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

Abstract

The dynamics of non-spherical systems described by modified Newtonian dynamics (MOND) theories arising from generalizations of the Poisson equation is affected by an extra MONDian quadrupolar potential ϕQ even if they are isolated (no external field effect) and if they are in the deep Newtonian regime. In general MOND theories quickly approaching Newtonian dynamics for accelerations beyond A0, ϕQ is proportional to a coefficient α ∼ 1, while in MOND models becoming Newtonian beyond κA0, κ ≫ 1, it is enhanced by κ2. We analytically work out some orbital effects due to ϕQ in the framework of QUMOND and compare them with the latest observational determinations of Solar System’s planetary dynamics, exoplanets, double lined spectroscopic binary stars and binary radio pulsars. The current admissible range for the anomalous perihelion precession of Saturn −0.5 mas cty−1 mas cty−1 yields |κ| ⩽ 3.5 × 103, while the radial velocity of α Cen AB allows us to infer |κ| ⩽ 6.2 × 104 (A) and |κ| ⩽ 4.2 × 104 (B).