DPS 35th Meeting, 1-6 September 2003
Session 46. Other Dynamics
Oral, Chair: N. J. Rappaport, Saturday, September 6, 2003, 11:20am-12:00noon, DeAnza III

[46.04] Generalized Lagrangian Points: Studies of Resonance for Highly Eccentric Orbits

M. Pan, R. Sari (Caltech)

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 \mu\ll 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~\mu-2/5 for the onset of chaos at large semimajor axis a; a range \mu< ~5\times 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.