Analytical solutions to the orbital motion of celestial objects have been nowadays mostly replaced by numerical solutions, but they are still irreplaceable whenever speed is to be preferred to accuracy, or to simplify a dynamical model. In this book, the most common orbital perturbations problems are discussed according to the Lie transforms method, which is the de facto standard in analytical orbital motion calculations.

• Preface
• Contents
• 1 Introduction
• Part I: Hamiltonian perturbations by Lie transforms
• 2 The method of Lie transforms
• 3 Application to integrable problems
• Part II: Perturbed elliptic motion: Artificial satellite theory
• 4 The Kepler problem
• 5 The main problem of the artificial satellite
• 6 Zonal perturbations
• 7 Tesseral perturbations
• 8 Lunisolar perturbations
• 9 Non-conservative effects
• Part III: Relative motion and perturbed non-Keplerian motion
• 10 The Hill problem
• 11 Motion inside Hill’s sphere
• 12 Motion about the libration points
• 13 Quasi-satellite orbits
• Bibliography
• Index