Abstract
Small bodies are ubiquitous in our Solar System, and they constitute a key element in understanding the origin of Earth and the emergence of life. Yet navigating a spacecraft around these bodies is very challenging, due to the difficulties of fully observing and characterizing these environments from the ground. These difficulties often translate into large uncertainties in the parameters that characterize these dynamical systems, ranging from uncertainties in the shape and mass distribution of the target bodies to those regarding the position and velocity of the spacecraft that navigates them. Small-body environments remain among the most perturbed and chaotic, making preliminary mission analysis particularly challenging. In particular, since the discovery of the first binary asteroids (Ida-Dactyl), binary systems have attracted much interest due to their considerable number (about 15% of the near-Earth orbit population) and their potential to reveal hints about the formation and evolution of our Solar System. Previous studies have modeled the dynamical environment of these systems using a perturbed version of the circular restricted three-body problem (CR3BP), where solar radiation pressure and irregularities of the gravity field of the body are accounted for. However, these analyses have predominantly focused on deterministic periodic orbits, which are then perturbed to examine sensitivity concerning initial conditions and/or parameter uncertainties. More recently, stochastic continuation approaches have been identified as a promising tool for integrating uncertainties into preliminary mission design for three-body systems. Unlike traditional iterative procedures, these techniques directly incorporate uncertainties, offering a more streamlined approach. By identifying natural regions of motion where spacecraft are statistically more likely to maintain periodic orbits, these methods offer a robust framework for bounded motion analysis. Expanding upon that, we extend the approach to small bodies, accounting for the irregularities in their gravity field. As a case study, we will apply these methodologies to the Hera spacecraft's mission to the Didymos & Dimorphos binary system, showing how these techniques can serve as a powerful preliminary mission design tool to identify safe regions of bounded motion around small bodies.