Numerical investigation on the orbital evolution of 1:2 resonant asteroids between Jupiter and Saturn |
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| Authors: | Noriaki Watanabe |
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| Institution: | (1) Chiba University of Commerce, 272 Ichikawa, Chiba, Japan |
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| Abstract: | According to some investigations (Lecar and Franklin, 1973; Franklin et al., 1989; Soper et al., 1990) asteroids cannot remain for along 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. |
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| Keywords: | Asteroids resonance restricted problem N-body problem |
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