With an aim on mission design for artificial satellites we revisit the long-term dynamics of an orbiter about a planetary moon. The main dynamical effects are modeled with the Hill-oblate problem, which is doubly averaged over the mean anomaly and the argument of the node in the rotating frame. The averaging is performed with Deprit's perturbation method and is carried up to the order three in a small parameter proportional to the ratio orbiter's mean motion system's rotation rate. However, we do not claim to have a complete third order theory because of the unconventional sorting of the Hamiltonian terms that we choose in order to extend the validity of the theory for high-altitude orbiters. The doubly averaged problem shows the existence of circular and eccentric frozen orbits, whose initial conditions in the original (non averaged) model are recovered through explicit transformation equations. In addition, control strategies based on stable-unstable manifold tours are easily designed in the averaged problem. Application to the Jupiter-Europa system illustrates the full procedure.