Equations of motion of extended bodies in general relativity theory with account for conservative corrections and radiative deceleration

Equations of motion for two spherically-symmetric extended bodies in the weak-field and slow-motion approximation are derived. Equations of motion were obtained by the post-Newtonian approximation (PNA) method and contain all conservative and first radiative relativistic terms. Residual terms were estimated and limitations on the small parameters of the PNA scheme were derived, under which the obtained equations of motion are valid. The equations of motion are shown to contain the only parameter, characterizing the bodies, namely their masses, and don't depend on the compactness of the bodies. This fact is a weighty argument in favour of applying the equations of motion, obtained in this article, to the systems which contain compact bodies, e.g. neutron stars and/or black holes