Regions of Stability of Asteroids

Abstract

Using Hill’s modified stability criterium, regions of orbital elements are established for conditions of stability. The model of the three-dimensional restricted problem of three bodies is used with the Sun and Jupiter as the primaries. Four different cases are studied: direct and retrograde, outside and inside asteroidal orbits. The directions of the asteroidal orbits refer to the synodical reference frame and the positions refer to Jupiter’s orbit. The orbital parameters of the asteroids are the semi-major axis (a), the eccentricity (e), and the inclination from Jupiter’s orbital plane (i). The effects of the other orbital elements are not investigated in this paper. The argument of the perihelion and the longitude of the ascending node are fixed at Ω = ω = 90° and the time of perihelion passage is T = 0 for all orbits.The aim of this paper is to give quantitative evaluation of the stability of asteroids, the results being also applicable to comets and meteor streams. The evolution of the solar system may be studied using planets, satellites or smaller bodies like asteroids. The unquestionable advantage of approaching the problem via the investigation of asteroids is that there are a very large number of asteroids with well defined orbital elements while the number of planets and natural satellites in the solar system is much smaller.Establishing regions of stability enhances the location and discovery of additional minor planets. On the other hand, bodies with unstable orbits might be, under certain conditions, available for capture or for significant orbital changes without large artificial perturbations. Furthermore, changes in the observed orbital parameters may change the character of the motion from stability to instability and various evolutionary trends could be observed concerning the solar system.