## ABSTRACT

In this chapter we consider the dynamics of two bodies under their mutual gravitational attraction, a fundamental problem in many astronomical situations, from the Earth, Moon, and Sun-planet systems, to binary stars and pairs of galaxies. The two bodies will be considered of very small extent with respect to their mutual distance, in order to regard them as point-like masses (particles). The present approach is based on Newtonian dynamics, with the underlying assumptions of Galilean relativity (space is homogeneous and isotropic, time is uniform, all inertial system are equivalent with respect to the dynamical properties), but occasionally we will introduce some modifications owing to general relativity. One of the basic disagreements with Newtonian dynamics indeed originated from astronomical evidence, namely the secular advance of Mercury’s perihelion: once allowance was made for all known planetary perturbations, it was realized that a fraction of the value observed, namely 43″/century out of the total 550″/century, could not be explained. The correct value was derived from general relativity, as described in Chapter 14.