ABSTRACT
In this chapter, the authors 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 exoplanets, binary stars and pairs of galaxies. The present approach is based on the Newtonian dynamics, with the underlying assumptions of Galilean relativity. 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). There are several practical consequences of this gain at infinity; for instance, one has to be careful not to reach the final destination with too high a velocity. Several gravitational and non-gravitational perturbing forces will act to perturb the orbit; appropriate corrections must be performed to keep the wanted position of the satellite, for instance, by occasional firings of small thrusters.
