Asymptotic ordination of artificial satellite Hamiltonian

Spatial Agencies’ projects for future artificial satellites continue to grow in number and complexity. These projects need the development of analytical theories in order to place the satellites in the most suitable orbit. The most common technique for constructing analytical theories is the Lie–Deprit method, which requires to expand in series of a small parameter the Hamiltonian of the problem. This expansion is not trivial but, usually, it is made without care. In this paper we provide a unified and systematic framework to get that development in a rigorous way.