  In this paper, we investigate the anomalous planets precession in the
nearly-newtonian gravitational regime. This limit is obtained from the
application of the slow motion condition to the geodesic equations without
altering the geodesic deviation equations. Using a non-standard expression for
the perihelion advance from the Weyl conformastatic vacuum solution as a model,
we can describe the anomaly in planets precession compared with different
observational data from Ephemerides of the Planets and the Moon (EPM2008 and
EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using the
Levenberg-Marquardt algorithm and calculating the related Chi-squared
statistic, we find that the anomaly is statistical irrelevant in accordance
with INPOP10a observations. As a complement to this work, we also do an
application to the relativistic precession of giant planets using observational
data calibrated with the EPM2011.
