Analysis of real systems in the structure of Saturn–Hyperion, Saturn–Titan and Earth–Moon systems.
Stability analysis of the first order resonant periodic orbits in the perturbed restricted three-body problem.
Effect of mass ratio, Jacobi constant and oblateness coefficient on geometrical parameters of the periodic orbits.
Identify the initial positions of periodic orbits using Poincaré surface of sections.
Identify the separation islands of zero size in Poincaré surface of sections.
In this work, the perturbed restricted three–body problem is investigated numerically. The problem is applied to three real systems: Saturn–Hyperion, Saturn–Titan, and Earth–Moon, for analyzing the stability of first order resonant periodic orbits. In particular, the nature of periodic orbits is studied for all three systems, where their masses ratios represent small, moderate and large values. Using different types of numerical techniques, we have identified how the parameter of mass ratio, the Jacobi constant, and the oblateness coefficient affect the geometrical properties, and the periodic solutions of system.