Chaos induced by De Haerdtl inequality in the Galilean system

This paper aims at studying the long-term orbital consequences of the perturbations related to De Haerdtl inequality, a current quasi-commensurability between the Galilean satellites of Jupiter Ganymede and Callisto. We used the method of Frequency Map Analysis to detect a chaotic behavior in a 5-bodies system where every inequality has been dropped, except of De Haerdtl one. We also used Frequency Analysis to draw the behavior of the arguments likely to become resonant, in several numerical integrations. We show that De Haerdtl inequality might have induced chaos in the past if Ganymede's and Callisto's eccentricities have been higher than 4×¹⁰⁻³. Moreover, we enlight the influence of Jupiter's obliquity on this chaos. We also enlight some aspects of this chaotic behavior, showing for instance stable chaos and single resonances. The main result of this study is that De Haerdtl inequality should be taken into account in every study of the long term orbital evolution of the Galilean satellites.