Hořava-Lifshitz gravity and Solar System orbital motions

We focus on Hořava-Lifshitz (HL) theory of gravity, and, in particular, on a spherically symmetric and asymptotically flat solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation we analytically work out the secular precession of the longitude of the pericentre ̟ of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein’s pericentre precession. Then, we compare it to the latest determinations of the corrections ∆ ̟̇ to the standard Newtonian/Einsteinian planetary perihelion precessions recently estimated with the EPM and the INPOP ephemerides. It turns out that the inner planets of the solar system, taken singularly one at a time, allow to put upper bounds on the adimensional HL parameter ψ0 of the order of 10 −12 − 10. The retrograde perihelion precession of Saturn, recently determined by processing large collections of Cassini ranging data by Pitjeva and Fienga et al., could, in principle, be explained by the HL model for ψ0 ≈ 1−0.7×10−18, which is in agreement with the constraints from the rocky planets taken singularly one at a time. Such a value is, instead, not able to account for the Pioneer anomalous acceleration for r > 20 AU. The ratios of the determined corrections to the perihelion rates for some pairs of inner planets cannot be explained by the corresponding theoretically predicted ratios of the HL precessions at more than 1σ level.