Orbital eccentricity and inclination distribution of main-belt asteroids—The Statistical model revisited

Abstract

The distribution and evolution of the Main-belt Asteroid (MBA) orbital eccentricity and inclination provide clues for a deeper understanding of the dynamic evolution of our solar system. This paper presents an analysis of the orbital eccentricity and inclination of 460,000 known MBAs and fits MBA eccentricities and inclinations to a distribution model and further onto a dynamic model. We find that outer-belt MBAs fully fit a Rayleigh distribution; the orbital inclination grouped by the absolute magnitude generally not fully conformed to a Rayleigh distribution. Three evolutionary models of the MBAs were built; Model 1 follows the assumptions of a Rayleigh distribution and Model 2 follows the assumptions of a 2D Cauchy distribution; for the only orbital inclination, a Gaussian distribution was assumed as Model 3. For eccentricity, the distribution mode parameter fits by about 0.074∼0.086 in Model 1 and about 0.03 in Model 2 for the cases grouped by the absolute magnitude, the excitation parameter decreases as the magnitude increases. For the cases grouped by the heliocentric distance, the Model 1 fits the samples better than Model 2; the outer belt also fits Model 1 well, and its fit goodness is about 0.21. For inclination, when the samples were grouped by the absolute magnitude, the distribution mode and excitation parameters were consistent as well. Model 3 overall fits the data better than Models 1 and 2. In summary, the MBA excitation mechanism appears basically consistent with all models when the MBAs were classified by absolute magnitude for both eccentricity and inclination. The cases grouped by absolute magnitude can be fit well in Model 1 for eccentricities and Model 3 for inclinations. When the samples classified by heliocentric distance, the eccentricity and inclination distribution mode was correlated with heliocentric distance, and the influence of excitation was highly related to that distance as well.