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 L1 moves towards the primaries with the increase in triaxiality, while L2 and L3 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 L1 and L3 is not observable; however it has an observable effect on the position of L2 in the presence of triaxiality except for the case 2.
International Frontier Science Letters (Volume 11)
B. Nakone and A. A. Hussain, "Collinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body", International Frontier Science Letters, Vol. 11, pp. 45-56, 2017