NUMERICAL INVESTIGATION ON THE ORBITAL EVOLUTION OF 1:2 RESONANT ASTEROIDS BETWEEN JUPITER AND SATURN

According to some investigations (Lecar and Franklin, 1973; Franklin et al., 1989; Soper et al., 1990) asteroids cannot remain for a long time between Jupiter and Saturn. But as it is well known there is a near 5: 2 commensurability between Jupiter and Saturn. So there might be a possibility that asteroids between Jupiter and Saturn could be trapped in a resonant relation. In order to investigate this possibility, the changes of orbital elements of an asteroid whose initial value of semi-major axis corresponds to that of a 1: 2 resonant orbit were investigated by means of a double precision Cowell method. The integration routine was kindly supplied by Dr Yoshikawa. We considered first a planar restricted problem of three bodies, Sun-Jupiter-Asteroid, then a four body problem, Sun-Jupiter-Asteroid-Saturn. When integrating the equations of motion, short periodic terms were not eliminated and in the second test the interactions between Jupiter and Saturn were retained. Whether a close approach occured or not was not investigated. In every case a(J) = 5.20, a(S) = 9.54 and a = 8.26 were adopted as initial values of the semi-major axis of Jupiter, Saturn and Asteroid respectively.