The problem of motion in GR has lost its academic status and become an active research area since the next generation of gravity wave detectors will rely upon its solution In this short contribution we will show, within scalar gravity, how an EFT approach can be used to solve the problem of motion in a systematic fashion. We will calculate the Einstein-Infeld-Hoffmann (EIH) action for the case of two scalar-gravitating bodies, accurate up to 1PN,, As we shall see a systematic perturbative expansion puts strong constraints on the couplings of non-derivative interactions in the theory.
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