Chaotic scattering in the restricted three-body problem II. Small mass parameters

Citation
L. Benet et al., Chaotic scattering in the restricted three-body problem II. Small mass parameters, CEL MEC DYN, 71(3), 1998, pp. 167-189
Citations number
33
Categorie Soggetti
Space Sciences
Journal title
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
ISSN journal
09232958 → ACNP
Volume
71
Issue
3
Year of publication
1998
Pages
167 - 189
Database
ISI
SICI code
0923-2958(1998)71:3<167:CSITRT>2.0.ZU;2-6
Abstract
We study the scattering motion of the planar restricted three-body problem for small mass parameters mu. We consider the symmetric periodic orbits of this system with mu = 0 that collide with the singularity together with the circular and parabolic solutions of the Kepler problem. These divide the p arameter space in a natural way and characterize the main features of the s cattering problem for small non-vanishing mu. Indeed, continuation of these orbits yields the primitive periodic orbits of the system for small mu. Fo r different regions of the parameter space, we present scattering functions and discuss the structure of the chaotic saddle. We show that for mu < mu( c) and any Jacobi integral there exist departures from hyperbolicity due to regions of stable motion in phase space. Numerical bounds for mu(c) are gi ven.