We present a novel solution of the Mercury perihelion advance shift in the new gravity model. It is found that the non-relativistic reduction of the Dirac equation with the gravitational potential produces the new gravitational potential of $\displaystyle{ V(r)=-{ GMm\over r}+{ G^2M^2m^2\over 2mc^2r^2}}$. This potential can explain the Mercury perihelion advance shift without any free parameters. Also, it can give rise to the $\omega-$shift of the GPS satellite where the advance shift amounts to $({ \Delta \omega\over \omega})_{ th} \simeq 3.4\times 10^{ -10}$ which should be compared to the recent observed value of $({ \Delta \omega\over \omega})_{ exp} \simeq 4.5\times 10^{ -10}$.
Categories: physics.gen-ph