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Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 436))

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Abstract

Semianalytical theories provide tools for propagating perturbed satellite orbits. The power of these theories lies in the ability to efficiently calculate, and thereby comprehend, the orbital dynamics of satellites. In many cases of practical interest, as we will see in Chap. 14, satellite orbit control laws also utilize mean orbital elements. The mean elements are most commonly defined as doubly-averaged elements, obtained from a doubly-averaged Hamiltonian. However, the mean elements in the current chapter will be singly-averaged elements, obtained by removing the short-periodic oscillations only.

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References

  • Battin, R.: An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics, Reston (1999)

    Book  MATH  Google Scholar 

  • Belyanin, S., Gurfil, P.: Semianalytical study of geosynchronous orbits about a precessing oblate Earth under lunisolar gravitation and tesseral resonance. J. Astronaut. Sci. 57 (3), 517–543 (2009)

    Article  ADS  Google Scholar 

  • Bezdek, A., Vokrouhlickı, D.: Semianalytic theory of motion for close-Earth spherical satellites including drag and gravitational perturbations. Planet. Space Sci. 52 (14), 1233–1249 (2004)

    Article  ADS  Google Scholar 

  • Breiter, S., Metris, G.: Keplerian expansions in terms of Henrard’s practical variables. Celest. Mech. Dyn. Astron. 58 (3), 237–244 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Broucke, R.A.: Numerical integration of periodic orbits in the main problem of artificial satellite theory. Celest. Mech. Dyn. Astron. 58 (2), 99–123 (1994). DOI 10.1007/BF00695787

    Article  ADS  MathSciNet  Google Scholar 

  • Brouwer, D.: Solution of the problem of artificial satellite theory without drag. Astron. J. 64, 378–396 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  • Brouwer, D., Clemence, G.M.: Methods of Celestial Mechanics. Academic Press, New York (1961)

    MATH  Google Scholar 

  • Brouwer, D., Hori, G.I.: Theoretical evaluation of atmospheric drag effects in the motion of an artificial satellite. Astron. J. 66, 193–225 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  • Cefola, P., McClain, W., Early, L., Green, A.: A semianalytical satellite theory for weak time-dependent perturbations. In: Flight Mechanics/Estimation Theory Symposium, vol. 1, pp. 67–91 (1980)

    ADS  Google Scholar 

  • Coffey, S.L., Deprit, A., Miller, B.R.: The critical inclination in artificial satellite theory. Celest. Mech. Dyn. Astron. 39 (4), 365–406 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Coffey, S.L., Deprit, A., Deprit, E.: Frozen orbits for satellites close to an Earth-like planet. Celest. Mech. Dyn. Astron. 59 (1), 37–72 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Cutting, E., Frautnick, J., Born, G.: Orbit analysis for SEASAT-A. J. Astronaut. Sci. 26, 315–342 (1978)

    ADS  Google Scholar 

  • Danielson, D.A., Sagovac, C.P., Neta, B., Early, L.W.: Semianalytic satellite theory. Tech. rep., DTIC Document (1995)

    Google Scholar 

  • Deprit, A.: The elimination of the parallax in satellite theory. Celest. Mech. 24 (2), 111–153 (1981)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Gedeon, G.: Tesseral resonance effects on satellite orbits. Celest. Mech. 1, 167–189 (1969)

    Article  ADS  MATH  Google Scholar 

  • Gurfil, P., Lara, M.: Motion near frozen orbits as a means for mitigating satellite relative drift. Celest. Mech. Dyn. Astron. 116 (3), 213–227 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  • Hoots, F.R.: Theory of the motion of an artificial earth satellite. Celest. Mech. Dyn. Astron. 23 (4), 307–363 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • Kamel, A.: Perturbation theory based on Lie transforms and its application to the stability of motion near sun-perturbed Earth-moon triangular libration points. NASA CR-1622 (1970)

    Google Scholar 

  • Kamel, A., Tibbitts, R.: Some useful results on initial node location for near-equatorial circular satellite orbits. Celest. Mech. 8, 45–73 (1973)

    Article  ADS  MATH  Google Scholar 

  • Kamel, A., Ekman, D., Tibbitts, R.: East-west stationkeeping requirements of nearly synchronous satellites due to Earth’s triaxiality and lunisolar effects. Celest. Mech. 8, 129–148 (1973)

