The planar restricted parabolic 3-body problem
by
Josep M. Cors
Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Manresa, Spain
Coauthors: Martha Alvarez-Ramírez and Joaquín Delgado

We study the planar restricted parabolic problem, mainly escape parabolic orbits and exchange orbits.

We obtain the equations of motion of the massless particle in a rotating-pulsating coordinate system where the primaries remain fixed. Introducing an appropriate time scaling we obtain two invariant subsystems corresponding to final evolutions. We show that the set of initial conditions leading to parabolic escape of the infinitesimal mass is the union of invariant manifolds of dimension 3 and 4 and tend asymptotically to a central configuration.

We also give a new criterion based in the Jacobi function analogous to the circular case, to guarantee elliptic capture by one the primaries.

Date received: June 11, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-96.