Solar system constraints on a Rindler-type extra-acceleration from modified gravity at large distances

Abstract

We analytically work out the orbital effects caused by a Rindlertype extra-acceleration ARin which naturally arises in some recent models of modified gravity at large distances. In particular, we focus on the perturbations induced by it on the two-body range {\rho} and range-rate {\rho}\cdot which are commonly used in satellite and planetary investigations as primary observable quantities. The constraints obtained for ARin by comparing our calculations with the currently available range and range-rate residuals for some of the major bodies of the solar system, obtained without explicitly modeling ARin, are 1 - 2 \times 10-13 m s-2 (Mercury and Venus), 1 \times 10-14 m s-2 (Saturn), 1 \times 10-15 m s-2 (Mars), while for a terrestrial Rindler acceleration we have 5 \times 10-16 m s-2 (Moon). Another approach which could be followed consists of taking into account ARin in re-processing all the available data sets with accordingly modified dynamical models, and estimating a dedicated solve-for parameter explicitly accounting for it. Anyway, such a method is time-consuming. A preliminary analysis likely performed in such a way by a different author yields A <= 8\times10-14 m s-2 at Mars' distance and A < = 1\times10-14 m s-2 at Saturn's distance. The method adopted here can be easily and straightforwardly extended to other long-range modified models of gravity as well.