Albedo effects on motion around equilibrium points of the restricted five-body problem

This study presents an analytical and computational analysis of motion in the vicinity of the triangular libration points of the restricted five-body problem (R5BP) when the first primary emits radiation and the second primary possesses reflective properties, while the remaining two primaries are treated as spherical, non-luminous and non-reflective bodies. The mathematical model incorporates solar radiation pressure, the albedo of Jupiter, and the luminosity parameters of the Sun-Jupiter system. The developed model is employed to investigate the dynamical behaviour of the Sun-Jupiter-Earth-Moon-satellite system. The governing equations of motion are derived in a rotating frame, and the positions of the triangular libration points are obtained numerically for different radiation and albedo parameters. The corresponding Jacobi constants and zero-velocity curves (ZVCs) are then examined, while the linear stability of the triangular points is investigated through the characteristic roots obtained after linearization. Orbital behaviour is further explored using Poincare surfaces of section (PSS) and orbit plots. The numerical results show that increasing Jupiter's albedo shifts the triangular libration points, while the combined radiation and reflection effects modify the accessible regions and the structure and frequency of the orbital motion. For the physical mass configuration considered, the triangular libration points remain linearly unstable because at least one characteristic root has a positive real part. The ZVCs indicate restricted motion in the vicinity of the Sun, whereas regular and quasi-periodic structures are observed around the Earth, Moon and Jupiter in the investigated cases. The study extends the treatment of radiation and albedo effects from previously investigated restricted three- and four-body models to the R5BP and provides a framework for examining non-gravitational effects in complex multi-body celestial systems.