Semi-analytical integration algorithms based on the use of several kinds of anomalies as temporal variable

One of the main problems in celestial mechanics is the management of long developments in Fourier or Poisson series used to describe the perturbed motion in the planetary system. In this work we shall develop a software package that is suitable for managing these objects. This package includes algorithms to obtain the inverse of the distance based on an iterative method, a set of integration algorithms according to several sets of temporal variables. This paper contains a comparative study on the use of the true, eccentric, and elliptic anomalies in semi-analytical methods on celestial mechanics. © 2008 Elsevier Ltd. All rights reserved