Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem
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We discuss a covariant generalization of the parametrized post-Newtonian (PPN) formalism in a class of scalar-tensor theories of gravity. It includes an exact construction of a set of global and local (Fermi-like) references frames for an isolated N-body astronomical system as well as PPN multipolar decomposition of gravitational field in these frames. We derive PPN equations of translational and rotational motion of extended bodies taking into account all gravitational multipoles and analyze the body finite-size effects in relativistic dynamics that can be important at the latest stages of orbital evolution of coalescing binary systems. We also reconcile the IAU 2000 resolutions on the general relativistic reference frames in the solar system with the PPN equations of motion of the solar system bodies used in JPL ephemerides.