This thesis work has been motivated by the growing interest in small-spacecraft small-body missions and more specifically inspired by a proposed mission to the largest Martian Trojan (5261) Eureka. This binary asteroid represents a promising target for a planetary mission, as a better understanding of its formation and evolution would provide valuable insights into the history of both the Martian system and binary asteroids. This work has focused on identifying orbital designs which would optimise the geodetic parameters estimate, and thus best help characterise the asteroid's internal structure. The orbit determination solutions have been computed from simulated tracking data in various orbital configurations. To compensate the highly perturbed nature of the binary asteroid's environment, pseudo-periodic solutions identified around Eureka have been used as stable initial conditions for the spacecraft orbits. As Eureka's shape, gravity field and rotational state are not well characterised yet, large resulting uncertainties have been accounted for. They have been propagated to assess the robustness of the spacecraft orbits and subsequent orbit determination solutions to dynamical mismodelling, in order to eventually limit the science risk of the mission. For single CubeSat configurations, an optimal semi-major axis has been identified, being the one closest to the asteroid before orbital instability would start deteriorating the orbit determination solution. Non-equatorial retrograde orbits have been found to provide the lowest formal errors for geodetic parameters. Moreover, the benefit of simultaneously deploying two or even three CubeSats around the asteroid has been demonstrated. In both the two and three CubeSats configurations, promising orbital designs have been identified. They provide an estimation of the geodetic parameters which is accurate enough to bring insights into Eureka’s internal structure, and has been proven to be robust to dynamical mismodelling.
The methodology developed in this work is of interest to design other small-spacecraft small-body missions, and optimise their achievable geodetic parameters estimate. Additionally, Eureka's dynamical model and the large uncertainties assigned to it have been mostly based on models available for other binary asteroids. This brings confidence in the possible applicability of the identified optimal orbital designs to CubeSats missions targeting other binary asteroids.