11 Central Force Motion

Abstract This chapter applies a combination of vector mechanics and Lagrangian mechanics to the general system of two point masses interacting by a central force depending only on their separation. The special case of an inverse square central force reproduces Newton's achievement in modern notation. Newton's Principia presented proof that elliptical orbits are a natural consequence of an inverse square gravitational attraction between the sun and the planets, and launched the topic of discussion in this chapter. The central force problem is thus central to the early history of analytical mechanics. An inverse square central force is also found between charged particles in electrodynamics. The orbital motion of an electron around a proton underlies both the Bohr model of the hydrogen atom and the old quantum theory that was superseded by Schroedinger's quantum mechanics.