Analysis of symmetric periodic orbits in a tripolar system with a segment

We consider a simplified model to study some types of elongated asteroids with three protuberances, two at the ends and one in the middle. An example considered in this work is the asteroid Holiday. To model these bodies, we consider a tripolar system with a segment, which consists of a massive segment and three spheres, two at the ends of the segment and one between them, rotating around their center of mass with uniform angular velocity. In particular, we restrict our case to variations in masses and their positions, as well as variations in the mass of the segment or rod. For this problem, we obtain the potential and calculate families of symmetric periodic orbits, analyzing asymptotic points that may represent heteroclinic orbits as well as orbits that may represent possible collisions with the studied body. Furthermore, it was possible to obtain zero velocity curves and equilibrium points of the system. The analysis of symmetric periodic orbits can contribute to improve the efficiency of space missions, prolonging the useful life of satellites or spacecraft, in addition to collaborating for a better understanding of the dynamics of a satellite around an asteroid. The asteroid Holiday was chosen due to its degree of importance, both for its proximity to our planet and its periodicity, which led NASA to classify it as potentially dangerous.