  As an alternative to dark matter models we use generalized Jordan-Brans-Dicke
scalar-vector-tensor (JBD-SVT) gravity model to study the behavior of the
rotational velocities of test particles moving around galaxies. To do so we
consider an interaction potential $U(\phi,N_{\mu})$ between the Brans-Dicke
scalar field $\phi$ and time like dynamical four-vector field $N_\mu$ which
plays as four velocity of a preferred reference frame. We show that at in weak
field limits metric solution of the galaxy under consideration reaches to a
modified Schwarzschild-de Sitter space in which mass of the vector field plays
as an effective cosmological constant. In fact the present work proposes
modification on the formulation of Newton's gravitational acceleration. This is
used to explain circular velocity of galaxies without postulating dark matter.
We also check our theoretical results with empirical baryonic Tully Fisher
relation which states a linear relations between the rotational speed of
galaxies and their mass. Mathematical calculation predict a good correspondence
between our theoretical results and experimental observations for a set of 12
spiral galaxies.
