Analytical modeling of the gravitational potential of irregularly shaped celestial bodies considering three distinct internal structures: application to (21) Lutetia

Abstract

The classical polyhedral model is one of the most accurate methods currently used to represent the gravitational field of irregularly shaped bodies. However, it assumes a homogeneous density distribution, which may not accurately reflect the internal composition of real objects. This study aims to analyze the effects of the internal structure of asteroid (21) Lutetia on gravitational potential modeling by considering a three-layered composition with distinct densities. The gravitational approach adopted in this study is the Potential Series Expansion Method (PSEM), represents models the body as a polyhedron and decomposes it into tetrahedral elements to estimate of the total potential around the asteroid. This estimation involves summing the contributions of each tetrahedron using a direct triple integral over its volume. Although this method does not achieve the same level of accuracy as the classical polyhedral approach, it offers a reasonable degree of precision, expresses the potential in analytical form, significantly reduces computational time, and, due to the simplified algebraic manipulation of the potential, facilitates the analysis of the asteroid's internal structural composition.