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

TL;DR

This paper derives general analytical expressions for the long-term orbital element variations caused by Lorentz-violating gravitomagnetism in the SME, enabling sensitivity analysis across various astrophysical scenarios.

Contribution

It provides the first general, assumption-free analytical formulas for orbital element rates due to SME gravitomagnetic effects, applicable to diverse orbital configurations.

Findings

All orbital elements except semimajor axis exhibit secular variations.

Preliminary bounds on SME parameters from planetary perihelion advances.

Satellite data bounds on SME parameters are of order 10^-3 to 10^-4.

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.