A particle-linkage model for elongated asteroids with three-dimensional mass distribution

The goal of this paper is to develop a simplified model to describe the gravitational fields of elongated asteroids. The proposed model consists of representing an elongated asteroid using a triple-particle-linkage system distributed in the three-dimensional space and it is an extension of previous planar models. A nonlinear optimization method is used to determine the parameters of our model, minimizing the errors of all the external equilibrium points with respect to the solutions calculated with a more realistic approach, the Mascon model, which are assumed to give the real values of the system. The model considered in this paper is then applied to three real irregular asteroids: 1620 Geographos, 433 Eros, and 243 Ida. The results show that the current triple-particle-linkage three-dimensional model gives better accuracy when compared to the axisymmetric triple-particle-linkage model available in the literature, and provides an advantage in terms of accuracy over the mass point model, while keeping computational time low. This model is also used to carry out simulations to characterize regions with solutions that remain bounded or that escape from around each asteroid under analysis. We investigated initial inclinations of 0° (direct orbits) and 180° (retrograde orbits). We considered the gravitational field of the asteroid, the gravitational attraction of the Sun, and the SRP. Our results are then compared to the results obtained using the Mascon gravitational model, based on the polyhedral shape source. We found good agreement between the two models.