Natural coupled orbit–attitude periodic motions in the perturbed-CRTBP including radiated primary and oblate secondary

This study investigated periodic coupled orbit–attitude motions within the perturbed circular restricted three-body problem (P-CRTBP) concerning the perturbations of a radiated massive primary and an oblate secondary. The radiated massive primary was the Sun, and each planet in the solar system could be considered an oblate secondary. Because the problem has no closed-form solution, numerical methods were employed. Nevertheless, the general response of the problem could be non-periodic or periodic, which is significantly depended on the initial conditions of the orbit–attitude states. Therefore, the simultaneous orbit and attitude initial states correction (SOAISC) algorithm was introduced to achieve precise initial conditions. On the other side, the conventional initial guess vector was essential as the input of the correction algorithm and increased the probability of reaching more precise initial conditions. Thus, a new practical approach was developed in the form of an orbital correction algorithm to obtain the initial conditions for the periodic orbit of the P-CRTBP. This new proposed algorithm may be distinguished from previously presented orbital correction algorithms by its ability to propagate the P-CRTBP family orbits around the Lagrangian points using only one of the periodic orbits of the unperturbed CRTBP (U-CRTBP). In addition, the Poincaré map and Floquet theory search methods were used to recognize the various initial guesses for attitude parameters. Each of these search methods was able to identify different initial guesses for attitude states. Moreover, as a new innovation, these search methods were applied as a powerful tool to select the appropriate inertia ratio for a satellite to deliver periodic responses from the coupled model. Adding the mentioned perturbations to the U-CRTBP could lead to the more accurate modeling of the examination environment and a better understanding of a spacecraft's natural motion. A comparison between the orbit–attitude natural motions in the unperturbed and perturbed models was also conducted to show this claim.