Chaos and the Effects of Planetary Migration on the Orbit of S/2000 S5 Kiviuq

Among the many new irregular satellites that have been discovered in the lastfive years, at least six are in the so-called Kozai resonance. Due to solarperturbations, the argument of pericenter of a satellite usually precesses from0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lowerthan 140.7 degrees a new kind of behavior occurs for which the argument ofpericenter oscillates around +/-90 degrees. In this work we will concentrate onthe orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of thesatellites currently known to be in such resonance Kiviuq's orbit is very closeto the separatrix of the Kozai resonance. Due to perturbations from the otherjovian planets, it is expected that orbits near the Kozai separatrix may showsignificant chaotic behavior. This is important because chaotic diffusion maytransfer orbits from libration to circulation, and vice versa. To identifychaotic orbits we used two well-known methods: the Frequency Analysis Method(Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Ourresults show that the Kozai resonance is crossed by a web of secondaryresonances, whose arguments involve combinations of the argument of pericenter,the argument of the Great Inequality, longitude of the node, and other termsrelated to the secular frequencies g5, g6, and s6. Many test orbits whoseprecession period is close to the period of the Great Inequality (883 yrs), orsome of its harmonics, are trapped by these secondary resonances, and showsignificant chaotic behavior. Planetary migration, by moving the locations ofthese secondary resonances, may have depleted an original population of Kozairesonators.Comment: 47 pages, 18 figures, submitted to the Astronomical Journa