Four Billion Year Stability of the Earth-Mars Belt

TL;DR

This study demonstrates that a narrow region of the Earth-Mars belt has remained stable for over 4.5 billion years, with only a few large asteroids likely surviving from the early Solar System.

Contribution

It provides a detailed numerical analysis of the long-term stability of the Earth-Mars belt, identifying the specific conditions and resonances affecting asteroid survival over Gyr timescales.

Findings

A narrow stable belt exists between 1.09 and 1.17 au.

Secular resonances contribute to instability in the outer belt.

Primordial asteroids larger than 100 km likely survived.

Abstract

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 $a\sim(1.09, 1.17)$ au, $e<0.04$, and $I<1^\circ$ 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 $\nu_3$, $\nu_4$, and $\nu_6$ 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 primordial asteroids with a diameter of 100 km or larger in the Earth-Mars belt would 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.