    Article  ADS  Google Scholar 

  • Kaula, W.M.: Theory of Satellite Geodesy. Blaisdell Publishing Company, Waltham, Massachusetts (1966). Reprinted by Dover Publications, Mineola (2000)

    Google Scholar 

  • Kechichian, J.A.: The analysis of the relative motion in general elliptic orbit with respect to a dragging and precessing coordinate frame. In: Proceedings of the AAS/AIAA Astrodynamics Conference, Sun Valley, ID, pp 2053–2074 (1997)

    Google Scholar 

  • Kozai, Y.: The motion of a close Earth satellite. Astron. J. 64, 367–377 (1959a)

    Article  ADS  MathSciNet  Google Scholar 

  • Kozai, Y.: On the effects of the Sun and the Moon upon the motion of a close Earth satellite. SAO Spec. Rep. 22 (2), 356–366 (1959b)

    ADS  Google Scholar 

  • Lane, M.H.: The development of an artificial satellite theory using a power-law atmospheric density representation. In: AIAA Second Aerospace Sciences Meeting, New York, NY, USA, AIAA Paper 65-35 (1965)

    Google Scholar 

  • Lane, M.H., Fitzpatrick, P.M., Murphy, J.J.: On the representation of air density in satellite deceleration equations by power functions with integral exponents. Tech. rep., DTIC, Report No. APGC-TDR-62-15 (1962)

    Google Scholar 

  • Lara, M.: Searching for repeating ground track orbits: A systematic approach. J. Astronaut. Sci. 47 (3-4), 177–188 (1999)

    Google Scholar 

  • Lara, M., Deprit, A., Elipe, A.: Numerical continuation of families of frozen orbits in the zonal problem of artificial satellite theory. Celest. Mech. Dyn. Astron. 62 (2), 167–181 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Lin, L., De-zi, Z.: Combined perturbation on near-Earth satellite orbits. Chin. Astron. Astrophys. 5 (4), 422–433 (1981)

    Article  ADS  Google Scholar 

  • Liu, J.J.F.: Advances in orbit theory for an artificial satellite with drag. J. Astronaut. Sci. 31 (2), 165–188 (1983)

    ADS  MathSciNet  Google Scholar 

  • Liu, J.J.F., Alford, R.L.: A semi-analytic theory for the motion of a close-Earth artificial satellite with drag. In: AIAA, Aerospace Sciences Meeting, New Orleans, LA, USA, AIAA Paper 79-0123 (1979)

    Google Scholar 

  • Liu, J.J.F., Alford, R.L.: Semianalytic theory for a close-Earth artificial satellite. J. Guid. Control Dyn. 3 (4), 304–311 (1980)

    Article  ADS  Google Scholar 

  • Rosborough, G.W., Ocampo, C.: Influence of higher degree zonals on the frozen orbit geometry. In: Kaufman, B., Alfriend, K.T., Roehrich, R.L., Dasenbrock, R.R. (eds.) Astrodynamics 1991, American Astronautical Society, Univelt, Inc., USA, Advances in the Astronautical Sciences, vol. 76, pp. 1291–1304 (1992)

    Google Scholar 

  • Seidelmann, P.K.: Explanatory Supplement to the Astronomical Almanac. University Science Books, Washington, DC (1992)

    Google Scholar 

  • Shapiro, B.E.: Phase plane analysis and observed frozen orbit for the Topex/Poseidon mission. Adv. Astronaut. Sci. 91, 853–872 (1995)

    Google Scholar 

  • Taylor, S.P., Cefola, P.J.: Semianalytical satellite theory and sequential estimation, vol. 46, p. 702 (1982)

    Google Scholar 

  • Vallado, D.: Fundamentals of Astrodynamics and Applications, 2nd edn. Microcosm Press and Kluwer Academic Publishers, London (2001)

    MATH  Google Scholar 

  • Zeis, E., Cefola, P.: Computerized algebraic utilities for the construction of nonsingular satellite theories. J. Guid. Control Dyn. 3 (1), 48–54 (1980)

    Article  ADS  MATH  Google Scholar 

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Gurfil, P., Seidelmann, P.K. (2016). Semianalytical Orbit Theory. In: Celestial Mechanics and Astrodynamics: Theory and Practice. Astrophysics and Space Science Library, vol 436. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-50370-6_13

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  • DOI: https://doi.org/10.1007/978-3-662-50370-6_13

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