Abstract
We have seen the complexity of the problem when more than two gravitating masses are involved. We have seen two methods of determining the orbits, Cowell’s and Encke’s methods . Now, let us look at the basic mathematical description of the perturbation problem.
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Battin, R.: An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics, New York (1999)
Brouwer, D., Clemence, G.M.: Methods of Celestial Mechanics. Academic Press, New York (1961)
Brown, E.W.: An Introductory Treatise on the Lunar Theory. The University Press, Cambridge (1896)
Carpenter, L.: Planetary perturbations in Chebyshev series. Tech. Rep. NASA TN D-3168, National Aeronautics and Space Administration, Washington, DC (1966)
Cook, A.H.: The contribution of observations of satellites to the determination of the Earth’s gravitational potential. Space Sci. Rev. 2, 355–437 (1963)
Cook, G.E.: Satellite drag coefficients. Planet. Space Sci. 13 (10), 929–946 (1965)
Efroimsky, M.: Equations for the orbital elements. hidden symmetry. Preprint No 1844 of the Institute of Mathematics and its Applications, University of Minnesota (http://www.ima.umn.edu/preprints/feb02/1844.pdf) (2002)
Efroimsky, M., Goldreich, P.: Gauge symmetry of the n-body problem in the Hamilton-Jacobi approach. J. Math. Phys. 44, 5958–5977 (2003)
Efroimsky, M., Goldreich, P.: Gauge freedom in the n-body problem of celestial mechanics. Astron. Astrophys. 415, 1187–1199 (2004)
Fukushima, T., Arakida, H.: Long-term integration error of Kustaanheimo-Stiefel regularized orbital motion. Astron. J. 120 (6), 3333–3339 (2000)
Fuller, J.D., Tolson, R.H.: Improved method for the estimation of spacecraft free-molecular aerodynamic properties. J. Spacecr. Rocket. 46 (5), 938–948 (2009)
Gutzwiller, M.C., Schmidt, D.S.: The motion of the Moon as computed by the method of Hill, Brown, and Eckert. Astron. Papers Part I 23, 1–272 (1986)
Hagihara, Y.: Stability in celestial mechanics. Scr. Metall. 1 (1957)
Hagihara, Y.: Celestial Mechanics, vol. II. Perturbation Theory. MIT Press, Cambridge (1972)
Hobson, E.W.: The Theory of Spherical and Ellipsoidal Harmonics. Chelsea Publishing, New York (1965)
Junkins, J.L., Singla, P.: How nonlinear is it? a tutorial on nonlinearity of orbit and attitude dynamics. J. Astronaut. Sci. 52 (1 and 2), 7–60 (2004)
King-Hele, D.G.: The effect of the Earth’s oblateness on the orbit of a near satellite. Proc. R. Soc. Lond. Sei. A Math. Phys. Sci. 247 (1248), 49–72 (1958)
Kustaanheimo, P., Stiefel, E.: Perturbation theory of Kepler motion based on spinor regularization. J. Reine. Angew. Math. 218, 204 (1965)
Laskar, J.: Chaotic diffusion in the solar system. Icarus 196 (1), 1–15 (2008)
Laskar, J., Fienga, A., Gastineau, M., Manche, H.: La2010: a new orbital solution for the long-term motion of the Earth. Astron. Astrophys. 532, A89 (2011)
Liu, L., Zhao, D.: Combined perturbation on near-Earth satellite orbits. Chin. Astron. Astrophys. 5, 422–433 (1981)
Marcos, F.A.: Accuracy of atmospheric drag models at low satellite altitudes. Adv. Space Res. 10 (3), 417–422 (1990)
McCuskey, S.W.: Introduction to Celestial Mechanics. Addison-Wesley, Reading (1963)
Moe, K., Moe, M.M., Wallace, S.D.: Improved satellite drag coefficient calculations from orbital measurements of energy accommodation. J. Spacecr. Rocket. 35 (3), 266–272 (1998)
Newman, W., Efroimsky, M.: The method of variation of constants and multiple time scales in orbital mechanics. Chaos 13, 476–485 (2003)
Prieto, D.M., Graziano, B.P., Roberts, P.C.E.: Spacecraft drag modelling. Prog. Aerosp. Sci. 64, 56–65 (2014)
Sharma, R.K., Raj, M.X.J.: Long-term orbit computations with KS uniformly regular canonical elements with oblateness. Earth Moon Planet. 42, 163–178 (1988)
Sharma, R.K., Raj, M.X.J.: Contraction of near-Earth satellite orbits using uniformly regular KS canonical elements in an oblate atmosphere with density scale height variation with altitude. Planet. Space Sci. 57, 34–41 (2009)
Smart, W.M.: Celestial Mechanics. Longmans, London (1960)
Stiefel, E., Scheifele, G.: Linear and Regular Celestial Mechanics. Springer, Berlin, Heidelberg, New York (1971)
Stone, W.C., Witzgall, C.: Evaluation of aerodynamic drag and torque for external tanks in low Earth orbit. J. Res. Natl. Inst. Stand. Technol. 111 (2), 143 (2006)
Storz, M.F., Bowman, B.R., Branson, M.J.I., Casali, S.J., Tobiska, W.K.: High accuracy satellite drag model (HASDM). Adv. Space Res. 36 (12), 2497–2505 (2005)
Sutton, E.K.: Normalized force coefficients for satellites with elongated shapes. J. Spacecr. Rocket. 46 (1), 112–116 (2009)
Fredo, R.M., Kaplan, M.H.: Procedure for obtaining aerodynamic properties of spacecraft. J. Spacecr. Rocket. 18 (4), 367–373 (1981)
Vallado, D.: Fundamentals of Astrodynamics and Applications, 2nd edn. Microcosm Press and Kluwer Academic Publishers, El Segundo (2001)
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Gurfil, P., Seidelmann, P.K. (2016). General Perturbations 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_11
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