The role of density distribution in dynamics around irregular asteroids

In recent years, asteroids have become increasingly important targets in space exploration. In this work, we study the effects of variable internal density on orbital dynamics around asteroids using a synthetic model consisting of a straight segment with a variable density distribution. We model the linear density of the asteroid as a degree-two polynomial, which allows us to distinguish between convex distributions, where mass accumulates at the ends of the segment, and concave distributions, where mass concentrates at the center. To validate this new model, we compare its gravitational potential with polyhedral models of the asteroids Gaspra and Toutatis. We then explore the dynamics induced by concave and convex density distributions, focusing on equilibria, periodic orbits, and heteroclinic orbits. The results show that internal density plays a critical role in shaping the orbital dynamics around asteroids.