Orbital Motions and the Conservation-Law/Preferred-Frame 3 Parameter

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 ψ̂. 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 ∆$̇ 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| . 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.