Approximations for Secular Variation Maxima of Classical Orbital Elements under Low Thrust

Zhaowei Wang, Lin Cheng and Fanghua Jiang ()
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Zhaowei Wang: School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
Lin Cheng: School of Astronautics, Beihang University, Beijing 100083, China
Fanghua Jiang: School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Mathematics, 2023, vol. 11, issue 3, 1-23

Abstract: The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high.

Keywords: low-thrust orbital transfer; trajectory optimization; variations of orbital elements; reachability assessment; estimation of velocity increment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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