EVOLUTION OF ASTEROIDAL ORBITS AT THE 5-2 RESONANCE

We numerically solved the full equations of the three-body problem (Sun-Jupiter-asteroid) in order to investigate the time dependence of eccentricities for fictitious asteroids initially located near the 5:2 Jovian commensurability. The runs covered a time span of T ≥ 5 × 103tJ (tJ is the heliocentric orbital period of Jupiter) for the planar model, of T ≥ 104tJ for cases with the initial inclination 5° ≤ i0 ≤ 20° and of T = 105tJ for cases at i0 = 40°. We investigated regions of the initial values of semimajor axes and eccentricities for which, at some starting orbital orientations and initial positions, the fictitious asteroids were Mars- and Earth-crossers. We found that, for initial eccentricities e0 ≤ 0.2 and i0 ≤ 20°, these ranges were almost the same. The range in which we found asteroids to be Mars-crossers is close to that free of real asteroids. Close encounters of asteroids with Mars and Earth might be one of the causes of the 5:2 Kirkwood gap. Usually the fictitious asteroids considered were Mars- and Earth-crossers for specific types of relationships between variations in asteroidal eccentricity and the difference of longitudes of perihelion of an asteroid and Jupiter as well as for the transitions between these types. Relationships between the periods of asteroidal variations in eccentricity, inclination, argument of perihelion, and ascending node were obtained for some fictitious asteroids with small initial eccentricities and inclinations. © 1992.