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M. Cuk, J. A. Burns (Cornell U.)
Although analytical studies on the secular motion of the irregular satellites' have recently been published (Kinoshita and Nakai 1999, Yokoyama et al. 2003), these available theories have not yet been satisfactory reconciled with the results of direct numerical integrations (Carruba et al. 2002, Nesvorný et al. 2003). These discrepancies occur because the disturbing function is generally averaged over the Sun's orbital motion, whereas one should take into account periodic terms, most notably the so-called ``evection'', which can be large for slow-moving satellites. This problem is identical to that initially encountered by Newton and other historical researchers when studying the Moon's motion. Here we demonstrate that the evection and other terms from lunar theory can be incorporated into the more modern Kozai approach, and that such an approach produces much better agreement with symplectic integrations. Using this method, we plot the locations of secular resonances in the orbital-element space inhabited by the irregular satellites. Our model is found to predict correctly those satellites which are resonant or near-resonant.
We also analyze the octupole term in the disturbing function (Yokoyama et al. 2003) to determine the strength of resonant-locking for satellites whose \varpi is librating. By independently integrating these satellites' nominal orbits using a symplectic integrator, we show that the strength of this resonance can be successfully obtained from simple analytical arguments. We note that the distribution of irregular-satellite clusters in the space of proper orbital elements appears to be non-random. We find that the large majority of irregular satellite groups cluster close to the secular resonances. None of the largest objects (with R > 100km) belong to this class, which may suggest they had a somewhat different origin.
The author(s) of this abstract have provided an email address for comments about the abstract: cuk@astro.cornell.edu
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.