  The goal of the present 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. It is an extension of previous
models that focused only on planar models. A non-linear 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 model, the polyhedron model, which are assumed to be the real
values of the system. The model considered in this article 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. Also,
this model is used to carry out simulations to characterize regions with
solutions that remain bounded or that escape from around each asteroid under
analysis. We investigated an initial inclination of 0 degree (direct orbits)
and 180 degrees (retrograde orbits). We considered the gravitational field of
the asteroid, the gravitational attraction of the Sun, and the solar radiation
pressure 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.
