Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Context. The orbital instability of minor solar system bodies (asteroids, small satellites, moonlets, and particles) is frequently studied in terms of the Lyapunov characteristic exponent (LCE). Asteroids interior to Jupiter often exihibit very short Lyapunov times, T-L, and very large radial variations, becoming Jupiter's crossers and escapers. However, a few cases of asteroids with very short T-L and no significant radial variation have been found. These orbits were called confined chaos or even stable chaos. This feature also appeared in the case of moonlets embedded in Saturn's F ring and disturbed by the nearby satellites Prometheus and Pandora.Aims. We present a simple approach to estimating the contribution of the radial component of the LCE to identify trajectories in the confined chaos regime.Methods. To estimate the radial contribution to the maximum LCE, we considered a rotating reference system in which one of the axis was aligned with the radial direction of the reference trajectory. Measuring the distance in the phase space between the two nearby orbits then allowed us to separate the contribution of the radial component from the others. We applied the method to two different dynamical systems: (a) an asteroid around the Sun disturbed by Jupiter; (b) a moonlet of Saturn's F-ring disturbed by the satellites Prometheus and Pandora.Results. In all cases, we found that the method of comparing the radial contribution of the LCE to the entire contribution allows us to correctly distinguish between confined chaos and escapers.