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We analytically calculate some orbital effects induced by theLorentz-invariance/momentum-conservation PPN parameter $\alpha_3$ in agravitationally bound binary system made of a compact primary orbited by a testparticle. We neither restrict ourselves to any particular orbital configurationnor to specific orientations of the primary's spin axis$\boldsymbol{\hat{\psi}}$. We use our results to put preliminary upper boundson $\alpha_3$ in the weak-field regime by using the latest data from SolarSystem's planetary dynamics. By linearly combining the supplementary perihelionprecessions $\Delta\dot\varpi$ of the Earth, Mars and Saturn, determined withthe EPM2011 ephemerides, we infer $|\alpha_3|\lesssim 6\times 10^{-10}$. Ourresult is about 3 orders of magnitude better than the previous weak-fieldconstraints existing in the literature, and of the same order of magnitude ofthe bound expected from the future BepiColombo mission to Mercury. It is, byconstruction, independent of the other preferred-frame PPN parameters$\alpha_1,\alpha_2$, both preliminarily constrained down to a $\approx 10^{-6}$level. The wide pulsar-white dwarf binary PSR J0407+1607 yields a preliminaryupper bound on the strong-field version $\hat{\alpha}_3$ of theLorentz-invariance/momentum-conservation PPN parameter of the order of $3\times10^{-17}$. It relies upon certain assumptions on the unknown values of thepulsar's spin axis orientation $\boldsymbol{\hat{\psi}}$, the orbital node$\Omega$ and the inclination $I$. Neither the pulsar's proper motion, stillundetected, nor a possible value of the pulsar's mass $m_{\rm p}$ up to twosolar masses substantially affect our result.

Orbital motions and the conservation-law/preferred-frame $\alpha_3$ parameter