Equilibrium Points in the Restricted Full Three Body Problem with Ellipsoidal Primaries

Abstract

Equilibrium points in the Restricted Full Three Body Problem with ellipsoidal primaries are investigated. The approach adopted by some in the literature that approximates the primaries by means of the spherical harmonic potential is demonstrated to be problematic when identifying equilibrium points in close vicinity of the primaries. Additional equilibrium points aside from the five well-known ones analogous to those in the Restricted Three Body Problem prove to be practically non-existent in general due to the intrinsic divergence of the spherical harmonic potential inside the Brillouin surface for irregular primaries. Accurate modeling of the primaries with the ellipsoid potentials is instead carried out. Locations and stability properties of the triangular equilibrium points in the double-ellipsoid systems of varying parameters are systematically studied and are compared with results obtained for the sphere–ellipsoid systems.