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Equilibrium points and stability analysis in binary asteroid systems using a double mass dipole model
Authors: de Almeida, A.K.; Santos, L.B.T.; Gomes, C.E.S.; Andrade, E.V.M.; Barros, A.L.S.; Santos, K.G.F.; Fernandes, G.M.; Monteiro, F.; Amarante, A.; Bastos, R.I.S.; Lima, N.B.; Nascimento, H.C.B.; Lima, N.B.D; Prado, A.F.B.A
Ref.: Adv. Space Res. 77(5), 6122-6142 (2026)
Abstract: Understanding the gravitational environment around binary asteroid systems is essential for mission planning and celestial mechanics studies. Due to their irregular shapes, these systems exhibit complex gravitational fields that influence the motion of nearby spacecraft or particles. In this work, we develop a new mathematical formulation to model the gravitational field of fully synchronous and elongated binary asteroid systems, employing a rotating mass-dipole representation for each primary body. After deriving the equations of motion in the synodic reference frame, we conduct a comprehensive dynamical analysis, examining how the equilibrium points vary with the system´s mass ratio and the characteristic dimensions of each body. We also investigate the Jacobi constant associated with the emergence of these points and explore their linear stability properties as functions of the asteroid parameters. Finally, we apply the proposed formulation to the binary asteroid 90 Antiope by performing a nonlinear optimization of the six parameters (l, k, d1, d2, a, b) that define the Double Dipole Model. The optimization minimizes the three-dimensional distance between the equilibrium points predicted by the dipole formulation and those obtained from the polyhedral model, ensuring that the simplified representation reproduces with high fidelity the dynamical structure of the real system. Our findings contribute to a deeper understanding of the dynamical behavior of binary asteroid systems, offering a framework for future studies on orbital dynamics and spacecraft trajectory design in such environments. (c) 2026 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
