An empirical Gravity law up to galactic scales

Modelling on the MOND proposal, we introduce an empirically motivated gravity law for galactic and sub-galactic scales. This, circumvents the need for the cumbersome and ill-defined transition regime which exists in MOND, when passing from the standard gravitational regime at high accelerations to the MOND regime at low accelerations. We show that the proposed force law does not violate dynamical constraints at sub-galactic and solar system scales, does not degrade the good fit of the MOND proposal at large galactic scales, and in fact, slightly improves the accordance with observations at dSph scales. The proposed gravity law hence yields a good description of gravitational phenomena from terrestrial to large galactic scales, within a unique framework, without the need to invoke the presence of the still undetected and hypothetically dominant dark matter. Isothermal equilibrium density profiles then yield projected surface density profiles for the local dSph galaxies in very good agreement with observational determinations, for values of the relevant parameters as inferred from recent observations of these Galactic satellites. The observed scaling relations for these systems are also naturally accounted for within the proposed scheme.