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We studied the dynamical environment in the vicinity of the primary of thebinary asteroid. The gravitational field of the primary is calculated by thepolyhedron model with observational data of the irregular shape. Theequilibrium points, zero velocity surfaces, as well as Jacobi integral havebeen investigated. The results show that the deviations of equilibrium pointsare large from the principal axes of moment of inertia. We take binary asteroid41 Daphne and S 2008 41 1 for example. The distribution of topological cases ofequilibrium points around 41 Daphne is different from other asteroids. Thetopological 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 isCase 1. Among the four outer equilibrium points E1 E4, E4 is linearly stableand other outer equilibrium points are unstable. Considering the shape varietyof the body from Daphne to a sphere, we calculated the zero velocity surfacesand the locations as well as eigenvalues of equilibrium points. It is foundthat the topological case of the outer equilibrium point E2 change from Case 5to Case 1, and its stability change from unstable to linearly stable. Using thegravitational force acceleration calculated by the polyhedron model with theirregular shape, we simulated the orbit for the moonlet in the potential of 41Daphne.

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