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A.L. Proctor, D.P. Hamilton, K.P. Rauch (University of Maryland)
Over the age of the Solar System, the orbits of the massive Galilean satellites have expanded significantly due to forces from the tidal bulges that they raise on Jupiter. This outward motion is believed to naturally lead to the development of the Laplace resonance that currently exists between Io, Europa, and Ganymede. Is this the only signature of tidal expansion still visible in the jovian system?
We propose that the anomalously large inclinations of the inner moonlets Amalthea (I=0.33\circ) and Thebe (I=1.09\circ) result from kicks imparted by Io's strong mean motion resonances as those resonances scan across the location of the moonlets. Both the eccentricities and inclinations of the moonlets are excited during resonant passages. But while the eccentricities decay rapidly due to the large satellite tides raised by the planet, the inclinations are basically preserved since they decay very slowly due to the tiny planetary tides raised by the satellite. For similar reasons, tides do not move the moonlets significantly outward.
Our numerical simulations show that two of Io's 3:1 resonances can impart an inclination of ~.3\circ to Amalthea when Io passes through a distance of aIo\approx5.27RJ (Jovian radii). The passage of Io's 4:2 resonances across Amalthea, at aIo\approx4.02RJ, would kick the moonlet's inclination by 0.6\circ, which is significantly larger than the observed value. Io's 4:2, 5:3, and 3:2 resonances cross Thebe when Io is at 4.92, 4.35, and 4.06 Jupiter radii, respectively. We find that either the 4:2 resonance acting alone, or in combination with the other resonances, causes Thebe's inclination to rise to about 1 degree. Our theory naturally explains the high inclinations of these two small satellites and limits Io's formation distance from Jupiter to between 4.02 and 4.92 Jovian Radii.