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We analytically work out the long-term rates of change of the six osculatingKeplerian orbital elements of a test particle acted upon by theLorentz-violating gravitomagnetic acceleration due to a static body, aspredicted by the Standard Model Extension (SME). We neither restrict to anyspecific spatial orientation for the symmetry-violating vector s nor make apriori simplifying assumptions concerning the orbital configuration of theperturbed test particle. Thus, our results are quite general, and can beapplied for sensitivity analyses to a variety of specific astronomical andastrophysical scenarios. We find that, apart from the semimajor axis a, all theother orbital elements undergo non-vanishing secular variations. By comparingour results to the latest determinations of the supplementary advances of theperihelia 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. Boundsfrom the terrestrial LAGEOS and LAGEOS II satellites are of the order of s\sim10^-3-10^-4.

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