Accurate and Fast Orbit Propagation with a New Complete Set of Elements

A formulation of the perturbed two-body problem that relies on a new set of seven orbital elements and a time-element is presented. The proposed method generalizes the special perturbation method published by Peláez et al. in 2007 for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into harmonic oscillators. In order to reduce the numerical error produced by the time transformation an element with respect to the physical time is defined and implemented as a dependent variable in place of the physical time itself. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new set of elements for different kinds of perturbations and eccentricities. Moreover, the method reveals to be competitive and even better than two very popular element methods derived from the Kustaanheimo-Stiefel and Sperling-Burdet regularizations.