  We investigate analytically and numerically the orbits of spinning particles
around black holes in the post Newtonian limit and in the presence of cosmic
expansion. We show that orbits that are circular in the absence of spin, get
deformed when the orbiting particle has spin. We show that the origin of this
deformation is twofold: a. the background expansion rate which induces an
attractive (repulsive) interaction due to the cosmic background fluid when the
expansion is decelerating (accelerating) and b. a spin-orbit interaction which
can be attractive or repulsive depending on the relative orientation between
spin and orbital angular momentum and on the expansion rate.
