  Owing to the existence of an invariant length at the Planck scale, Einstein
special relativity breaks down at that scale. A possible solution to this
problem is arguably to replace the Poincar\'e invariant Einstein special
relativity by a de Sitter invariant special relativity. In addition to
reconciling Lorentz symmetry with the existence of an invariant length, such
replacement produces concomitant changes in all relativistic theories,
including general relativity, which becomes what we have called 'de Sitter
modified general relativity'. In this paper, the Newtonian limit of this theory
is used to study the circular velocity of stars around the galactic center. It
is shown that the de Sitter modified Newtonian force---which includes
corrections coming from the underlying local kinematics---could possibly
explain the rotation curve of galaxies without the necessity of supposing the
existence of a dark matter halo.
