  In this paper we address a $n+1$-body gravitational problem governed by the
Newton's laws, where $n$ primary bodies orbit on a plane $\Pi$ and an
additional massless particle moves on the perpendicular line to $\Pi$ passing
through the center of mass of the primary bodies. We find a condition for that
the configuration described be possible. In the case that the primaries are in
a rigid motion we classify all the motions of the massless particle. We study
the situation when the massless particle has a periodic motion with the same
minimal period than primary bodies. We show that this fact is related with the
existence of certain pyramidal central configuration.
