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S.J. Peale, M.H. Lee (UCSB)
The differential migration of the newly formed Galilean satellites induced by disk-satellite interaction leads most of the time to the current configuration of 2:1 resonances among the orbital mean motions ni, which include the Laplace relation, n1-3n2+2n3=0. But if Io and Europa start sufficiently far apart, capture of this pair into resonances at the 5:2, 7:3 or 9:4 mean motion commensurabilities after Ganymede has collected Europa into the 2:1 resonances occurs occasionally. Capture of Io-Europa into a high order resonance depends on Europa's orbital eccentricity being large due to its previously established 2:1 resonances with Ganymede. The Io-Europa high order resonances sometimes become unstable as Europa' eccentricity is further elevated, and migration continues toward the 2:1 commensurability. Callisto is initially left behind in the migration scheme because of its smaller mass and probably a smaller disk surface mass density at its distance from Jupiter, but Callisto might start gaining on Ganymede after the latter's migration is slowed by its coupling with Europa and Io. Callisto is currently near the 7:3 resonance with Ganymede, but there is no obvious means of increasing the orbital eccentricity of either Ganymede or Callisto sufficiently to make capture possible during migration. Io may migrate sufficiently fast to escape capture into the 2:1 resonances with Europa while the disk is in place. Subsequent expansion of Io's orbit due to tides raised on Jupiter can then lead to capture into 2:1 resonances with Europa, and the origin of the Laplace relation would then be due to a combination of processes. Provided higher order resonances can be avoided, capture of the Galilean satellites into 2:1 resonances establishing the Laplace relation is robust for reasonable differential migration rates.
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.