Spatial p-q Resonant Orbits of the RTBP

E. Barrabes & G. Gomez

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
andM 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.