On stability of triangular points of the restricted relativistic elliptic three-body problem with triaxial and oblate primaries

Abstract

This paper investigates the location and linear stability of triangular points under combined effects of perturbations: triaxialty of a massive primary, oblateness of a less massive one, and relativistic corrections. The primaries in this system are assumed to move in elliptical orbits around their common barycenter. It is found that the locations of the triangular points are affected by the involved perturbations. The stability of orbits near these points is also examined. We observed that these points are stable for the mass ratio, μ, range 0 < μ < μc, where μc is the critical mass ratio, and unstable for the range μc ≤ μ ≤ 0.5.

Keywords

• Celestial mechanics