Instantaneous Photo-Gravitational Equilibria and Solar-Sail Dynamics in the Sun-Earth-Moon System

For solar-sail missions operating in the Sun–Earth system, analytical and numerical tools based on simplified two-body and three-body models may become inadequate. This work addresses the need to extend existing analytical and numerical methods to the Photo-gravitational Bi-Circular Restricted Four-Body Problem, which provides a more accurate dynamical description of the Sun–Earth–Moon system. In particular, the non-autonomous perturbation induced by the Earth–Moon relative motion introduces time-dependent effects that cannot be captured within Earth–Moon barycentric approximations. These effects become increasingly relevant when approaching the Earth–Moon system and are of particular interest for missions operating near the photo-gravitational L1 region, such as for the Planetary Sunshade concept, a space-based solar geoengineering strategy aimed at mitigating climate change effects. Within this framework, instantaneous photo-gravitational equilibrium points are identified, together with the admissible regions in which such equilibria exist. These regions formbubble-shaped sets that evolve in time as a consequence of the non-autonomous nature of the system. Moreover, periodic orbits can be obtained by actively exploiting Solar Radiation Pressure as a control input, rather than as a perturbation, through attitude modulation of the sail. The local dynamics are investigated through linearization of the equations of motion. Stability properties are assessed by computing instantaneous eigenvalues and linear solutions, which are compared with those of the classical Circular Restricted Three-Body Problem to highlight the effects introduced by the Earth–Moon perturbation