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Third-Order Solution of An Artificial-Satellite Theory

Published online by Cambridge University Press:  12 April 2016

Hiroshi Kinoshita
Hiroshi Kinoshita*
Affiliation:
Center for Astrophysics, Harvard College Observatory and Smithsonian Astrophysical Observatory, Cambridge, Massachusetts 02138

Abstract

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A third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the Earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori’s perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.

Type
Part IV. Satellites of Jupiter and Saturn, and Artificial Satellites
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 241 - 257
Copyright
Copyright © Reidel 1978

References

Aksnes, K.: 1970, Astron. J. 75, 1066–1076.Google Scholar
Campbell, A and Jefferys, W. H.: 1970, Celes. Meah. 2, 467–473.Google Scholar
Deprit, A. and Rom, A.: 1970, Celes. Meah. 2, 166–206.Google Scholar
Deprit, A. and Zahar,, R.: 1966, Z. angew. Math. Phys. 17, 426–430.Google Scholar
Hall, N. M. and Cherniack, J. R.: 1969, Smithsonian Astrophys. Obs. Special Report No. 291, 49 pp.Google Scholar
Hori, G.: 1966, Publ. Astron. Soa. Japan 18, 287–296.Google Scholar
Hori, G.: 1970a., Publ. Astron. Soc. Japan 22, 191–198.Google Scholar
Hori, G.: 1970b, unpublished (paper read by Garfinkel, B. at IAU General Assembly, Commission No. 7, Brighton, England, August 1970).Google Scholar
Hori, G. and Kozai, Y.: 1975, Satellite Dynamics (ed. by Giacaglia, G.E.O.), Springer-Verlag, Berlin, pp. 1–15.Google Scholar
Kinoshita, H.: 1968, Publ. Astron. Soa. Japan 20, 1–23.Google Scholar
Kozai, Y.: 1962, Astron. J. 67, 446–461.CrossRefGoogle Scholar
Kutuzov, A. L.: 1975, Soviet Astron. Lett. 1, 42–44.Google Scholar
Rabe, E.: 1961, Astron. J. 66, 500–513.CrossRefGoogle Scholar
vinti, J. P.: 1959, J. Res. Nat. Bur. Standards, 63B, 105–116.Google Scholar
Yuasa, M.: 1971, Publ. Astron. Soa. Japan 23, 399–403.Google Scholar