Albedo-Induced Perturbation in the Sitnikov Three-Body Problem

In this paper, the circular Sitnikov three-body problem is studied under the combined influence of radiation pressure and albedo. The model consists of two equal-mass primaries moving in circular orbits about their center of mass and an infinitesimal body constrained to oscillate along the perpendicular axis. The radiative emission from one primary and the reflected radiation from the other are incorporated into the effective potential through radiation and reflectivity parameters. Using the Jacobi integral, we determine the energetically admissible region for vertical motion and examine how radiative effects modify the accessible phase space. The study shows that the system admits a single vertical equilibrium point at the origin, which remains linearly stable within the physically admissible parameter range. Radiation and albedo reduce the effective restoring force and increase the oscillation period, producing a measurable rescaling of the physical time without altering the geometrical structure of the phase trajectories. The phase-space dynamics are further explored by means of Poincare (first-return) maps obtained from numerical integration of the nonlinear equation of motion. The resulting invariant curves confirm that the motion remains regular and bounded, while their progressive contraction reflects the reduction in the oscillation amplitude with increasing radiative effects. Overall, the results show that albedo acts as a quantitative modifier of the vertical Sitnikov dynamics by changing the effective potential, the admissible energy domain, and the observable time scale, without generating new qualitative phase-space structures.