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

Two-body and Three-body orbital models may become inadequate to accurately capture essential dynamics of Solar Sail Satellites (SSSs) operating in the Sun-Earth-Moon system, specfically near the cislunar region. This work addresses the need to extend the existing analytical and numerical frameworks to the Photo-Gravitational Bi-Circular Restricted Four-Body Problem (PBCR4BP), with acting Solar Radiation Pressure (SRP). The purpose is to provide a more accurate representation of the Sun-Earth-Moon environment under bi-circular coplanar motion assumptions. In particular, the inherently perturbation due to the Earth-Moon relative motion introduces non-autonomous dynamical effects. These become increasingly remarkable when approaching the Earth-Moon system and can be of relevant interest for missions operating in proximity to the photo-gravitational region. This include Planetary Sunshade infrastructures, a space-based solar geoengineering concept aimed to mitigate climate change on Earth by deploying swarm of SSSs to reduce part of the oncoming solar radiation. Within the PBCR4BP framework, instantaneous photo-gravitational equilibrium points can be identified, together with those admissible volumes in which such equilibria exist. These regions consist of detached bubble-shaped domains that dynamically evolve over time as consequence of the system's non autonomous nature. Furthermore, from equilibria are discussed the required SSS attitude angles and associated lightness factor $\beta$, i.e. directly referred to its area-to-mass ratio. Moreover, a dynamical analysis is shown by actively exploiting SRP effects, assumed to be aligned with the SSS normal unit vector, to obtain closed periodic orbits in the PBCR4BP. Local dynamics are investigated through linearization of the equations of motion, by applying the perturbation theory. Their stable and unstable properties are assessed and mapped by computing instantaneous eigenvalues from the linearized system, discussing about periodic, aperiodic and quasi-periodic response modes. Finally, PBCR4BP results are compared with Photo-Gravitational Circular Restricted Three-Body Problem ones to quantify the perturbative influence of the Earth-Moon system.