Abstract
Abstract The interactions among objects in a mean motion resonance are important for the orbital evolution of satellites and rings, especially Saturn’s ring arcs and associated moons. In this work, we examine interactions among massive bodies in the same corotation eccentricity resonance site that affect the orbital evolution of those bodies using numerical simulations. During these simulations, the bodies exchange angular momentum and energy during close encounters, altering their orbits. This energy exchange, however, does not mean that one body necessarily moves closer to exact corotation when the other moves away from it. Indeed, if one object moves toward one of these sites, the other object is equally likely to move toward or away from it. This happens because the timescale of these close encounters is short compared to the synodic period between these particles and the secondary mass (i.e., the timescale where corotation sites can be treated as potential maxima). Because the timescale of a gravitational encounter is comparable to the timescale of a collision, we could expect energy to be exchanged in a similar way for collisional interactions. In that case, these findings could be relevant for denser systems like the arcs in Neptune’s Adams ring and how they can be maintained in the face of frequent inelastic collisions.
Highlights
IntroductionBoth Saturn and Neptune have ring arcs. Saturn’s ring arcs are confined longitudinally due to corotation eccentricity resonances with Saturn’s moon Mimas: Aegaeon and its ring arc are in a 7:6 corotation resonance with Mimas (Hedman et al 2007, 2010) (see Figure 1), Anthe and its ring arc are in a 10:11 corotation resonance with Mimas (Cooper et al 2008; Hedman et al 2009), while Methone and its ring arc are in a 14:15 corotation resonance with Mimas (Spitale et al 2006; Hedman et al 2009)
In our solar system, both Saturn and Neptune have ring arcs
We examine interactions among massive bodies in the same corotation eccentricity resonance site that affect the orbital evolution of those bodies using numerical simulations
Summary
Both Saturn and Neptune have ring arcs. Saturn’s ring arcs are confined longitudinally due to corotation eccentricity resonances with Saturn’s moon Mimas: Aegaeon and its ring arc are in a 7:6 corotation resonance with Mimas (Hedman et al 2007, 2010) (see Figure 1), Anthe and its ring arc are in a 10:11 corotation resonance with Mimas (Cooper et al 2008; Hedman et al 2009), while Methone and its ring arc are in a 14:15 corotation resonance with Mimas (Spitale et al 2006; Hedman et al 2009). I=1 where G is the gravitational constant, M1 is the mass of the primary body, r is the distance between the test particle and the center of M1, the J2i terms are zonal gravity harmonic coefficients, and the P2i terms are Legendre polynomials in sinα, where the angle α is measured from the equatorial plane of the primary body. These terms in the potential alter the expressions for the particle’s mean motion n and radial epicyclic frequency κ
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