  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.
