×

Third-body perturbation in the case of elliptic orbits for the disturbing body. (English) Zbl 1151.70011

Summary: This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed.

MSC:

70M20 Orbital mechanics
70F07 Three-body problems
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] L. Spitzer, “The stability of the 24 hr satellite,” Journal of the British Interplanetary Society, vol. 9, p. 131, 1950.
[2] Y. Kozai, “On the effects of the sun and moon upon the motion of a close earth satellite,” Smithsonian Astrophysical Observatory, 1959, Special Report 22.
[3] P. Musen, “On the long-period lunisolar effect in the motion of the artificial satellite,” Journal of Geophysical Research, vol. 66, pp. 1659-1665, 1961. · Zbl 0105.44403
[4] L. Blitzer, “Lunar-solar perturbations of an earth satellite,” American Journal of Physics, vol. 27, pp. 634-645, 1959. · Zbl 0096.45503
[5] M. M. Moe, “Solar-lunar perturbation of the orbit of an earth satellite,” ARS Journal, vol. 30, p. 485, 1960. · Zbl 0096.38604
[6] G. E. Cook, “Luni-solar perturbations of the orbit of an earth satellite,” The Geophysical Journal of the Royal Astronomical Society, vol. 6, no. 3, pp. 271-291, 1962. · Zbl 0101.42104
[7] W. M. Kaula, “Development of the lunar and solar disturbing functions for a close satellite,” The Astronomical Journal, vol. 67, no. 5, pp. 300-303, 1962.
[8] G. E. O. Giacaglia, “Lunar perturbations of artificial satellites of the earth,” Smithsonian Astrophysical Observatory, p. 59, 1973, Special Report 352. · Zbl 0343.70019
[9] Y. Kozai, “A new method to compute lunisolar perturbations in satellite motions,” Smithsonian Astrophysical Observatory, pp. 1-27, 1973, Special Report 349.
[10] M. E. Hough, “Orbits near critical inclination, including lunisolar perturbations,” Celestial Mechanics and Dynamical Astronomy, vol. 25, no. 2, pp. 111-136, 1981. · Zbl 0471.70014
[11] M. T. Lane, “On analytic modeling of lunar perturbations of artificial satellites of the earth,” Celestial Mechanics and Dynamical Astronomy, vol. 46, no. 4, pp. 287-305, 1989. · Zbl 0682.70025
[12] R. A. Broucke, “The Double Averaging of the Third Body Perturbations,” Texas University, Austin, Tex, USA, 1992.
[13] R. A. Broucke, “Long-term third-body effects via double averaging,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 1, pp. 27-32, 2003.
[14] A. F. B. A. Prado and I. V. Costa, “Third body perturbation in spacecraft trajectory,” in Proceedings of the 49th International Astronautical Congress, Melbourne, Australia, September-October 1998, IAF Paper 98-A.4.05.
[15] I. V. Costa and A. F. B. A. Prado, “Orbital evolution of a satellite perturbed by a third body,” in Advances in Space Dynamics, A. F. B. A. Prado, Ed., pp. 176-194, Instituto Nacional de Pesquisas Espaciais, Sao Paulo, Brazil, 2000.
[16] C. R. H. Sol√≥rzano, Third-body perturbation using a single averaged model, M.S. thesis, National Institute for Space Research (INPE), Sao Paulo, Brazil. · Zbl 1138.93380
[17] A. F. B. A. Prado, “Third-body perturbation in orbits around natural satellites,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 1, pp. 33-40, 2003.
[18] E. P. Aksenov, “The doubly averaged, elliptical, restricted, three-body problem,” Soviet Astronomy, vol. 23, no. 2, pp. 236-240, 1979 (Russian). · Zbl 0424.70011
[19] E. P. Aksenov, “Trajectories in the doubly averaged, elliptical, restricted, three-body problem,” Soviet Astronomy, vol. 23, no. 3, pp. 351-355, 1979 (Russian). · Zbl 0436.70014
[20] M. , “On the double averaged three-body problem,” Celestial Mechanics, vol. 29, no. 3, pp. 295-305, 1983. · Zbl 0518.70009
[21] C. D. Murray and S. F. Dermott, Solar System Dynamics, Cambridge University Press, Cambridge, UK, 1999. · Zbl 0957.70002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.