Orbital effects of Lorentz-violating Standard Model Extension gravitomagnetism around a static body: a sensitivity analysis

Abstract

We analytically work out the long-term rates of change of the six osculating Keplerian orbital elements of a test particle acted upon by the Lorentz-violating gravitomagnetic acceleration due to a static body, as predicted by the Standard Model Extension (SME). We neither restrict to any specific spatial orientation for the symmetry-violating vector s nor make a priori simplifying assumptions concerning the orbital configuration of the perturbed test particle. Thus, our results are quite general, and can be applied for sensitivity analyses to a variety of specific astronomical and astrophysical scenarios. We find that, apart from the semimajor axis a, all the other orbital elements undergo non-vanishing secular variations. By comparing our results to the latest determinations of the supplementary advances of the perihelia of some planets of the solar system we preliminarily obtain s_x = (0.9 +/- 1.5) 10^-8, s_y = (-4 +/- 6) 10^-9, s_z = (0.3 +/- 1) 10^-9. Bounds from the terrestrial LAGEOS and LAGEOS II satellites are of the order of s\sim 10^-3-10^-4.

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