Mapping and maneuvering long-term natural orbits around Titania, a satellite of Uranus

In this work, we present the results of a set of numerical simulations carried out to obtain long-duration orbits for a probe around Titania, Uranus' largest satellite. We also propose orbital maneuvers to extend the lifetime of some orbits. Titania's $J_2$ and $C_{22}$ gravitational coefficients and Uranus' gravitational perturbation are considered. The analysis of lifetime sensitivity due to possible errors in $J_2$ and $C_{22}$ values is investigated using multiple regression models. Simulations were performed for eccentricity equal 10-4, and lifetime maps were constructed. The results show that low-altitude orbits have longer lifetimes due to the balance between the disturbance of Uranus and the gravitational coefficients of Titania. The results also show that non-zero values of periapsis longitude ($\omega$) and ascending node longitude ($\Omega$) are essential to increase lifespan. Furthermore, the results indicate that the most economical maneuver occurs for final orbits of radius equal to 1050 km, this is observed for all inclination values.