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

TL;DR

This paper develops a semi-analytic method using normal form approximations to analyze and design spacecraft maneuvers near the L4 and L5 Lagrangian points in the CPRTBP, enabling efficient transfer planning.

Contribution

It introduces a novel semi-analytic approach based on Hamiltonian averaging in Poincaré-Delaunay coordinates for the CPRTBP, facilitating the study of wide tadpole orbits and optimal transfers.

Findings

Constructed (quasi) invariant tori near L4-L5

Applied the method to Earth-Moon system transfers

Enabled efficient transfer design near Lagrangian points

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.