Effect of Orbital Characteristic of Inclined Third-body on Motion of Secondary-body for a Hierarchical Triple Systems

The influence of a third-body's orbital elements on the second-body's motion in a hierarchical triple system is a crucial problem in astrophysics.Most prolonged evaluation studies have focused on a distant zero-inclined thirdbody.This study presents a new perspective on second-body motion equations that addresses a perturbing-body in an elliptic orbit derived with consideration of the axial-tilt(obliquity)of the primary.The proposed model is compared by the dual-averaged method and the N-body problem algorithm.After validation,a generalized threebody model is derived to investigate the effects of the third-body's orbital elements on secondary-body motion behavior.The proposed model considers short-time oscillations that affect secular evaluation and applies to exoplanets with all the primary and third body eccentricities,inclinations,and mass ratios.It is shown that the obliquity of the primary(or third-body's inclination)must be considered for precise long-term assessment,even in highly-hierarchical systems.

Long-term effects of main-body's obliquity on satellite formation perturbed by third-body gravity in elliptical and inclined orbit

A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.

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 Poincarémap 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.