Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis

Abstract

In this paper of the series, a regularisation approach is proposed based on the idea of orbit segmentation into sectors. For this approach, general transformation equations to the sectors independent variables will be established. Also we develop the formulation of general and arbitrary divisions of elliptic orbits through one function for all sectors so as to facilitate analytically and computationally the expansion theory in terms of the sectors independent variables. The elliptic equations in terms of these variables are also given. The convergence of the series developments in each sector for a given division is discussed, a theorem is established for the parameters of an initial division situation. Numerical results for the parameters of some divisions are also included, and finally a suggested function for the analyses is given with the corresponding elliptic equations.