  Arjuna-type orbits are characterized by being Earth-like, having both
low-eccentricity and low-inclination. Objects following these trajectories
experience repeated trappings in the 1:1 commensurability with the Earth and
can become temporary Trojans, horseshoe librators, quasi-satellites, and even
transient natural satellites. Here, we review what we know about this peculiar
dynamical group and use a Monte Carlo simulation to characterize geometrically
the Arjuna orbital domain, studying its visibility both from the ground and
with the European Space Agency Gaia spacecraft. The visibility analysis from
the ground together with the discovery circumstances of known objects are used
as proxies to estimate the current size of this population. The impact
cross-section of the Earth for minor bodies in this resonant group is also
investigated. We find that, for ground-based observations, the solar elongation
at perigee of nearly half of these objects is less than 90 degrees. They are
best observed by space-borne telescopes, but Gaia is not going to improve
significantly the current discovery rate for members of this class. Our results
suggest that the size of this population may have been underestimated by
current models. On the other hand, their intrinsically low encounter velocities
with the Earth induce a 10-1000-fold increase in the impact cross-section with
respect to what is typical for objects in the Apollo or Aten asteroid
populations. We estimate that their probability of capture as transient natural
satellites of our planet is about 8%.
