Geometric characterization of the Arjuna orbital domain

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\degr. 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 %.