Orbital Stability Analysis of Lagrange Points under Solar Radiation Pressure

The study explores the orbital stability of the triangular Lagrange points L4 and L5 within the Sun-Earth Circular Restricted Three-Body Problem (CR3BP) under the influence of solar radiation pressure. The system's effective gravitational parameter was analytically modified to calculate the exact spatial shifts of the equilibrium coordinates. Linear stability was then evaluated by computing the eigenvalues of the modified Jacobian matrix. To validate the analytical framework, numerical integration was performed using the ode45 solver to simulate the 2D phase-space trajectories of locally perturbed bodies. The results demonstrated that increasing radiation pressure forces L4 and L5 to migrate inward toward the Sun, these shifted points remain linearly stable. Numerical simulations confirmed this stability, showing that the Coriolis force successfully traps the perturbed bodies in strictly bounded, epicyclic orbits without exponential divergence.