In this book, analytic methods of orbit prediction and control are investigated for important low-thrust and impulsive orbit change and station-keeping applications, and the results compared with actual exact numerically-integrated counterparts to evaluate their accuracy and applicability. With one eye on future autonomous on-orbit navigation applications both in near-circular and general elliptic orbit, with minimal computational eff ort and high accuracy, the orbit prediction and control segments of such autonomous navigation systems are explored by also taking into account the shadowing eff ect where no thrust is allowed, such as for electric propulsion applications. This book shows that many of these orbit prediction and station-keeping problems can be solved entirely in analytic form with very high accuracy, and allow the practitioners to solve similar problems by tailoring them to their own applications, and to better understand and evaluate the pertinent variables and parameters that drive and infl uence the resulting description and evolution of the orbits.