Analytical computation of the Mercury perihelion precession via the relativistic gravitational law and comparison with general relativity

Let $r(\varphi)$ denote the orbit of Mercury. We compare the formulae obtained via general relativity for $r(\varphi)$ and for the corresponding perihelion precession angle $\Delta \varphi$, with the formulae obtained via the relativistic gravitational law, $F=GMm\gamma^6/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest masses of the Sun and Mercury. Remarkably, it is found that the two expressions for the dominant part of $r(\varphi)$ are identical and that the two expressions for $\Delta\varphi$ are also identical.