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J. A. Burns, V. Carruba (Cornell University), D. Nesvorny (Southwest Research Institute), M. Cuk (Cornell University), K. Tsiganis (Observatoire de la Cote D' Azur)
Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than ~q 39.3 degrees and lower than ~q 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around ± 90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such a resonance.
Carruba et al. (2002) describe a simple secular model of orbital evolution of satellites in the Kozai resonance. Their model, having only one-degree of freedom and not considering gravitational perturbations from other jovian planets, does not allow any chaotic behavior like that noticed in numerical simulations at the separatrix between circulating and librating orbits.
Here we study chaotic orbits in the region of the Kozai resonance near the orbit of Kiviuq. For this purpose we used two well-known methods for identifying chaotic behavior: the Frequency Analysis Method (Laskar 1990) and the Maximum Lyapunov Exponents (Benettin et al. 1980). Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality, longitude of the node, and other terms related to the planetary frequencies g5, g6, and s6. Many test orbits whose precession periods are close to the period of the Great Inequality (883 yrs), or some of its harmonics, are trapped by these secondary resonances, and show significant chaotic behavior.
Because the period of the Great Inequality is connected to the semimajor axes of Jupiter and Saturn, and because the positions of the jovian planets may have changed since their formation (Malhotra 1995), the location in phase space of these secondary resonances should have been different in the past. By simulating the effect of planetary migration, we show that a mechanism of sweeping secondary resonances, similar to the one studied by Ferraz-Mello et al. (1998) for the asteroids in the 2:1 mean motion resonance with Jupiter, could significantly deplete a primordial population of Kozai resonators and push several circulators near the Kozai separatrix. This mechanism is not limited to Kiviuq's region, and could have worked to destabilize any initial population of satellites in the Kozai resonance around Saturn and Jupiter.
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.