Orbital effects of Lorentz-violating standard model extension gravitomagnetism around a static body: a sensitivity analysis

We analytically work out the long-term rates of the 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. We neither restrict to any specific spatial orientation for the symmetry-violating vector s = {-(s) over bar (01), -(s) over bar (02),-(s) over bar (03)} 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) x 10(-8), s(y) = (-4 +/- 6) x 10 (9) and s(z) = (0.3 +/- 1) x 10 (9). Bounds from the terrestrial LAGEOS and LAGEOS II satellites are of the order of s similar to 10(-3)-10(-4).