arXiv subjects

Gabriel Teixeira Guimarães

Publications and source records attributed to Gabriel Teixeira Guimarães.

4 recordsLinked to original sources

arXiv2026

Orbital Stability of Apsidally Aligned Planetary Systems

The dynamical stability of compact planetary systems is known to depend strongly on orbital eccentricities, but the physical role of apsidal alignment remains poorly understood. We investigate this problem using direct {\em N}-body simulations by separating planetary eccentricities into a systematic component shared by all planets and a random component that determines the degree of apsidal alignment. We find that these two components play fundamentally different dynamical roles. Random eccentricity destabilizes planetary systems by driving neighboring planet pairs into the regime of mean-motion resonance overlap, leading to chaotic evolution. In contrast, systematic eccentricity has little effect on the instability timescale over a wide range of values because the planetary orbits remain in apsidal alignment, preserving nearly fixed relative orbital orientations despite finite eccentricities. As a result, systems that start in apsidal alignment are nearly as stable as initially circular systems. This protection mechanism has a finite domain of validity. Beyond a critical systematic eccentricity, coherent apsidal precession breaks down, differential precession develops, and the instability timescale decreases rapidly. Our results demonstrate that the long-term stability of compact planetary systems cannot be characterized solely by orbital eccentricities but also depends on the maintenance of coherent apsidal precession, providing a new direction for analytical stability criteria.

astro-ph.EP↗

arXiv2026

Revisiting the dynamics of the Prometheus-Pandora system

This study revisits the dynamics of Prometheus and Pandora. The analysis focuses on their current orbits and considers mutual perturbations and the non-spherical shape of Saturn. Numerical integrations of the full equations of motion were performed in the context of the N-body problem using a dense set of initial conditions. Spectral analysis of these orbits, together with an interpretation of the dynamical maps, revealed several resonance domains of various orders between Prometheus and Pandora, including the 121:118 resonance domain. Resolving the secular equations for eccentricity and inclination revealed the absence of a forced component in both cases. The period associated with the precession rate, $Δ\varpi$, corresponds to the anti-alignment period. Chaos was quantified by analysing the diffusion of independent frequencies, which indicates dynamics governed by weak chaos. Minor perturbations caused by the Janus-Epimetheus pair on the orbits of Prometheus and Pandora were also considered. Finally, we investigated the dynamical history of the Prometheus Pandora system, accounting for Pandora's migration due to tidal interactions with Saturn. This revealed several past cross-resonances with a low probability of capture, as well as a scenario in which the Prometheus-Pandora pair exhibited a co-orbital configuration.

astro-ph.EP↗

arXiv2025

Orbital Dynamics of Atlas (S XV): Its Current Orbit and the Recent Past

This study comprehensively analyzes Atlas's current orbit, focusing on the secular and resonant perturbations caused by Prometheus, Pandora, and Saturn's oblateness. We performed numerical integration of the exact equations of motion for a dense ensemble of Atlas clone satellites. Through spectral analysis and interpretation of these orbits on dynamical maps, we identified the domain of the 54:53 Prometheus-Atlas and 70:67 Pandora-Atlas mean-motion resonances, showing that Atlas lies on the boundary of the separatrices of each of these resonances. We also identified the domains for the multiplets $Ψ_{1}$, $Ψ_{2}$, $Ψ_{3}$ and $Ψ_{4}$ associated with 70:67 resonance. Additionally, we explored the variation in Prometheus's eccentricity, demonstrating that as eccentricity increases (or decreases) in the 54:53 resonance domain correspondingly decreases (or increases). This combined analysis, between the above mappings, revealed qualitatively the overlap between the 54:53 and 70:67 resonances, which are responsible for the chaotic behavior of Atlas's orbit. We quantified chaotic motion in frequency space and found that the vicinity of Atlas is characterized by weak to moderate chaos, rather than strong chaos. Finally, we investigated Atlas's recent past, considering Prometheus's migration under the influence of Saturn's tidal forces. This analysis reveals several resonances crossed in the past, particularly focusing on the Atlas-Prometheus pair, which exhibited a co-orbital configuration.

astro-ph.EP↗

arXiv2023

Chaotic diffusion in the action and frequency domains: estimate of instability times

Purpose: Chaotic diffusion in the non-linear systems is commonly studied in the action framework. In this paper, we show that the study in the frequency domain provides good estimates of the sizes of the chaotic regions in the phase space, also as the diffusion timescales inside these regions. Methods: Applying the traditional tools, such as Poincaré Surfaces of Section, Lyapunov Exponents and Spectral Analysis, we characterise the phase space of the Planar Circular Restricted Three Body Problem (PCR3BP). For the purpose of comparison, the diffusion coefficients are obtained in the action domain of the problem, applying the Shannon Entropy Method (SEM), also as in the frequency domain, applying the Mean Squared Displacement (MSD) method and Laskar's Equation of Diffusion. We compare the diffusion timescales defined by the diffusion coefficients obtained to the Lyapunov times and the instability times obtained through direct numerical integrations. Results: Traditional tools for detecting chaos tend to misrepresent regimes of motion, in which either slow-diffusion or confined-diffusion processes dominates. The SEM shows a good performance in the regions of slow chaotic diffusion, but it fails to characterise regions of strong chaotic motion. The frequency-based methods are able to precisely characterise the whole phase space and the diffusion times obtained in the frequency domain present satisfactory agreement with direct integration instability times, both in weak and strong chaotic motion regimes. The diffusion times obtained by means of the SEM fail to match correctly the instability times provided by numerical integrations. Conclusion: We conclude that the study of dynamical instabilities in the frequency domain provides reliable estimates of the diffusion timescales, and also presents a good cost-benefit in terms of computation-time.

nlin.CD↗