Abstract
In this manuscript, we explore the elliptic Sitnikov problem to elliptic Sitnikov kite problem within the framework of Newtonian mechanics, where four massive masses occupy the vertices of a kite and move along elliptical orbits around their common center of mass. An infinitesimal particle is constrained to oscillate along the \(\zeta \) -axis, perpendicular to the orbital plane of the primary masses and passing through the center of mass \(O\) . The primary aim of this study is to investigate how reflected radiation, or albedo effects, influence the dynamics of an infinitesimal mass within this problem. The influence of key physical parameters including the albedo factor \(\alpha \) and orbital eccentricity \(e\) on the dynamical behavior of the system is explored using time series analysis, first return map (FRM), families of periodic orbits, and Newton–Raphson basins of convergence (N–R BoC). Numerical simulations reveal that increasing \(\alpha \) enhances the stability and persistence of periodic oscillations, while increasing \(e\) leads to complex transitions, including quasi-periodic and chaotic behaviors. The convergence analysis using Newton–Raphson schemes highlights the sensitivity of initial conditions and the fractal nature of the phase space. These findings provide new insights into the long-term stability and complexity of celestial systems influenced by radiation and geometrical configurations.
