Computing Classical Orbital Elements with Improved Efficiency and Accuracy

TL;DR

This paper introduces improved algorithms for converting spacecraft state vectors to orbital elements, significantly enhancing accuracy and efficiency across various orbit types through novel coding strategies and thorough benchmarking.

Contribution

It proposes new implementation techniques that simplify the process and improve accuracy and speed for computing classical orbital elements from state vectors.

Findings

Accuracy improved by two orders of magnitude

Computational cost reduced by 40%

Effective for arbitrary eccentricity and inclination orbits

Abstract

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.