Coordinate and Time Systems -- Keplerian Orbits -- Perturbations on the Orbits -- Solutions of C20 Perturbation -- Solutions of Geopotential Perturbations -- Solutions of Extraterrestrial Disturbances -- Numerical Orbit Determination -- Analytic Orbit Determination -- Singularity-Free Theory and Discussions. The development of the orbits theory lags behind the development of satellite technology. This book provides, for the first time in the history of human satellite development, the complete third order solution of the orbits under all possible disturbances. It describes the theory of satellite orbits, derives the complete solutions of the orbital disturbances, describes the algorithms of orbits determination based on the theory, describes the applications of the theory to the phenomenon of the satellite formation physically. The subjects include: Orbits Motion Equations, Disturbance theory, Solutions of the differential Equations, Algorithms of Orbits determinations, Applications of the theory to the satellite formation.