Abstract
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.
Highlights
This make the study of dynamical environment in the gravitational potential of asteroids become significative and important, and can help to understand the dynamical behaviors of moonlets relative to the primary of the binary asteroid systems [2]. 41 Daphne is a large asteroid from the main belt [3, 4]
Our interest is to analyze the dynamical environments around the primary of large-size-ratio binary asteroid systems with considering the gravitational potential generated by the irregular shape of the primary
The inner equilibrium point is near the mass center of the asteroid
Summary
Since the detection of a moonlet around the asteroid 243 Ida [1] by the spacecraft. Galileo in 1993, several binary asteroid systems have been found in Solar system. We investigate the dynamics in the gravitational potential of (41) Daphne; the results are useful to understand the dynamical behaviors in other large-size-ratio binary asteroid systems. Wang et al [16] used the irregular shape model of asteroids generated by observed data and calculated the positions and topological cases of several contact binary asteroids, including 1996 HW1, 4769 Castalia, 25143 Itokawa, etc. Bosanac et al [17] used the restricted three-body problem (CR3BP) to model the gravitational force of the primary in the large mass ratio binary system, and investigated the stability of motion of a massless moonlet in the potential of the primary. Our interest is to analyze the dynamical environments around the primary of large-size-ratio binary asteroid systems with considering the gravitational potential generated by the irregular shape of the primary. The Conclusion section presents a brief review of the results
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