TITLE:
   Spatial p-q resonant orbits of the RTBP
   
AUTHORS:
   Esther Barrabes 
   Departament d'Informatica i Matematica Aplicada,
   Universitat de Girona, 
   Av. Lluis Santalo, s/n, 17071 Girona, Spain. 
   barrabes@ima.udg.es

   Gerard Gomez
   IEEC & Departament de Matematica Aplicada i Analisi,
   Universitat de Barcelona,
   Gran Via 585, 08007 Barcelona, Spain.
   gomez@cerber.mat.ub.es
   
ABSTRACT:
   The purpose of this paper is to extend the study of the so called
   p-q resonant orbits of the planar restricted three body problem
   to the spatial case. The p-q resonant orbits are solutions of the
   restricted three body problem which have consecutive close encounters
   with the smaller primary.  If E, M and P denote the larger
   primary, the smaller one and the infinitesimal body, respectively,
   then p and q are the number of revolutions that P gives around
   M and M around E, respectively, between two consecutive close
   approaches. For fixed values of p and q and suitable initial
   conditions on a sphere of radius \mu^{\alpha} around the smaller
   primary, we will derive expressions for the final position and
   velocity on this sphere for the orbits under consideration.


