| Abstract: | Considering a long range scalar interaction (LRSI) acting between dark matter (DM) particles implies deviations from the Weak Equivalence Principle (WEP) in the dark sector. A signi cant challenge is to construct a measurable test which can detect this e ect, for it is negligible to laboratory physics and the usual cosmological tests. A dwarf galaxy traveling in the Milky Way (MW) gravitational eld can be a very interesting scenario of scienti c importance in exploring this theoretical interaction, since according to the ΛCDM model should contain DM and can be found in scales which the LRSI is signi cant. By studying the physical and observational properties of local group dwarf spheroidal (dSph) galaxies we conclude that Draco dSph which assumed to be highly abundant with DM, relatively close to the MW galactic center and in dynamical equilibrium, is the best candidate for constructing an observational based test for WEP violation. Our goal is to constrain the relative strength of the LRSI to gravity using numerical simulation of Draco dSph orbiting the Milky Way, considering Newtonian+LRSI physics and to obtain a physical scenario that is consistent with WEP violation, namely a stable system that resembles Draco as observed today. |