The role of secondary resonances in the orbital history of Miranda

Statistics – Computation

Scientific paper

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Miranda, Orbital Elements, Orbital Resonances (Celestial Mechanics), Satellite Surfaces, Gravitational Constant, Planetary Orbits, Tides, Uranus, Satellites, Miranda, Orbits, History, Resonance, Resurfacing, Celestial Mechanics, Tides, Evolution, Umbriel, Orbital Elements, Origin, Formation, Dynamics, Models, Numerical Methods, Eccentricity, Timescale, Inclination, Damping, Procedure, Calculations, Frequency, Scaling, Distribution, Thermal Effects

Scientific paper

A simple 'perturbed pendulum' model is developed in order to ascertain the origin and dynamics of the secondary resonances in the tidal evolution of Miranda and Umbriel through the 1:3 mean motion commensurability. Long-term evolution is addressed on the basis of the computation-accelerating method of algebraic mappings. It is found that the present 4.34-deg value of Miranda's orbital inclination is probably a result of capture into the primary resonance, as well as subsequent capture into the 3/1 secondary resonance. The damping of an eccentricity as high as 0.035 by tidal dissipation in the satellite may account for the surface features of Miranda.

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