# A discrete design method of repeat ground track orbit for Earth observation satellites

A discrete design method of repeat ground track orbit for Earth observation satellites This paper proposes a target orbit design scheme based on Pareto optimization for Earth observation satellites with injection error. To avoid high fuel consumption of satellite from injection orbit to original reference orbit, a new target orbit is designed. This target orbit not only requires low fuel consumption, but also can achieve no leakage coverage to the ground. First, the analytical model of sun-synchronous repeating orbit is established under J2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$J_{{2}}$$\end{document} perturbation. Based on this analytical model, in the neighborhood of injection orbit, the feasible solution set of the target orbit is constructed. This solution set constitutes a discrete search list. Second, a multi-objective optimization problem about fuel consumption and ground coverage is established. As the feasible solutions are constrained in the search list, the optimization of continuous variables in continuous space is transformed into the optimization of finite variables in discrete space, which greatly reduces the optimization time. Meanwhile, a weighted parameter α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document} is proposed. It represents the decision-maker’s preference for a specific indicator. Then, a preference function of fuel consumption and ground coverage is constructed based on α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document}. The preference function will help the decision-maker to select the most appropriate solution from the Pareto front. Finally, the above orbital elements are corrected under J4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$J_{{4}}$$\end{document} perturbation by differential correction. The simulation results show that for satellites with large injection, maneuvering the satellite to the redesigned target orbit can save 97.36% of fuel compared with maneuvering to the original reference orbit. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aerospace Systems Springer Journals

# A discrete design method of repeat ground track orbit for Earth observation satellites

, Volume OnlineFirst – Mar 21, 2023
8 pages

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Publisher
Springer Journals
Copyright © Shanghai Jiao Tong University 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2523-3947
eISSN
2523-3955
DOI
10.1007/s42401-022-00188-0
Publisher site
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### Abstract

This paper proposes a target orbit design scheme based on Pareto optimization for Earth observation satellites with injection error. To avoid high fuel consumption of satellite from injection orbit to original reference orbit, a new target orbit is designed. This target orbit not only requires low fuel consumption, but also can achieve no leakage coverage to the ground. First, the analytical model of sun-synchronous repeating orbit is established under J2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$J_{{2}}$$\end{document} perturbation. Based on this analytical model, in the neighborhood of injection orbit, the feasible solution set of the target orbit is constructed. This solution set constitutes a discrete search list. Second, a multi-objective optimization problem about fuel consumption and ground coverage is established. As the feasible solutions are constrained in the search list, the optimization of continuous variables in continuous space is transformed into the optimization of finite variables in discrete space, which greatly reduces the optimization time. Meanwhile, a weighted parameter α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document} is proposed. It represents the decision-maker’s preference for a specific indicator. Then, a preference function of fuel consumption and ground coverage is constructed based on α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document}. The preference function will help the decision-maker to select the most appropriate solution from the Pareto front. Finally, the above orbital elements are corrected under J4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$J_{{4}}$$\end{document} perturbation by differential correction. The simulation results show that for satellites with large injection, maneuvering the satellite to the redesigned target orbit can save 97.36% of fuel compared with maneuvering to the original reference orbit.

### Journal

Aerospace SystemsSpringer Journals

Published: Mar 21, 2023

Keywords: Repeat ground track orbit; Search list; Pareto optimality; Multi-objective discrete optimization

### References

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