An analytic solution of full-sky spherical geometry for satellite relative motions

Abstract Herein, an exact and efficient analytic solution for an unperturbed satellite relative motion was developed using a direct geometrical approach. The derivation of the relative motion geometrically interpreted the projected Keplerian orbits of the satellites on a sphere (Earth and celestial...

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Autores principales:	Soung Sub Lee, Christopher D. Hall
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/f565b7177bb94f75adb0f089fab49345
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spelling	oai:doaj.org-article:f565b7177bb94f75adb0f089fab493452021-12-02T17:39:20ZAn analytic solution of full-sky spherical geometry for satellite relative motions10.1038/s41598-021-88483-22045-2322https://doaj.org/article/f565b7177bb94f75adb0f089fab493452021-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-88483-2https://doaj.org/toc/2045-2322Abstract Herein, an exact and efficient analytic solution for an unperturbed satellite relative motion was developed using a direct geometrical approach. The derivation of the relative motion geometrically interpreted the projected Keplerian orbits of the satellites on a sphere (Earth and celestial spheres) using the solutions of full-sky spherical triangles. The results were basic and computationally faster than the vector and plane geometry solutions owing to the advantages of the full-sky spherical geometry. Accordingly, the validity of the proposed solution was evaluated by comparing it with other analytic relative motion theories in terms of modeling accuracy and efficiency. The modeling accuracy showed an equivalent performance with Vadali’s nonlinear unit sphere approach, which is essentially equal to the Yan–Alfriend nonlinear theory. Moreover, the efficiency was demonstrated by the lowest computational cost compared with other models. In conclusion, the proposed modeling approach illustrates a compact and efficient closed-form solution for satellite relative motion dynamics.Soung Sub LeeChristopher D. HallNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Soung Sub Lee Christopher D. Hall An analytic solution of full-sky spherical geometry for satellite relative motions
description	Abstract Herein, an exact and efficient analytic solution for an unperturbed satellite relative motion was developed using a direct geometrical approach. The derivation of the relative motion geometrically interpreted the projected Keplerian orbits of the satellites on a sphere (Earth and celestial spheres) using the solutions of full-sky spherical triangles. The results were basic and computationally faster than the vector and plane geometry solutions owing to the advantages of the full-sky spherical geometry. Accordingly, the validity of the proposed solution was evaluated by comparing it with other analytic relative motion theories in terms of modeling accuracy and efficiency. The modeling accuracy showed an equivalent performance with Vadali’s nonlinear unit sphere approach, which is essentially equal to the Yan–Alfriend nonlinear theory. Moreover, the efficiency was demonstrated by the lowest computational cost compared with other models. In conclusion, the proposed modeling approach illustrates a compact and efficient closed-form solution for satellite relative motion dynamics.
format	article
author	Soung Sub Lee Christopher D. Hall
author_facet	Soung Sub Lee Christopher D. Hall
author_sort	Soung Sub Lee
title	An analytic solution of full-sky spherical geometry for satellite relative motions
title_short	An analytic solution of full-sky spherical geometry for satellite relative motions
title_full	An analytic solution of full-sky spherical geometry for satellite relative motions
title_fullStr	An analytic solution of full-sky spherical geometry for satellite relative motions
title_full_unstemmed	An analytic solution of full-sky spherical geometry for satellite relative motions
title_sort	analytic solution of full-sky spherical geometry for satellite relative motions
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/f565b7177bb94f75adb0f089fab49345
work_keys_str_mv	AT soungsublee ananalyticsolutionoffullskysphericalgeometryforsatelliterelativemotions AT christopherdhall ananalyticsolutionoffullskysphericalgeometryforsatelliterelativemotions AT soungsublee analyticsolutionoffullskysphericalgeometryforsatelliterelativemotions AT christopherdhall analyticsolutionoffullskysphericalgeometryforsatelliterelativemotions
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An analytic solution of full-sky spherical geometry for satellite relative motions

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