  We study the geodesic motion of test particles in the space-time of two
Abelian-Higgs strings interacting via their magnetic fields. These bound states
of cosmic strings constitute a field theoretical realization of p-q-strings
which are predicted by inflationary models rooted in String Theory, e.g. brane
inflation. In contrast to previously studied models describing p-q-strings our
model possesses a Bogomolnyi-Prasad-Sommerfield (BPS) limit. If cosmic strings
exist it would be exciting to detect them by direct observation. We propose
that this can be done by the observation of test particle motion in the
space-time of these objects. In order to be able to make predictions we have to
solve the field equations describing the configuration as well as the geodesic
equation numerically. The geodesics can then be classified according to the
test particle's energy, angular momentum and momentum along the string axis. We
find that the interaction of two Abelian-Higgs strings can lead to the
existence of bound orbits that would be absent without the interaction. We also
discuss the minimal and maximal radius of orbits and comment on possible
applications in the context of gravitational wave emission.
