Recent dynamical results (Gladman et al. 1997. Dynamical lifetimes of objects injected into asteroid belt resonances. Science 277, 197-201) have pointed out that the bodies injected by collisions into the main resonances of the asteroid belt could not sustain the observed population of Earth-crossers of large diameter. In this paper, we present our numerical exploration of the dynamical evolution of Mars-crosser asteroids initiated by Migliorini et al. (1998. Origin of multikilometer Earth and Mars-crossing asteroids: A quantitative simulation. Science 281, 2022-2024.) and improved by computing the evolution over 100 Myr of the orbits of the whole observed sample of this population. Mars-crossers are about 35 times more numerous than Earth-crossers (at least down to 5 km in diameter). On the basis of their current orbital elements, we show that this population can be divided in different groups which have wellcharacterized dynamical behaviors, lifetimes, and end-states. From the dominant group, the asteroids evolve to intersect the Earth's orbit on a median time scale of about 60 Myr. Then, they can interchange between the Earth-crosser state and an evolved solely Mars-crosser one before colliding with the Sun or being ejected outside Saturn's orbit. Based on these dynamical results, we show that Mars-crosser asteroids can sustain about half of the multikilometer Earth-crossing population, and the expected orbital distribution of Earth-crossers coming from Mars-crossers is computed. Then, from an estimate of the size distribution of the Mars-crosser population and the spectral analysis of its different groups, we derive expected numbers of Earth-crossers and ratios of different taxonomic types in the Earth-crosser population that are not in disagreement † Died on November 2, 1997, in a mountain accident. This paper is devoted to his memory.
with the observed ones. We also confirm by spectral analysis the viability of the scenario, according to which the Mars-crosser population is sustained by asteroids which leak out from the main belt.