Abstract
<title>Abstract</title> <p>This study aims to create efficient analytical models for the gravitational fields of several asteroids: (21) Lutetia, (101955) Bennu, (99942) Apophis, (25143) Itokawa, and (87) Sylvia. For this purpose, we establish an analytical model that reproduces the gravitational field around non-spherical bodies with constant density, while also allowing the analysis of modeling effects when considering bodies composed of multiple layers and, therefore, different densities. Due to the non-spherical geometry of such bodies, their gravitational potential deviates from a central field. By representing the body as a polyhedron and decomposing it into tetrahedral elements, we apply the Series Potential Expansion Method (PSEM) to approximate the total potential by summing the contributions of each tetrahedron.Our results show that, although this model does not provide higher accuracy than the classical polyhedral approach, it achieves relative errors below 0.1% for points outside the body when developed to higher orders (e.g., orders 11 and 12). On the other hand, the model proposed in this paper significantly reduces execution time, thereby improving computational efficiency. We determine equilibrium points, analyze their stability, investigate zero-velocity planes, and compute the relative errors between the gravitational field modeled by PSEM and those obtained using both the classical polyhedral method of Tsoulis and Petrović and the mass concentration method.These results demonstrate the computational efficiency of the proposed approach for modeling the gravitational potential of irregularly shaped bodies. The model provides a robust framework for more complex analyses, such as the study of periodic orbits around non-spherical celestial bodies, stability assessments, and the planning of smooth spacecraft landing trajectories. Furthermore, this technique can be extended to other irregular bodies.</p>