Restricted 3-body Problem with 1-PN and Solar Sail Effects

This paper investigates the dynamics of solar sails in the restricted three-body problem (RTBP), incorporating solar radiation pressure (SRP) and post-Newtonian (1PN) relativistic corrections to improve the accuracy and applicability of space mission design. Over the past three decades (1990–2025), significant advances in both circular and elliptical RTBP models have revealed artificial equilibrium points (AEPs), displaced periodic orbits, and novel trajectories enabling propellant-free space exploration. Control strategies such as Linear Quadratic Regulators (LQR) and reflectivity modulation have been instrumental in stabilizing these AEPs, as demonstrated by missions like JAXA’s IKAROS (2010) and LightSail-2 (2019). Applications extend to solar observation, lunar communication, asteroid rendezvous, and interstellar precursor missions. This study derives the modified equations of motion under SRP and 1PN effects and illustrates the equilibrium points, their stability, and basins of attraction. The findings provide key insights into how perturbations influence the dynamics of an infinitesimal body, supporting future developments in celestial mechanics and dynamical astronomy.