The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to interactions with Mimas and the oblateness of the planet. This work is devoted to Anthe, Methone and Aegaeon, which are currently involved in the 11:10, 15:14 and 6:7 Mean-Motion Resonance with Mimas. We give an in deep study the current orbits of the small satellites by analyzing and identifying the short, resonant and long-term gravitational perturbations on their orbit. In addition, we perform numerical integrations of full equations of motion of ensembles of close-in small bodies orbiting the non-central field of Saturn. Spectral analyses of the orbits and interpretation of them in dynamical maps allow us to describe the orbits and the dynamics of Anthe, Methone and Aegaeon in view of resonant and long-term dynamics.
We show that the current geometric orbit of Methone is aligned with Mimas’ due to a forced resonant component in eccentricity, leading to simultaneous oscillations of several critical angles of the expanded disturbing function. Thus, we explain the simultaneous oscillations of four critical arguments associated to the resonance. The mapping of the Mimas-Methone resonance shows that the domains of the 15:14 Mimas-Methone resonance are dominated by regular motions associated to the Corotation resonance located at osculating eccentricities lower than ~0.015 and osculating semi-major axis in the interval 194,660-194,730 km. Methone is currently located deeply within this site (Callegari et al. 2021, CMDA – https://rdcu.be/cA7KO).
In the case of Anthe, it is shown that the current resonant state of the pair Mimas-Anthe is characterized uniquely by the stable libration of the corotation angle, C. The component C is identified in the time variations of the orbital elements and in the other arguments of the disturbing function, all of them which circulate in prograde sense driven by secular components, despite showing episodic oscillations in short time intervals (Callegari and Yokoyama 2021, Icarus). The mapping of the 11:10 Mimas-Anthe resonance in the eccentricity-semi-major axis phase space shows the non-chaotic regions around both the Corotation and Lindblad resonances, which are separated by chaotic zones. The orbit of Anthe is located deeply inside the stable regions of the Corotation resonance.
The current resonant dynamics of Aegaeon is also dominated by Corotation resonance with Mimas (Hedman et al. 2010, Icarus). The phase space of Aegaeon shows many differentiated structures, like secondary resonances (Callegari et al. 2021 – work in progress).
We are grateful to Fapesp (Sao Paulo State Research Funding Agency), through the processes 2019/15162-2, 2020/06807-7.