Orbital Distribution of Minor Planets in the Inner Solar System and their Impact Fluxes on the Earth, the Moon and Mars

Abstract

The planet crossing asteroids in the inner solar system have strongly chaotic orbits and the distributions of their angular elements (longitude of ascending node, Ω; argument of perihelion, ω; and longitude of perihelion, ϖ) are often regarded as uniform random. In the last decade, the known population of these minor planets has increased by more than a factor of four, providing a sufficiently large dataset for statistical analysis of their distribution. By choosing the observationally complete set of bright objects, we quantified the level of intrinsic non-uniformities of the angular elements for the following dynamical subgroups of Near Earth Objects (NEOs) and Mars Crossing Objects (MCOs): three subgroups of NEOs (Atens, Apollos, and Amors) and two inclination subgroups of MCOs (high and low inclination MCOs, with the boundary at inclination of 15°). Using the methods of angular statistics, we found several statistically significant departures from uniform random angular distributions. We were able to link most of them with the effects of secular planetary perturbations. The distribution of the longitude of ascending node, Ω, for NEOs is slightly enhanced near the ascending node of Jupiter due to the secularly forced inclination vector. Apollos and high inclination MCOs have axial enhancement of ω due to secular dynamics associated with inclination-eccentricity-ω coupling; these enhancements show opposite trends in these two subgroups. The ϖ distributions of Amors and of MCOs are peaked towards the secularly forced eccentricity vector, close to the ϖ value of Jupiter. These non-uniform distributions of the angular elements may affect the asteroidal impact fluxes on the planets. We developed a new approach that accounts for the non-uniform angular elements of planet crossing asteroids to investigate the impact flux and its seasonal variation on the Earth, the Moon, and Mars. The calculation for this study was achieved by generating many clones of the observationally complete subset of bright planet-crossing objects, measuring the Minimum Orbit Intersection Distance (MOID) between the planet and the clones, and making use of the classical formulation of Wetherill (1967) for the collision probability of two objects on independent Keplerian orbits. We developed a novel method to calculate the collision probability for near-tangential encounters; this resolves a singularity in the Wetherill formulation. The impact flux of NEOs on the Earth-Moon system is found to be not affected significantly by the non-uniform distribution of angular elements of NEOs. The impact flux on Mars, however, is found to be reduced by a factor of about 2 compared to the flux that would obtain from the assumption of uniform random distributions of the angular elements of MCOs. Moreover, the impact flux on Mars has a strong seasonal variation, with a peak when the planet is near aphelion. We found that the amplitude of this seasonal variation is a factor of 4-5 times smaller compared to what would be obtained with a uniform random distribution of the angular elements of MCOs. We calculate that the aphelion impact flux on Mars is about three times larger than its perihelion impact flux. We also calculate the current Mars/Moon impact flux ratio as 2.9-5.0 for kilometer size projectiles.