Other
Scientific paper
May 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dps....35.4604p&link_type=abstract
American Astronomical Society, DPS meeting #35, #46.04; Bulletin of the American Astronomical Society, Vol. 35, p.1010
Other
Scientific paper
A number of dynamically interesting aspects of the solar system---including, for example, the scattered Kuiper Belt objects and the creation of the Oort cloud---involve small bodies on eccentric orbits which are perturbed by a dominant major planet. Due to the sizeable eccentricities involved, these situations are hard to study using the usual eccentricity expansion of the disturbing function applied to the restricted circular three-body problem.
As an alternate approach, we develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits in the restricted circular planar three-body problem with Jacobi constant close to 3 and with secondary to primary mass ratio μ << 1. We use this framework to explore mean-motion resonances between the test particle and the massive bodies. This approach leads to a redefinition of resonance orders for the high-eccentricity regime in which a p:p+q resonance is called `pth order' instead of the usual `qth order' to reflect the importance of interactions at periapse. This approach also produces a pendulum-like equation describing the librations of resonance orbits about fixed points which correspond to periodic trajectories in the rotating frame. A striking analogy exists between these new fixed points and the Lagrangian points as well as between librations around the fixed points and the well-known tadpole and horseshoe orbits; we call the new fixed points the `generalized Lagrangian points'. Finally, our approach gives a condition a ˜ μ -2/5 for the onset of chaos at large semimajor axis a; a range μ < ˜ 5x 10-6 in secondary mass for which a test particle initially close to the secondary cannot escape from the system, at least in the planar problem; and a simple explanation for the presence of asymmetric librations in exterior 1:N resonances and the absence of these librations in other exterior resonances.
Pan Margaret
Sari Re'em
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