Investigating Attraction Zones in the Photogravitational Four-Body Problem: Effects of Asteroid Belt and Small Perturbations in Coriolis and Centrifugal Forces

Abstract

In this study, we have examined the effects of small perturbations on the Coriolis force and centrifugal force in the photogravitational restricted four-body problem within the circular asteroid belt. We investigate the existence, parametric evolution, and stability of equilibrium points considering various parameters. Our findings reveal that a small perturbation in the centrifugal force significantly influences the location of equilibrium points, while a perturbation in the Coriolis force has no impact on their location. To illustrate the permissible region of motion for the infinitesimal mass relative to the Jacobi constant, we plot the zero-velocity curves. Furthermore, we conduct a comprehensive analysis to determine the influence of the Coriolis force (\(\alpha \)) and centrifugal force (\(\beta \)) on the geometry of the basins of convergence (BoCs). In order to quantify the unpredictability of the BoCs, we thoroughly study the basin entropy. Significantly, we have found the presence of unpredictable (fractal) regions in close proximity to the boundaries of the basins of convergence.