and time. The chapter exposes three main strands of argument: dimensional realization of time and space in movement of matter, striving towards inner and outer centers of extended bodies, and the realization of a system of bodies in motion which materializes a complexity paralleling not only of the tripartite system general-particular-individual of his logic but additionally includes two particulars – as necessary in Hegel’s account of nature. Lastly, the chapter comments briefly on the relationship to Kant, Newton, and classical mechanics, as well as on modern aspects. As it demonstrates, Hegel’s treatment of mechanics is not an idiosyncratic way of presenting celestial mechanics but contains radical, quite modern metaphysical concepts which are not only interesting in their own right but furnish a key to the understanding of his system.