  We derive a particular approximate solution of Einstein equations, describing
the gravitational field of a mass distribution that slightly deviates from
spherical symmetry. The deviation is described by means of a quadrupole
parameter that is responsible for the appearance of a curvature singularity,
which is not covered by a horizon. We investigate the motion of test particles
in the gravitational field of this naked singularity and show that the
quadrupole parameter affects the properties of Schwarzschild trajectories. By
investigating radial geodesics, we find that no effects of repulsive gravity
are present. We interpreted this result as indicating that repulsive gravity is
non-linear effect.
