On the stability of the triangular points in the relativistic R3BP with a bigger triaxial primary

Abstract This paper studies the motion of a third body (test particle) in the vicinity of the triangular points L4,5 by considering the more massive as a triaxial body in the frame work of the relativistic restricted three-body problem (R3BP). It is seen that the positions and stability of the triangular points are affected by both relativistic and triaxiality factors. It turns out both the coordinates of the infinitesimal mass axe affected. It is seen that for these points, the range of stability region increases or decreases according as p>0 or p<0 where p depends upon the triaxiality and relativistic factors. Furthermore we have studied the periodic orbits around the triangular points in the range 0 < µ < µc. It is found that these orbits axe elliptical; the frequencies of long and short orbits of the periodic motion,the eccentricities,semi-major and semi-minor axes, orientation and coefficients of long and short periodic terms are all affected by triaxiality and relativistic factors.