15:1 Resonance effects on the orbital motion of artificial satellites

Formiga, Jorge Kennety S.; Moraes, Rodolpho Vilhena de

doi:10.5028/jatm.2011.03032011

Abstract

The motion of an artificial satellite is studied considering geopotential perturbations and resonances between the frequencies of the mean orbital motion and the Earth rotational motion. The behavior of the satellite motion is analyzed in the neighborhood of the resonances 15:1. A suitable sequence of canonical transformations reduces the system of differential equations describing the orbital motion to an integrable kernel. The phase space of the resulting system is studied taking into account that one resonant angle is fixed. Simulations are presented showing the variations of the semi-major axis of artificial satellites due to the resonance effects.

Keywords:
Resonance; Artificial satellites; Celestial mechanics

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REFERENCES

Anselmo, L., Pardini, C., 2009, "Dynamical evolution of high area-to-mass ratio debris released into GPS orbits", Advances in Space Research, Vol. 43, No. 10, p. 1491-1508.
Beletskii, V. V., Resonance Phenomena at Rotations of Artificial and Natural Celestial Bodies. In: Giacaglia, G.E.O. "Satellites dynamics". Berlin: Verlang, 1975.
Celestrak, 2004, "Apresenta os elementos 2-line do NORAD", Retrieved in August 10, 2004, from http://www.celestrak.com
» http://www.celestrak.com
Chao, C.C., Gick, R.A., 2004, "Long-term evolution of navigation satellite orbits: GPS/GLONASS/GALILEO", Advances in Space Research, Vol. 34, p. 1221-1226.
Ferraz Melo, S., 1979, Periodic orbits in a region of instability created by independent small divisors. In: Nagoz, Y. E., Ferraz Melo, S. "Natural and artificial satellite motion". Austin: University of Texas Press, p. 283-292.
Florent, D., Alessandro, R., Christophe, P., Gilles, M., François, B., 2011, "Semi-analytical investigations of the long term evolution of the eccentricity of Galileo and GPS-like orbits", Advances in Space Research, Vol. 47, No. 5, p. 811-821.
Formiga, J. K. S., 2005, "Estudo de ressonâncias no movimento orbital de satélites artificiais". 133f. Dissertação (Mestrado em Física) - Faculdade de Engenharia do Campus de Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá.
Hamill, P. J., Blitzer, L., 1974, "Spin-orbit coupling: a unified theory of orbital and rotational resonance", Celestial mechanics, Vol. 9, p. 127-146.
Hugues, S., 1980, "Earth satellite Orbits with Resonant Lunisolar Perturbations". Resonances dependent only inclination. Proceedings of the Royal society of London serie A. London, Vol. 372, No. 1745, p. 243-264.
Lima, Jr. P. H. C. L., 1998, "Sistemas ressonantes a altas excentricidades no movimento de satélites artificiais". Tese (Doutorado), Instituto tecnológico de aeronáutica, São José dos Campos.
Osório, J. P., 1973, "Perturbações de órbitas de satélites no estudo do campo gravitacional terrestre". Porto: Imprensa Portuguesa.
Rossi, A, 2008, "Resonant dynamics of medium earth orbits: space debris issues", Celestial Mechanics and Dynamical. Astronomy, Vol. 100, p. 267-286.
Tapley, B. D., Watkins, M. M., Ries, J. C., Davis, G. W., Eanes, R. J., et alz, 1996, "The Joint Gravity Model 3", Journal of Geophysical Research, Vol. 101, No. B12, p. 28029-28050.
Vilhena de Moraes, R., Silva, P. A. F., 1990, "Influence of the resonance in gravity- gradient stabilized satellite". Celestial Mechanics and Dynamical Astronomy, Vol. 47, p. 225-243.

Publication Dates

Publication in this collection
Sep-Dec 2011

History

Received
23 May 2011
Accepted
07 Aug 2011

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Anselmo, L., Pardini, C., 2009, "Dynamical evolution of high area-to-mass ratio debris released into GPS orbits", Advances in Space Research, Vol. 43, No. 10, p. 1491-1508.

[2] Beletskii, V. V., Resonance Phenomena at Rotations of Artificial and Natural Celestial Bodies. In: Giacaglia, G.E.O. "Satellites dynamics". Berlin: Verlang, 1975.

[3] Celestrak, 2004, "Apresenta os elementos 2-line do NORAD", Retrieved in August 10, 2004, from http://www.celestrak.com
» http://www.celestrak.com

[4] Chao, C.C., Gick, R.A., 2004, "Long-term evolution of navigation satellite orbits: GPS/GLONASS/GALILEO", Advances in Space Research, Vol. 34, p. 1221-1226.

[5] Ferraz Melo, S., 1979, Periodic orbits in a region of instability created by independent small divisors. In: Nagoz, Y. E., Ferraz Melo, S. "Natural and artificial satellite motion". Austin: University of Texas Press, p. 283-292.

[6] Florent, D., Alessandro, R., Christophe, P., Gilles, M., François, B., 2011, "Semi-analytical investigations of the long term evolution of the eccentricity of Galileo and GPS-like orbits", Advances in Space Research, Vol. 47, No. 5, p. 811-821.

[7] Formiga, J. K. S., 2005, "Estudo de ressonâncias no movimento orbital de satélites artificiais". 133f. Dissertação (Mestrado em Física) - Faculdade de Engenharia do Campus de Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá.

[8] Hamill, P. J., Blitzer, L., 1974, "Spin-orbit coupling: a unified theory of orbital and rotational resonance", Celestial mechanics, Vol. 9, p. 127-146.

[9] Hugues, S., 1980, "Earth satellite Orbits with Resonant Lunisolar Perturbations". Resonances dependent only inclination. Proceedings of the Royal society of London serie A. London, Vol. 372, No. 1745, p. 243-264.

[10] Lima, Jr. P. H. C. L., 1998, "Sistemas ressonantes a altas excentricidades no movimento de satélites artificiais". Tese (Doutorado), Instituto tecnológico de aeronáutica, São José dos Campos.

[11] Osório, J. P., 1973, "Perturbações de órbitas de satélites no estudo do campo gravitacional terrestre". Porto: Imprensa Portuguesa.

[12] Rossi, A, 2008, "Resonant dynamics of medium earth orbits: space debris issues", Celestial Mechanics and Dynamical. Astronomy, Vol. 100, p. 267-286.

[13] Tapley, B. D., Watkins, M. M., Ries, J. C., Davis, G. W., Eanes, R. J., et alz, 1996, "The Joint Gravity Model 3", Journal of Geophysical Research, Vol. 101, No. B12, p. 28029-28050.

[14] Vilhena de Moraes, R., Silva, P. A. F., 1990, "Influence of the resonance in gravity- gradient stabilized satellite". Celestial Mechanics and Dynamical Astronomy, Vol. 47, p. 225-243.

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