ISSN:
1572-9478
Keywords:
restricted three‐body problem
;
chaotic phenomena
;
scattering
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008335232601
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