  In this paper we put on the test the new mechanism of gravitational origin
recently put forth by Jaekel and Reynaud in order to explain the Pioneer
anomaly in the framework of their post-Einsteinian metric extension of general
relativity. According to such a proposal, the secular part of the anomalous
acceleration experienced by the twin spacecraft of about 1 nm s^-2 could be
caused by an extra-potential \delta\Phi_P=c^2\chi r^2, with \chi=4 10^-8 AU^-2,
coming from the second sector of the considered model. When applied to the
motion of the planets of the Solar System, it would induce anomalous secular
perihelion advances which amount to tens-hundreds of arcseconds per century for
the outer planets. As for other previously proposed non-conventional
gravitational explanations of the Pioneer anomaly, the answer of the latest
observational determinations of the residual perihelion rates by RAS IAA is
neatly and unambiguously negative. The presence of another possible candidate
to explain the Pioneer anomaly, i.e. the extra-potential \delta\Phi_N, linear
in distance, from the first sector of the Jaekel and Reynaud model, is ruled
out not only by the residuals of the optical data of the outer planets
processed with the recent RAS IAA EPM2004 ephemerides but also by those
produced with other, older dynamical theories like, e.g., the well known NASA
JPL DE200.
