Constraints on modified Newtonian dynamics theories from radio tracking data of the Cassini spacecraft

Abstract

The modified Newtonian dynamics (MOND) is an attempt to modify the gravitation theory to solve the dark matter problem. This phenomenology is very successful at the galactic level. The main effect produced by MOND in the Solar System is called the external field effect parametrized by the parameter ${Q}_{2}$. We have used nine years of Cassini range and Doppler measurements to constrain ${Q}_{2}$. Our estimate of this parameter based on Cassini data is given by ${Q}_{2}=(3\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}27}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}2}$, which shows no deviation from General Relativity and excludes a large part of the relativistic MOND theories. This limit can also be interpreted as a limit on an external tidal potential acting on the Solar System coming from the internal mass of our Galaxy (including dark matter) or from a new hypothetical body.