2013/11/01 by L. IORIO
Physics and Astronomy · Mathematics · #Noncommutative and Quantum Gravity Theories #Advanced Differential Geometry Research #Algebraic and Geometric Analysis
paper · doi:10.1142/s0218271814500060
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 α 1 , α 2 . Preliminary constraints on α 1 , α 2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] 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 α 2 -induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α 1 = (0.8±4) × 10 -6 and α 2 = (4±6) × 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 α 1 = (-1 ± 6) × 10 -6 , α 2 = (-0.9 ± 3.5) × 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 α 1 and α 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 α 1 , α 2 simultaneously with the other PPN parameters as well.