Constraints on a MOND effect for isolated aspherical systems in deep Newtonian regime from orbital motions

Abstract

Non-spherical systems described by MOND theories of modified gravity arising from generalizations of the Poisson equations are affected by a MONDian extra-quadrupolar potential \phi_M even if they are isolated and they are in deep Newtonian regime. In general MOND theories quickly approaching Newtonian dynamics for accelerations beyond A_0, \phi_M is proportional to a multiplicative scaling coefficient \alpha \sim 1, while in MOND models becoming Newtonian beyond \kappa A_0, \kappa >> 1, it is enhanced by \kappa^2. We analytically work out some orbital effects due to \phi_M in the framework of QUMOND, and compare them with the latest observational determinations of Solar System's planetary dynamics, exoplanets and double lined spectroscopic binary stars. The current admissible range for the anomalous perihelion precession of Saturn yields |\kappa| <= 3.5 x 10^3, while the radial velocity of \alpha Cen AB allows to infer |\kappa|<= 6.2 x 10^4 (A) and |\kappa|<= 4.2 x 10^4 (B). In evaluating such preliminary constraints it must be recalled that QUMOND is not the nonrelativistic limit of TeVeS.