Kozai Resonantors among Distant Moons of the Jovian Planets

Details Kozai Resonantors among Distant Moons of the Jovian Planets Kozai Resonantors among Distant Moons of the Jovian Planets

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dda....34.1001c&link_type=abstract

American Astronomical Society, DDA meeting #34, #10.01; Bulletin of the American Astronomical Society, Vol. 35, p.1044

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Scientific paper

S/2000 S5 and S/2000 S6 at Saturn, and S/2001 J10 at Jupiter, three recently discovered satellites that are currently trapped in the Kozai resonance, pose interesting new questions about the origin and dynamics of the jovian planets' moons. Here we report an initial study of this problem where we analyze the current orbits of the moons, as well as the surrounding orbital space. Such a study is central to improve our understanding of the origin of the resonant behavior of S/2000 S5, S/2000 S6, S/2001 J10, and of the distant moons in general.
Above inclination i = 39.23 degrees of inclination, two classes of secular evolution are possible: circulation, for which the argument of pericenter goes from 0 to 360 degrees, and libration, for which this angle oscillates around +/- 90 degrees. When we consider the full problem with perturbations from all jovian planets, a chaotic layer emerges near the separatrix between circulating and librating orbits. This chaotic layer must have been crossed by orbits that switched from circulation to libration in the past. Thus, to evaluate the capture efficiency into the Kozai resonance, the size and strength of this chaotic layer must be determined.
Among the methods to determine if an orbit is chaotic or not, the Frequency Analysis Method (Laskar 1993, 1999) is one of the most efficient tools. The main idea of this method is that, for a regular orbit (i.e., the orbit that either lies on a KAM torus or is periodic), the fundamental orbital and secular frequencies are constant with time. By contrast, these frequencies jitter about with time for a chaotic orbit. We determine our system's main frequency (the one that is associated with the precession period of the argument of pericenter) during several consecutive time intervals and check whether sigma(j)= 1-fj/f1 (where fj is the frequency for the jth period) varies with j. This quantity gives a measure of the regular or chaotic behavior of the orbit in question.
We have applied this method to a grid of initial orbits around S/2000 S5. We are currently running simulations with the other satellites. Preliminary results suggest that the chaotic boundary between circulating and librating orbits is asymmetric and fractal. Surprisingly, the orbit of S/2000 S5 is located very close to the chaotic layer. This suggests that S/2000 S5 might have interacted with this layer in the past. Simulations of slow dissipative transition of orbits through this layer are in progress. We believe that these experiments will help us constrain the amount of dissipation that accounts for the capture of these distant moons.

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