Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998cemda..71..167b&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 71, Issue 3, p. 167-189 (1998).
Astronomy and Astrophysics
Astronomy
8
Restricted Three-Body Problem, Chaotic Phenomena, Scattering, Restricted Three&Hyphen, Body Problem
Scientific paper
We study the scattering motion of the planar restricted three-body problem for small mass parameters μ. We consider the symmetric periodic orbits of this system with μ = 0 that collide with the singularity together with the circular and parabolic solutions of the Kepler problem. These divide the parameter space in a natural way and characterize the main features of the scattering problem for small non-vanishing μ. Indeed, continuation of these orbits yields the primitive periodic orbits of the system for small μ. For different regions of the parameter space, we present scattering functions and discuss the structure of the chaotic saddle. We show that for μ < μc and any Jacobi integral there exist departures from hyperbolicity due to regions of stable motion in phase space. Numerical bounds for μc are given.
Benet Luis
Seligman Thomas H.
Trautmann Dirk
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