Stability and velocity sensitivities of libration points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary

Abstract

The study investigates the stability and velocity sensitivities of libration points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman-16 and HD188753 systems. We have observed that the position of L4 moves away from the centre of origin for both systems as the oblateness and the half mass dipole distance increases. As the oblateness and the half mass dipole distance increase, there is a shift in the position of L5 closer to the centre of the origin for both systems. The Poincare Surfaces of Section (PSS) for both systems have revealed that the behaviour of the system changes significantly with a bit change in the initial conditions, oblateness and the half mass dipole distance. We have observed that the sensitivity of both systems to change in position and velocities results in either regular orbits or irregular orbits. Hence, the dynamical behaviour of the systems is chaotic. Considering the range of a stable and unstable libration points for the problem under study given as 0<ν<νc and νc≤ν≤14respectively, our study has revealed that, the triangular libration points are stable and unstable for some values of oblateness for the binary systems. In the absence of oblateness, the νc* indicates that triangular points are stable for Luhman-16 system. When the parameters are varied differently with order of commensurability k, the critical mass parameters show that the triangular points are stable for Luhman-16 and unstable for HD188753 system. Using binary systems in our study, the results obtained can be used as springboards for broading the scope of interest in Celestial Mechanics and its investigations have shown significant improvement in the study of this longstanding problem.