Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems, which are modelled as the two tri-axial ellipsoids with various shape and system parameters. Particularly, the influences of shape and system parameters on equilibria are discussed analytically. Firstly, the geometrical models of doubly synchronous binary asteroid systems are established. The dual second degree and order gravity field is employed to approximate the gravitational potential of the system. Six shape and system parameters are defined. Then, based on the linearized perturbation equations, the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived, which clearly illustrate the relationship between the distribution of equilibria and the variations of shape parameters. Further, the approximate expressions are applied to estimate the offsets of equilibria due to parameter errors, respectively. Finally, in order to have a better insight into the equilibriaum structure, the stabilities of equilibria under different system parameters are investigated. In particular, critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail. This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.