Four-billion year stability of the Earth-Mars belt

Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth-Mars belt' from 1.08 < a < 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04-1.30 au for the age of the Solar system. We show that on this time-scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower 'Earth-Mars belt' covering a ∼ (1.09, 1.17) au, e < 0.04, and I < 1° has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν₃, ν₄, and ν₆ secular resonances contribute to long-term instability in the outer (1.17-1.30 au) region on Gyr time-scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth-Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200 m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis and use these to estimate that a diameter of ∼100 km or larger would allow primordial asteroids in the Earth-Mars belt to likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belt's region at the end of the terrestrial planet formation.