Time transformations and Cowell's method

The precise numerical integration of Cowell's equations of satellite motion is frequently performed with an independent variables defined by an equation of the form dt=crⁿds, wheret represents time,r the radial distance from the center of attraction,c is a constant, andn is a parameter. This has been primarily motivated by the uniformizing effects of such a transformation resulting in desirable analytic stepsize control for elliptical orbits. This report discusses the proper choice of the parametern defining the independent variables for various types of orbits and perturbation models, and develops a criterion for its selection.