Orbital and solar resonance in the Jovian Moon system

The periodic orbit representing the motion of the inner three Galilean satellites of Jupiter is constructed in a rotating frame. Stability analysis indicates linear instability; but the repeated Poincaré exponents are associated with time and rotational symmetries, and it is concluded that the system is orbitally stable. Analysis of system frequencies reveals two resonances with the Sun. The rotation rate of the reference frame is close to 8910 the mean motion of Jupiter, and the period of the reference orbit is nearly 1710446 the period of Jupiter. The 8910 resonance is investigated via the method of averaging. The Jovian system currently circulates just outside the capture boundary with a period of about 117000 year, but with rotation rate of the reference frame varying by over an order of magnitude. Including tidal interaction, the system is evolving towards temporary capture in this resonance.