Stability of equilibrium points in the restricted full three-body problem

The stability of equilibrium points is investigated for a particle in orbit about a model that mimics a binary asteroid. First, the equations of motion of a particle in the gravitational field of a sphere–ellipsoid system are derived. As in the restricted three-body problem (R3BP), five equilibrium solutions are found. In the R3BP, the stability condition for the equilateral points is given by the Routh criterion. However, in this problem, since the non-spherical mass distribution of one of the primaries is taken into account, stability is a function of the mass ratio, the distance between the bodies and the size parameters of the ellipsoid. Analytic stability criteria for the equilibria are derived and presented for a range of these parameters. In general, although some exceptions exist, it is found that the presence of the ellipsoid body reduces the stability region from the R3BP.