Emilie Verheylewegen’s research while affiliated with University of Namur and other places

We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.

Miranda has a unusually high inclination ($I=4.338^\circ$), and its surface reveals signs of past endogenic activity. Investigations of the dynamical aspects of its orbital evolution suggest probable resonant processes, in particular with Umbriel, as an explanation for the present high inclination of Miranda. The tidal heating induced by gravitational interactions can lead to the rise of eccentricities and, consequently, to the increased dissipation of energy inside the satellite and higher internal temperatures. We study here the possible increase in eccentricities caused by orbital resonances and the resulting endogenic heating on Miranda taking into account its temperature dependent rheology. The coupled orbital-thermal evolution model was run with different rheological models and the thermal parameters starting form a cold thermal state, in radiative equilibrium with the environment. For the nominal parameters of the evolution scenarios studied, the resonances were not sufficient to rise neither the eccentricities nor the internal temperatures significantly. Lowest dissipation function Q of around 100 and final eccentricity of $e\approx0.02$ were obtained during the resonance 3:1 with Umbriel.

Some of the main satellites of Uranus, in particular Miranda and Ariel, present evidence of a past geophysical activity. This activity is due to heating during its history, but several causes for this heating are envisaged, in particular the tides and an / some impact(s), following radiogenic heating at the early stage of the evolution of these bodies. We here present a coupled thermal-orbital model of the history of the main satellites of Uranus, in which not only the orbit acts on the heating, but the heating acts also on the orbit in affecting dissipation function Q. We focus in particular on the way the past mean-motion resonance Miranda-Umbriel, responsible for Miranda's inclination, could have differentiated it. This way we estimate the contribution of the tides into the heating of these bodies, especially Miranda.

The Uranian satellite Miranda presents a high inclination (4 $_{.}^{\circ}$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 of Miranda and the secondary resonances associated, likely to have stopped the rise of Miranda's inclination at 4 $_{.}^{\circ}$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 $_{.}^{\circ}$395.

Since Voyager 2 space mission, we know some properties of the main Uranian satellites (Miranda, Ariel, Umbriel, Titania, Oberon): on the one hand, we observe an important resurfacing of both Miranda and Ariel, and on the other hand some strangenesses in the orbital elements such as the anomalously high inclinaison of Miranda or the anomalously high eccentricity of Ariel. The aim of this study is to use some modern methods including advances in computing resources to revise some studies developed in the last 20 years (see for instance [1], [2], [3], [4]). We therefore consider a model of a n-body problem which takes into account of the mutual perturbations of the five main satellites and of the planet Uranus and meet/improve some previous results.