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 PPN parameters \alpha _ { 1 } , \alpha _ { 2 } . Preliminary constraints on \alpha _ { 1 } , \alpha _ { 2 } are inferred from the latest determinations of the observationally admitted ranges \Delta \dot { \varpi } 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 } | \lessapprox 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 \alpha _ { 2 } -induced torque throughout the entire Solar System ’ s existence .
Taken individually , the supplementary precessions \Delta \dot { \varpi } of Earth and Mercury , recently determined with the INPOP10a ephemerides without modeling PFE , yield \alpha _ { 1 } = ( 0.8 \pm 4 ) \times 10 ^ { -6 } and \alpha _ { 2 } = ( 4 \pm 6 ) \times 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 unmodelled/mismodelled 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 \pm 6 ) \times 10 ^ { -6 } , \alpha _ { 2 } = ( -0.9 \pm 3.5 ) \times 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 \alpha _ { 1 } , \alpha _ { 2 } simultaneously with the other PPN parameters as well .