Dynamical Substitutes and Energy Surfaces in the Bicircular Sun-Earth-Moon System

The dynamics of a bicircular restricted Sun-Earth-Moon system in which all massive bodies orbit around the center of mass on circular orbits is studied. The equivalent equilibria of Lagrangian points (Dynamical substitutes) are found in a similar fashion as for the derivation of the Lagrangian points of the Earth-Moon system. Generalizations to non-gravitational perturbations due to solar radiation pressure (SRP), solar wind, and Poynting-Robertson drag are also considered through numerical continuation. A locus of points leading to the rates of change of the Hamiltonian and total energy to be zero is identified, and the behavior of the determinant of the pseudo-potential as a function of time is also analyzed in order to draw conclusions on the stability of the system. It is investigated that the equivalent equilibria of collinear Lagrangian points are still collinear in some particular cases. Moreover, the locations of these points are shifted toward the radiating body with increasing the parameter of drag force value. Finally we conclude that the pervasive discussion of the BCM system describes a bridges gap between the Sun-Earth/Moon and the Earth-Moon system.