ABSTRACT
This chapter considers 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. In the barycentric system the Lagrange function formally coincides with that of a single particle of mass m in movement in an external field, which is symmetric with respect to the fixed origin of coordinates. Owing to the properties of the force field, the isotropy of space imposes the conservation of the angular momentum K of the fictitious particle. Six initial arbitrary constants are needed in order to specify fully the movement of the particles, for instance position and velocity at a given time. The vectors velocity V and acceleration a can be decomposed in two components, one along the radial direction and one along the perpendicular to the radius vector.
