Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

Abstract

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.

Quaternion methods and models of regular celestial mechanics and astrodynamics

“…Amato et al [44] showed that special perturbation methods based on regularized formulations can compete and even outperform the semi-analytical methods for the long-term propagations (on the order of decades) of objects orbiting around the Earth. For this kind of applications, the Cowell formulation has never been used because of the required small integration step sizes, which causes strong accumulation of round-off error and long computational time.…”

“…Stiefel and Scheifele [37] , Bordovitsyna [38] , Bordovitsyna and Avdyushev [39] , Fukushima [40][41] , Pelaez et al [42] , Bau et al [43] , Amato et al [44] , and Bau and Roa [45] demonstrated the results of comparing the numerical solutions to the equations of orbital motion of celestial and cosmic bodies in the KS variables, Euler parameters, and other variables. These results prove the efficiency of the KS variables and Euler parameters in celestial mechanics and astrodynamics.…”

Space Occupancy in Low-Earth Orbit

“…This is a very demanding process in terms of CPU time (the computation of MiSO initial conditions for an individual constellation plane can take a few hours with an Intel Core processor i7-4790@3.6GHz) where the use of a very efficient orbit propagator is paramount. All numerical propagations were performed using the THALASSA orbit propagator [16], [17].…”

A method for accurate and efficient propagation of satellite orbits: A case study for a Molniya orbit

“…Discussions on symplectic integration methods applied to celestial mechanics and astrodynamics can be found in [21,22,23,24]. Formulations tailored for specific problems include the DROMO regularized propagator [25] and its developments [26,27,28]. [29] describes a fast numerical integration technique using a low-fidelity force model for tracking purposes.…”