A generalized dipole-segment model for the gravitational field of elongated bodies

¹ CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal
² CICGE, DGAOT, FCUP, Vila Nova De Gaia, Portugal
³ Department of Mathematics, School of Engineering and Sciences - São Paulo State University (FEG/UNESP), Av. Ariberto Pereira da Cunha 333, 12516-410 Guaratinguetá, Brazil
⁴ PostGrad Program in Systems Engineering (PPGES) - University of Pernambuco (UPE), Brazil
⁵ Instituto Universitario de Matemáticas y Aplicaciones - Universidad de Zaragoza, EPS, Crta. de Cuarte s/n 22071, Huesca, Spain
⁶ School of Aerospace and Mechanical Engineering, The University of Oklahoma, 865 Asp Ave., Norman, OK 73019, USA
⁷ National Institute for Space Research (INPE), Av. dos Astronautas 1.758, 12227-010 São José dos Campos, SP, Brazil

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Received: 4 November 2025
Accepted: 5 January 2026

Abstract

Context. Various simplified models have been investigated to understand the complex dynamical environment near irregular asteroids. Aims. We propose a generalized dipole-segment model (GDSM) to describe the gravitational fields of elongated bodies. The proposed model extends the dipole-segment model (DSM) by including variable pole masses and a connecting rod while also accounting for the spheroidal shape of the poles instead of assuming point masses.

Methods. A nonlinear optimization method was employed to determine the model parameters, which minimizes the errors between the equilibrium points predicted by the GDSM and those obtained using a more realistic approach, such as the polyhedron model, which is assumed to provide the accurate values of the system. The model was applied to three real irregular bodies: the Kuiper belt objects Arrokoth, Kleopatra, and comet 103P∕Hartley.

Results. The results show that the GDSM represents the gravitational field more accurately than the DSM and significantly reduces computational time and effort when compared with the polyhedron model. This reduction in computational complexity does not come at the cost of efficiency. This makes the GDSM a valuable tool for practical applications. The model was further employed to compute heteroclinic orbits that connect the unstable triangular equilibrium points of the system. These trajectories, obtained from the intersections of the stable and unstable manifolds, represent natural pathways that enable transfers between equilibrium regions without continuous propulsion. The results for Arrokoth, Kleopatra, and 103P∕Hartley are consistent and validate the GDSM as an accurate and computationally efficient framework for studying the dynamical environment and transfer mechanisms around irregular small bodies.