Description: We analytically calculate some orbital effects induced by the Lorentz-invariance/ momentum-conservation   parameterized   post-Newtonian (PPN)  parameter α3 in   a gravitationally bound binary system made of a primary orbited by a test particle.  We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary’s spin axis ψˆ.  We use our results to put preliminary  upper bounds on α3 in the weak-field regime by using the latest data from Solar System’s planetary dynamics. By linearly combining the supplementary perihelion  precessions ∆w˙ of the Earth, Mars and Saturn, determined by astronomers with the Ephemerides of Planets and the Moon (EPM) 2011 ephemerides for the general relativistic  values of the PPN parameters β = γ = 1, we infer |α3| ;5 6 × 10−10.   Our result is about three orders of magnitude better than the previous weak-field  constraints existing  in the literature and of the same  order of magnitude of the constraint expected from the future BepiColombo mission to Mercury. It is, by construction, independent of the other preferred-frame PPN parameters α1, α2, both preliminarily constrained down to a ≈ 10−6 level. Future analyses should be performed by explicitly including α3 and a selection  of other PPN parameters in the models fitted by the astronomers to the observations and estimating them in dedicated covariance analyses.