Fig. 7
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Simulations of the crossing of the 4:2:1 resonant chain between Ariel, Umbriel, and Titania, obtained setting tα,2 = 2.3 Gyr, Q2 = 200, and initial e4 = 0.0001. Top: evolution of the eccentricities and inclinations of the three moons in the case where the 2:1 mean motion resonance between Ariel and Umbriel is disrupted (case A). Middle: evolution of the eccentricities and inclinations of the three moons in the case where also Titania is captured into mean motion resonance with Ariel and Umbriel (case B). Bottom: evolution of the ratios of the mean motions in both cases.
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