arXiv subjects

Sérgio R. A. Gomes

Publications and source records attributed to Sérgio R. A. Gomes.

5 recordsLinked to original sources

arXiv2026

Dynamical evolution of the Uranian satellite system III. The passage through the7/4 MMR between Miranda and Ariel

The passage through the $5/3$ mean-motion resonance between Ariel and Umbriel, two of Uranus's largest moons, still raises several open questions. Previous studies suggest that, in order to reproduce the current orbital configuration, Ariel must have had an eccentricity of approximately $\sim 0.01$ before the resonance encounter, which would prevent resonant capture. However, the rapid tidal circularization of Ariel's orbit implies that some prior mechanism must have excited its eccentricity before the resonance encounter. In this work, we performed a large number of simulations using an N-body integrator to assess whether the earlier $7/4$ mean-motion resonance between Miranda and Ariel could serve as a mechanism to increase Ariel's eccentricity. Our results show that, due to divergent migration, resonance capture does not occur. As the satellites cross the nominal resonance, Ariel's eccentricity is only excited to $3.4 \times 10^{-4}$, substantially smaller than the required value. Therefore, the $7/4$ mean-motion resonance is not a viable mechanism for increasing Ariel's eccentricity.

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arXiv2024

Dynamical evolution of the Uranian satellite system II. Crossing of the 5/3 Ariel-Umbriel mean motion resonance

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 $(e_1^2 + e_2^2)^{1/2} < 0.007$. Moreover, we observe that the eccentricity of Ariel is the key variable to evade the 5/3 MMR with a high probability. We determine that for $e_1 > 0.015$ and $e_2 < 0.01$, the system avoids capture in at least $60\%$ of the cases. We also show that, to replicate the currently observed system, the initial inclinations of Ariel and Umbriel must lay within $I_1 \le 0.05^{\circ}$ and $0.06^{\circ} \le I_2 \le 0.11^{\circ}$, respectively. We checked these results using a complete $N-$body model with the five main satellites and did not observe any significant differences.

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arXiv2024

Dynamical evolution of the Uranian satellite system I. From the 5/3 Ariel-Umbriel mean motion resonance to the present

Mutual gravitational interactions between the five major Uranian satellites raise small quasi-periodic fluctuations on their orbital elements. At the same time, tidal interactions between the satellites and the planet induce a slow outward drift of the orbits, while damping the eccentricities and the inclinations. In this paper, we revisit the current and near past evolution of this system using a $N-$body integrator, including spin evolution and tidal dissipation with the weak friction model. We update the secular eigenmodes of the system and show that it is unlikely that any of the main satellites were recently captured into a high obliquity Cassini state. We rather expect that the Uranian satellites are in a low obliquity Cassini state and compute their values. We also estimate the current variations in the eccentricities and inclinations, and show that they are not fully damped. We constrain the modified quality factor of Uranus to be $Q_U' = ( 1.2 \pm 0.4 ) \times 10^5$, and that of Ariel to be $ Q_A' = (7 \pm 3) \times 10^4 $. We find that the system most likely encountered the 5/3 mean motion resonance between Ariel and Umbriel in the past, at about $(0.7 \pm 0.2)$ Gyr ago. We additionally determine the eccentricities and inclinations of all satellites just after the resonance passage that comply with the current system. We finally show that, from the crossing of the 5/3 MMR to the present, the evolution of the system is mostly peaceful and dominated by tides raised on Uranus by the satellites.

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arXiv2023

Stability maps for the 5/3 mean motion resonance between Ariel and Umbriel with inclination

The evolution of the five largest satellites of Uranus during the crossing of the 5/3 mean motion resonance between Ariel and Umbriel is strongly affected by chaotic motion. Studies with numerical integrations of the equations of motion and analysis of Poincaré surface sections provided helpful insights to the role of chaos on the system. However, they lack of a quantification of this chaos in the phase-space. Here, we construct stability maps using the frequency analysis method. We determine that for low energies (small eccentricity and/or inclinations), the phase-space is mainly stable. As the energy increases, the chaotic regions replace the stable motion, until only small, localized libration regions remain stable.

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arXiv2023

Effect of the inclination in the passage through the 5/3 mean motion resonance between Ariel and Umbriel

The orbits of the main satellites of Uranus are expected to slowly drift away owing to tides raised in the planet. As a result, the 5/3 mean motion resonance between Ariel and Umbriel was likely encountered in the past. Previous studies have shown that, in order to prevent entrapment in this resonance, the eccentricities of the satellites must be larger than $\sim 0.01$ at the epoch, which is hard to explain. On the other hand, if the satellites experience some temporary capture and then escape, the inclinations rise to high values that are not observed today. We have revisited this problem both analytically and numerically focussing on the inclination, using a secular two-satellite model with circular orbits. We show that if the inclination of Umbriel was around $0.15^{\circ}$ at the time of the 5/3 resonance encounter, capture can be avoided in about $60\%$ of the cases. Moreover, after the resonance crossing, the inclination of Umbriel drops to a mean value around $0.08^{\circ}$, which is close to the presently observed one. The final inclination of Ariel is distributed between $0.01^{\circ}$ and $0.25^{\circ}$ with a nearly equal probability, which includes the present mean value of $0.02^{\circ}$.

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