Stability analysis of first order resonant periodic orbit

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.