Computing classical orbital elements with improved efficiency and accuracy

This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements, with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and proposes changes to the implementation to address orbits of arbitrary eccentricity and inclination in a simple and robust way. It presents two coding strategies that simplify the program structure, while improving the accuracy and speed of the transformation on modern computer architectures. Comprehensive numerical benchmarks demonstrate accuracy improvements by two orders of magnitude, together with a 40% reduction of computational cost relative to the standard implementation.