The dynamical structure of the Earth co-orbital region and implications for the near-Earth asteroid population

We investigate the structure of the Earth co-orbital region at low eccentricity and low inclination using a semi-analytical model of the 1:1 mean-motion resonance. The dynamics of asteroids in co-orbital motion with the Earth is described through a resonant semi-secular Hamiltonian, allowing the classification of orbits into circulation, Trojan, horseshoe, and quasi-satellite states. By systematically exploring the phase space in the space of the orbital elements, we compute the fraction of each type of motion and quantify how different co-orbital states fill the Earth co-orbital region. We find that horseshoe orbits dominate the phase space, occupying more than half of the volume, followed by Trojan and circulating orbits, while quasi-satellites represent only a small fraction. The distribution of co-orbital states exhibits strong inhomogeneities, particularly as a function of the argument of perihelion, with clear concentration regions of horseshoe orbits associated with node-crossing geometries. We also study the short-term stability of this portion of phase space by means of the MEGNO indicator, and how the level of chaos differs between different co-orbital states. Finally, we discuss the implications of these results for the expected population of Earth co-orbitals and for planetary defence, showing that a large fraction of co-orbitals remains undiscovered.