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 au < 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 degree 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 <200m scale of these NEOs, we estimated the Yarkovsky effect drift rates in semimajor axis, and use these to estimate that a diameter of ∼100km or larger would allow primordial asteroids in the Earth-Mars belt to likely survive. We conclude that only a few 100 km scale asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.