International Journal of Science, Engineering and TechnologyAuthors: Audu Abdulmalik, Onubedo, Idris Babaji Muhammad, Mohammed Garba
Abstract: The present study investigates the equilibrium structure and local stability characteristics of a planar photo gravitational restricted four-body problem under the combined influence of radiation pressure and an axisymmetric circumstellar belt. The dynamical model considers three primaries arranged in an equilateral triangular configuration, while the motion of an infinitesimal particle is governed by radiation-modified gravitational forces and the gravitational potential of the belt. The equilibrium equations are solved numerically using a systematic search procedure with multiple initial conditions, followed by residual verification and eigenvalue-based stability analysis. The influence of the dominant-primary radiation factor and belt mass parameter on equilibrium locations is examined. The results show that radiation pressure produces systematic displacement of equilibrium points by modifying the effective gravitational balance, although the stability classification remains unchanged for the investigated parameter sets. In the stellar application, the numerical search identifies additional axial equilibrium solutions beyond the previously reported configurations. These solutions are verified using high-precision calculations to confirm their satisfaction of the equilibrium conditions. Linear stability analysis reveals that the near-origin equilibrium possesses purely imaginary characteristic roots and is therefore linearly stable within the adopted infinitesimal-particle approximation, whereas the remaining detected equilibria exhibit instability due to characteristic roots with positive real components.The results demonstrate that circumstellar belt perturbations and radiation effects significantly influence equilibrium multiplicity and local dynamics in modified restricted four-body systems. The study highlights the importance of accurate numerical exploration and stability verification for identifying closely located equilibrium solutions. Further investigations involving nonlinear stability analysis and global dynamical evolution are required to extend the present results beyond the linear approximation.
