ABSTRACT
This chapter focuses on the problem of two celestial bodies. Both bodies are considered to be spherical in form and to possess spherical symmetry, i.e. they consist of homogeneous spherical layers with an arbitrary law of distribution of density of matter along the radius. The radii of both bodies are arbitrary but finite, and both masses are also finite and constant. The center of mass of a two-body system moves in space in a straight line and with a constant velocity. The solution of the two body problem may be reached only by rejection of the concept of absolute motion. The relative motion represents a definite simplification not only from a mathematical point of view; it has an obvious practical interest. The differential equations of relative motion are also of second order; however, the number of equations is less by a factor of two – only three.
