Abstract
This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyze 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 with 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.
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Regardless of the orbit propagation method, uncertainties in the orbit determination, in the predictions of solar activity, and in the modeling of the atmosphere–spacecraft interaction make GTOs unpredictable in the long term.
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Exceptions are given by translunar orbits, impulsive maneuvers, and the terminal phase of reentry trajectories.
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Acknowledgements
D. A. gratefully acknowledges the advice by Juan-Félix San Juan, Martin Lara, Denis Hautesserress, and Florent Deleflie during numerous occasions, and in particular during the KePASSA conferences and CNES conference on HEO orbits. D. A. recognizes the extremely helpful assistance by Hodei Urrutxua in the implementation of the non-singular geopotential code.
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Amato, D., Bombardelli, C., Baù, G. et al. Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods. Celest Mech Dyn Astr 131, 21 (2019). https://doi.org/10.1007/s10569-019-9897-1
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DOI: https://doi.org/10.1007/s10569-019-9897-1