Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem

The classical Hill's problem is a simplified version of the restricted thre e body problem (RTBP) where the distance of the two massive bodies (say, pr imary for the largest one and secondary for the smallest) is made infinity through the use of Hill's variables and a limiting procedure so that a neig hborhood of the secondary can be studied in detail. In this way it is the z eroth-order approximation in powers of mu(1/3). The Levi-Civita regularizat ion takes the Hamiltonian into the form of two uncoupled harmonic oscillato rs perturbed by the Coriolis force and the Sun action, polynomials of degre e 4 and 6, respectively. The goal of this paper is multiple. It presents a detailed description of the main features, including a global description o f the dynamics, when the zero velocity curve (zvc) confines the motion. The n it focuses on the collinear equilibrium points and its nearby periodic or bits. Several homoclinic and heteroclinic connections are displayed. Persis tence of confined motion when the zvc opens is one of the major concerns. T he geometrical behavior of the center-stable/unstable manifolds of the libr ation points L-1 and L-2 is studied. Suitable Poincare sections make appare nt the relation between these manifolds and the destruction of the invarian t KAM tori surrounding the secondary. These results extend immediately to t he RTBP. Some practical applications to astronomy and space missions are me ntioned. The methodology presented here can be useful on a more general fra mework for many readers in other areas and not only in celestial mechanics. (C) 2000 Elsevier Science B.V. All rights reserved.