Design of maneuvers based on new normal form approximations: The case study of the CPRTBP

Abstract

In this work, we study the motions in the region around the equilateral Lagrangian equilibrium points L4 and L5, in the framework of the Circular Planar Restricted Three-Body Problem (hereafter, CPRTBP). We design a semi-analytic approach based on some ideas by Garfinkel in [4]: the Hamiltonian is expanded in Poincar\'e-Delaunay coordinates and a suitable average is performed. This allows us to construct (quasi) invariant tori that are moderately far from the Lagrangian points L4-L5 and approximate wide tadpole orbits. This construction provides the tools for studying optimal transfers in the neighborhood of the equilateral points, when instantaneous impulses are considered. We show some applications of the new averaged Hamiltonian for the Earth-Moon system, applied to the setting-up of some transfers which allow to enter in the stability region filled by tadpole orbits.