  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 $({\Delta \omega\over \omega})_{exp} \simeq 4.5\times
10^{-10}$.
