Equilibrium Points and Periodic Orbits in the Circular Restricted Synchronous Three-Body Problem with Radiation and Mass Dipole Effects: Application to Asteroid 2001SN263

Abstract

This study numerically explores the dynamics of the photogravitational circular restricted three-body problem, where an infinitesimal particle moves under the gravitational influence of two primary bodies connected by a massless rod. These primary masses revolve in circular orbits around their common center of mass, which remains fixed at the origin of the coordinate system. The distance between the two masses remains constant, independent of their rotation period. The third body, being infinitesimally small compared to the primary masses, has a negligible effect on their motion. The primary mass is considered as a radiating body, while the secondary is modeled as an elongated one comprising two hypothetical point masses separated by a fixed distance. The analysis focuses on determining the number, location, and stability of equilibrium points, as well as examining the structure of zero-velocity curves under the influence of system parameters such as mass and force ratio, radiation pressure and geometric configuration of the secondary body. The system is found to allow up to six equilibria: four collinear and two non-collinear. Their number and positions are significantly affected by variations in the system’s parameters. Stability analysis reveals that the two non-collinear equilibrium points can exhibit stability under specific parameter configurations, while the four collinear points are typically unstable. An exception is the innermost collinear equilibrium point, which can be stable for certain parameter values. Our numerical investigation on periodic orbitsaroundthecollinearequilibriumpointsoftheasteroidtriple-system2001SN263 show that a variation, either to the values of radiation or the force ratio parameters, influence their special characteristics such as period and stability. Also, their continuation in the spaceofinitialconditionsshowsthatallfamiliesterminatenaturallyatcollisionorbitswith either the primary or the secondary.