Semi-Analytical Approach for Distant Encounters in the Spatial Circular Restricted Three-Body Problem

This paper presents a three-dimensional semi-analytical formulation to model the third-body effect on a massless particle in the circular restricted three-body problem dynamical regime. The final expressions are obtained by means of the classical Lagrange planetary equations, by considering as small parameter of the perturbative approach the mass parameter of the system. The variations of the Keplerian orbital elements of the massless particle over one orbital period are computed as a function of the relative phasing between the massless particle and the secondary, and the overall behavior is described in terms of kick maps. Several applications to mission design are introduced, and the accuracy provided by the methodology is discussed on the basis of different initial conditions and physical systems.