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The orbit of Aegaeon and the 7:6 Mimas-Aegaeon resonance

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Abstract

Aegaeon (S/2008 S 1) is the last satellite discovered by the Cassini spacecraft at the end of the 2000 s. Like the satellites Methone and Anthe, it is involved in mean motion resonance with the mid-sized Mimas. In this work, we give a detailed analysis of the current orbit of Aegaeon identifying the resonant, secular and long-term perturbations due to Mimas and the oblateness of Saturn, and the effects of Tethys. For this task, we perform thousands of numerical simulations of full equations of motion of ensembles of small bodies representing clones of Aegaeon. We have mapped the domain of the 7:6 Mimas-Aegaeon resonance in the phase space of the semi-major axis and eccentricity. It displays a large area dominated by regular motions associated with the 7:6 corotation resonance surrounded by chaotic layers. Aegaeon is currently located very close to the periodic orbit of the resonance, which extends up to eccentricities \(\sim 0.025\) centered at semi-major axis \(\sim 168,028\) km. We show that the current orbit of Aegaeon has an important forced component in eccentricity due to the 7:6 resonance. The orbital inclination of Aegaeon has a non-negligible forced value due to long-term perturbations of Mimas. These two forced modes explain the complex perturbed orbit of Aegaeon without requiring the co-existence of multiple resonances.

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Acknowledgements

Thanks to XX Brazilian Colloquium on Orbital Dynamics (2021 virtual Edition), and Tadashi Yokoyama.

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Authors and Affiliations

  1. São Paulo State University (Unesp), Institute of Geosciences and Exact Sciences (IGCE), Avenue 24-A, 1515, Rio Claro, SP, 13506-900, Brazil

    Nelson Callegari Jr.

  2. Observatório do Valongo, Universidade Federal do Rio de Janeiro, Ladeira do Pedro Antônio 43, Rio de Janeiro, RJ, 20080-090, Brazil

    Adrián Rodríguez

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  1. Nelson Callegari Jr.
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  2. Adrián Rodríguez
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Correspondence to Nelson Callegari Jr..

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NCJ is grateful to Fapesp (Sao Paulo State Research Funding Agency), for the processes 2019/15162-2, 2020/06807-7. AR is grateful to FAPERJ (process 210.419/2022).

Appendix: Initial conditions and parameters

Appendix: Initial conditions and parameters

Table 2 gives the initial osculating elements and masses of the mid-sized satellites of Saturn and Aegaeon provided by Horizons system of ephemerides at date January 01, 2016.

The physical data for Saturn are \(M_S=5.6834\times 10^{26}\) kg, \(R_S=60,268\pm 4\) km (equatorial radius), \(J_2=0.01629071\) and \(J_4=-0.0009358\) (Jacobson et al. 2006).

Table 2 Orbital elements and masses of Saturnian satellites taken from the Horizons system refereed to date 2016-January-01, 00:00. Values collected from the update August 08, 2019. For Mimas and Aegaeon, we also show the geometric elements calculated as described in Sect. 2. The assumption of significant digits is purely formal. \(\omega \), \(\Omega \) are the argument of the pericenter and the longitude of ascending node, respectively
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Callegari, N., Rodríguez, A. The orbit of Aegaeon and the 7:6 Mimas-Aegaeon resonance. Celest Mech Dyn Astron 135, 21 (2023). https://doi.org/10.1007/s10569-023-10125-8

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