Collinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body Nakone Bello 1,a and Aminu Abubakar Hussain 2,b 1 Department of Mathematics, Faculty of Science, Usmanu Danfodiyo University, Sokoto, Nigeria 2 Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria a bnakone@yahoo.com (corresponding author), b dadinduniya@gmail.com Keywords: Celestial Mechanics, Triaxiality, Relativity, R3BP. 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. 1. Introduction In the restricted three-body problem (R3BP), two massive bodies of finite masses 1 2 m and m called bigger and smaller primary respectively having spherical symmetry move about their center of mass in circular orbits. A third mass 3 m , the infinitesimal one, moves under the combined gravitational attraction of the two bodies but does not influence their motion. This problem possesses five equilibrium points, three collinear points 1 2 3 , L L and L which are in general unstable and two triangular points 4 5 L and L which are stable for the mass ratio 0 0.038520... µ µ < = Szebehely [1]. The relativistic restricted three-body problem was originally studied by Brumberg [2]. Bhatnagar and Hallan [3] were the first to study the stability of triangular points of the same model problem and found that the triangular point are unstable in the whole region 1 0 2 µ ≤ ≤ contrary to the classical case where they are stable for 0 µ µ < where µ is the mass ratio and 0 0.038520... µ = Douskos and Perdios [4] reinvestigated the same model problem and found the region of stability of triangular points as 0 2 17 69 0 486c µ µ < < − , where c is the dimensionless speed of light and 0 0.038520... µ = is the Routh’s value. Later on, Ahmed et al. [5]reexamined the same model problem and found the region of stability of triangular points as 0 0.03840 µ ≤ < . Ragos et al. [6] studied the existence, position and stability of collinear points in the relativistic R3BP. In recent years, there has been a strong revival of interest in the relativistic R3BP. Many perturbing forces i.e. radiation, oblateness, perturbations in the centrifugal and Coriolis forces etc. have been included in the study of relativistic R3BP. Several authors (Abd El-Bar and Abd El- Salam [7]; Abd El-Bar and Abd El-Salam [8]; Abd El-Salam and Abd El-Bar [9]; Katour et al. [10]; International Frontier Science Letters Submitted: 2016-11-22 ISSN: 2349-4484, Vol. 11, pp 45-56 Accepted: 2017-03-03 doi:10.18052/www.scipress.com/IFSL.11.45 Online: 2017-03-28 2017 SciPress Ltd, Switzerland SciPress applies the CC-BY 4.0 license to works we publish: https://creativecommons.org/licenses/by/4.0/