Title:Constraining MOND with Solar System dynamics

Abstract: In this letter we investigate the deep Newtonian regime of the MOND paradigm from a purely phenomenological point of view by exploiting the least-square estimated corrections to the secular rates of the perihelia of the inner and of some of the outer planets of the Solar System by E.V. Pitjeva with the EPM2004 ephemerides. By using $\mu(x)\approx 1-k_0(1/x)^n$ for the interpolating MONDian function, and by assuming that $k_0$, considered body-independent so to avoid violations of the equivalence principle, experiences no spatial variations throughout the Solar System we tightly constrain $n$ with the ratios of the perihelion precessions for different pairs of planets. We find that the range $1\leq n\leq 2$ is neatly excluded at much more than $3-\sigma$ level. Such a test would greatly benefit from the use of extra-precessions of perihelia independently estimated by other groups as well.