Abstract
With the obtainment of the Synge equations of motion in third approximation for a test particle, we determine the relativistic force in the field generated by a massive body obtained previously in terms of its potentials. Afterwards, in order to study the motion, we obtain the integral of energy and the integral of angular momentum. By means of them, the general form for the trajectory of an equatorial orbit and for the advance of its apsidal line are obtained. As we will see, the known diverse contributions for this advance appears in the general form after strong supplementary conditions on the potentials. As application, with such assumptions these contributions are derived in a unified way.
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