Slow motion approximation in predictive relativistic mechanics. I. Approximated dynamics up to order c−4

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Abstract
We obtain the most general two‐body system relativistic invariant having a Newtonian limit up to c−4 order. In particular, it includes the scalar, gravitational, and other well‐known dynamics up to c−2 order. It also includes to c−4 order the dynamics obtained recently by Lapiedra and Mas in predictive relativistic time symmetric electrodynamics.