Dynamical Environment in the Vicinity of Asteroids with an Application to 41 Daphne

We studied the dynamical environment in the vicinity of the primary of the binary asteroid. The gravitational field of the primary is calculated by the polyhedron model with observational data of the irregular shape. The equilibrium points, zero velocity surfaces, as well as Jacobi integral have been investigated. The results show that the deviations of equilibrium points are large from the principal axes of moment of inertia. We take binary asteroid 41 Daphne and S 2008 41 1 for example. The distribution of topological cases of equilibrium points around 41 Daphne is different from other asteroids. The topological cases of the outer equilibrium points E1 E4 are Case 2, Case 5, Case 2, and Case 1. The topological case of the inner equilibrium point E5 is Case 1. Among the four outer equilibrium points E1 E4, E4 is linearly stable and other outer equilibrium points are unstable. Considering the shape variety of the body from Daphne to a sphere, we calculated the zero velocity surfaces and the locations as well as eigenvalues of equilibrium points. It is found that the topological case of the outer equilibrium point E2 change from Case 5 to Case 1, and its stability change from unstable to linearly stable. Using the gravitational force acceleration calculated by the polyhedron model with the irregular shape, we simulated the orbit for the moonlet in the potential of 41 Daphne.