A numerical exploration of miranda's dynamical history

The Uranian satellite Miranda presents a high inclination (4. ° 338) and evidence of resurfacing. For the past 20 years it has been accepted that this inclination is due to the past trapping into the 3:1 resonance with Umbriel. These last years there is a renewal of interest for the Uranian system since the Hubble Space Telescope permitted the detection of an inner system of rings and small embedded satellites, their dynamics being of course ruled by the main satellites. For this reason, we here propose to revisit the long-term dynamics of Miranda, using modern tools like intensive computing facilities and new chaos indicators [Mean Exponential Growth factor of Nearby Orbits (MEGNO) and frequency map analysis]. As in the previous studies, we find the resonance responsible for the inclination ofMiranda and the secondary resonances associated, likely to have stopped the rise of Miranda's inclination at 4. ° 5, identify with the frequency analysis tool the libration arguments of the secondary resonances involved, and show in particular that capture into a 3:1 secondary resonance and subsequent capture into a 2:1 secondary resonance may have disrupted the primary resonance with an inclination of Miranda of 4.°395.