Collinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body

Abstract

Abstract. This study examines the effect of the relativistic factor as well as the triaxiality effect of the bigger primary on the positions and stability of the collinear points in the frame work of the post-Newtonian approximation. Using semi-analytical and numerical approach the collinear points are found to be unstable. A numerical exploration in this connection, with the Earth-Moon system, reveals that the relativistic factor has an effect on these positions. It is also found that under the combined effect of relativistic factor and triaxiality, the collinear point 1 L moves towards the primaries with the increase in triaxiality, while 2 L and 3 L move away from the bigger primary. It is also seen that in most of the cases in the presence of triaxiality, the effect of relativistic factor on the positions of 1 L and 3 L is not observable; however it has an observable effect on the position of 2 L in the presence of triaxiality except for the case 2.

Investigation of the Stability of a Test Particle in the Vicinity of Collinear Points with the Additional Influence of an Oblate Primary and a Triaxial-Stellar Companion in the Frame of ER3BP

“…The results of this study confirm the results obtained by [13,31,33,34] when some of the parameters in both works are relaxed. Also, our result agree with [25] in the absence of relativistic parameter and triaxiality of the bigger primary ( It is observed numerically and graphically that, the perturbing forces under consideration are unable to change the stability behaviour of the collinear libration points ( ( 1,2,3) i L i = ) due to the appearance of the real roots of the characteristic equation (equation 31) (see Tables 2-17). This means that, the system is unbounded hence the collinear libration points are unstable in the Lyapunov sense.…”

“…Graphically, has been highlighted the instability of the collinear libration point 1 L of CEN X-4. This validates [13,25,33,34].…”

Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

“…Over decades, the study of the existence of some families of particular solutions in both circular and elliptic R3BP has received the attention of various researchers like [1][2][3][4][5][6][7][8][9][10][11][12][13] among others.…”