Investigating the Effect of Eccentricity and Mass Ratio of Primaries on the Structure of Lyapunov Orbits

A way to improve the accuracy of the three-body problem model is taking into account the eccentricity of primary attractors. Elliptic Restricted Three-Body Problem (ER۳BP) is a model for studying spacecraft trajectory within the three-body problem such that the orbital eccentricity of primaries is reflected in it. As the principal cause of perturbation in the employed dynamical model, the primaries eccentricity changes the structure of orbits compared to the ideal Circular Restricted Three-Body Problem (CR۳BP). In this paper, the orbit dynamics of a spacecraft in the ER۳BP are exploited to find periodic orbits as the spacecraft is considered to be in planar orbits around Lagrangian points. Periodic orbits are repetitious behaviors in which spacecraft orbital dynamics repeated periodically, these periodic behaviors are the main interest of this study because they are beneficial for future mission designs and allow delineation of the system's governing dynamics. Previous studies laid the foundation for finding periodic orbits or analyzing the stability of the obtained orbits in the ER۳BP regime. While in this paper, at first, initial guesses for correction algorithms were derived through the well-known family of orbits in the CR۳BP, then correction algorithms were used to refine the calculated orbit. Periodic orbits are portrayed and compared to previous studies and simpler models. Finally, the periodic orbits for the systems with different values of eccentricity and mass ratios are compared to determine their effect on the shape of the orbits in the ER۳BP.