Stability of the Triangular Points L4,5 in the ER3BP under the Influence of the Octupolar Mass Moment J4 of the Secondary

This paper investigates the effects of the quadruple J2 and octupolar mass moment J4 of the secondary on the triangular points L4,5 in the elliptic restricted three-body problem (ER3BP). The positions and stability of the triangular points are affected by the perturbations in the shape of the smaller primary (oblateness up to J4 ) and the elliptic nature of the orbits. An application of the results to double white dwarf binaries, reveals that the triangular points of the binaries are unstable due to the mass ratio falling outside the stability range 0 < µ < µc ; where (µ≤1/2).