Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel-Umbriel mean motion resonance
S’ergio R. A. Gomes, Alexandre C. M. Correia
arXiv:2403.17897v1 Announce Type: new
Abstract: At present, the main satellites of Uranus are not involved in any low order mean motion resonance (MMR). However, owing to tides raised in the planet, Ariel and Umbriel most likely crossed the 5/3 MMR in the past. Previous studies on this resonance passage relied on limited time-consuming N-body simulations or simplified models focusing solely on the effects of the eccentricity or the inclination. In this paper, we aim to provide a more comprehensive view on how the system evaded capture in the 5/3 MMR. For that purpose, we developed a secular resonant two-satellite model with low eccentricities and low inclinations, including tides using the weak friction model. By performing a large number of numerical simulations, we show that capture in the 5/3 MMR is certain if the initial eccentricities of Ariel, $e_1$, and Umbriel, $e_2$, are related through $(e_1^2 + e_2^2)^{1/2} 0.015$ and $e_2 arXiv:2403.17897v1 Announce Type: new
Abstract: At present, the main satellites of Uranus are not involved in any low order mean motion resonance (MMR). However, owing to tides raised in the planet, Ariel and Umbriel most likely crossed the 5/3 MMR in the past. Previous studies on this resonance passage relied on limited time-consuming N-body simulations or simplified models focusing solely on the effects of the eccentricity or the inclination. In this paper, we aim to provide a more comprehensive view on how the system evaded capture in the 5/3 MMR. For that purpose, we developed a secular resonant two-satellite model with low eccentricities and low inclinations, including tides using the weak friction model. By performing a large number of numerical simulations, we show that capture in the 5/3 MMR is certain if the initial eccentricities of Ariel, $e_1$, and Umbriel, $e_2$, are related through $(e_1^2 + e_2^2)^{1/2} 0.015$ and $e_2