  We investigate the natural families of periodic orbits associated with the
equilibrium configurations of the the planar restricted $1+n$ body problem for
the case $2\leq n \leq 4$ equal mass satellites. Such periodic orbits can be
used to model both trojan exoplanetary systems and parking orbits for captured
asteroids within the solar system. For $n=2$ there are two families of periodic
orbits associated with the equilibria of the system: the well known horseshoe
and tadpole orbits. For $n=3$ there are three families that emanate from the
equilibrium configurations of the satellites, while for $n=4$ there are six
such families as well as numerous additional connecting families. The families
of periodic orbits are all of the horseshoe or tadpole type, and several have
regions of neutral linear stability.
