d CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters alpha(1), alpha(2). Preliminary constraints on alpha(1), alpha(2) are inferred from the latest determinations of the observationally admitted ranges triangle(sic) for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint |alpha(2)| (sic) 10(-7) based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a a2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions triangle(sic) of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield alpha(1) = (0.8 +/- 4) x 10(-6) and alpha(2) = (4 +/- 6) x 10(-6), respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense-Thirring precessions and the classical rates due to the Sun's oblateness J(2), allows to infer alpha(1) = (-1 +/- 6) x 10(-6), alpha(2) = (-0.9 +/- 3.5) x 10(-5). Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of alpha(1) and alpha(2). Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate a1, a2 simultaneously with the other PPN parameters as well.