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Zonal Harmonics of the Gravity Field in Def-Variables

Published online by Cambridge University Press:  12 April 2016

Ignacio Aparicio  and
Luis Floría
Ignacio Aparicio
Affiliation:
Grupo de Mecánica Celeste I, Departamento de Matemática Aplicada a la Ingeniería, ETSII.Universidad de Valladolid. E-47 011 Valladolid, Spain
Luis Floría
Affiliation:
Grupo de Mecánica Celeste I, Departamento de Matemática Aplicada a la Ingeniería, ETSII.Universidad de Valladolid. E-47 011 Valladolid, Spain

Extract

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To take advantage of the linear and regular formulation and treatment of Celestial Mechanics problems (Kustaanheimo & Stiefel 1965; Stiefel & Scheifele 1971; Deprit, Elipe & Ferrer 1994), Sharaf & Saad (1997) have given an analytical expansion of the Earth’s gravitational zonal potential in terms of Kustaanheimo-Stiefel (KS) regular elements (Stiefel & Scheifele 1971, §19), with special emphasis on its application to elliptic-type two-body orbits and, consequently, using a generalized (elliptic) eccentric anomaly as the independent variable.

Motivated by these and other considerations based on the definition and use of KS elements, and following a treatment similar to that of Stiefel & Scheifele (1971, §19), we develop element equations corresponding to a DEF-formulation of the satellite problem under the effect of the zonal potential.

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 455 - 456
Copyright
Copyright © Kluwer 1999

References

Burdet, C.A.: 1969, J. reine angew. Math., 238, 71–84.Google Scholar
Deprit, A., Elipe, A. & Ferrer, S.: 1994, Celest. Mech. and Dyn. Astron., 58, 151–201.Google Scholar
Kustaanheimo, P., & Stiefel, E.L.: 1965, J. reine angew. Math., 218, 204–219.Google Scholar
Sharaf, M.A. & Saad, A.S.: 1997, Celest. Mech. and Dyn. Astron., 66, 181–190.Google Scholar
Stiefel, E.L. & Scheifele, G.: 1971, “Linear and Regular Celestial Mechanics.”, Springer-Verlag, Berlin-Heidelberg-New York.CrossRefGoogle Scholar