Long-term dynamical survival of deep Earth co-orbitals

Abstract

We investigate the long-term dynamical survival of Earth co-orbital asteroids, focusing on near-circular, near-planar orbits that existing studies suggest are the most stable. Through numerical integration of test particles, we show that about a quarter of an initial population can survive for at least 50 per cent of the age of the Solar system with horseshoe particles being four to five times more likely to survive than L4/L5 Trojans. From the end state statistics, we constrain the existence of planetesimal-sized objects originally in co-orbital libration, finding that typically $5^{-2}_{+7}$ such planetesimals and no more than $27^{-9}_{+30}$ (95 per cent confidence) could have been present. Our simulations also suggest that episodic variations in the terrestrial orbital eccentricity may have caused bulk escape of co-orbitals, though variations large enough (>0.01) to generate such episodes are statistically unlikely. We then consider the orbital evolution of co-orbital asteroids of sizes down to D = 50 m under the Yarkovsky effect and find that objects with D < 1 km should escape over 4 Gyr with the smallest asteroids escaping after 200 Myr. Further, we test whether the Earth's co-orbital region may be populated by asteroids arriving via outward Yarkovsky drift, as conjectured by Zhou et al. We find this is an inefficient process, as planetary close encounters rapidly scatter the orbits far from the Earth's and towards the asteroid belt. Finally, we discuss how the destabilizing action of Yarkovsky may be mitigated through spin state evolution or late collisional comminution of large parent asteroids.