Abstract
After an introduction, the principle of the derivations of the geopotential perturbations on an Earth satellite will be discussed first. Then the disturbed basic Lagrangian equations of satellite motion and the simplifying algorithms are outlined. The orbit solutions disturbed by the geopotential are derived up to 8 × 8 orders and degrees, which are sufficient and necessary for orbit determination of satellites similar to that of GPS.
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References
Battin R.H. (1999) An Introduction to the Mathematics and Methods of Astrodynamics, revised version, AIAA Education Series
Boccaletti D & Pucacco G, 2001, Theory of Oribts, Vol. 1: Integrable systems and non-perturbative methods; Vol. 2: Perturbative and geometrical methods, Springer Berlin
Bronstein IN, Semendjajew KA (1987) Taschenbuch der Mathematik. B.G. Teubner Verlagsgesellschaft, Leipzig, Germany. ISBN 3-322-00259-4
Brouwer D, Clemence GM (1961) Methods of celestial mechanics. Academic Press, New York
Chobotov VA (ed) (1991) Orbital mechanics. AIAA, Washington, D.C.
Cui C (1990) Die Bewegung künstlicher Satelliten im anisotropen Gravitationsfeld einer gleichmässig rotierenden starren Modellerde. Deutsche Geodätische Kommission, Reihe C: Dissertationen, Heft Nr 357
Desmars J, Arlot S, Arlot JE, Lainey V, Vienne A, 2009, Estimating the accuracy of satellite ephemrides using the bootstrap method, Astronomy & Astrophysics, Vol. 499 No.1
Eberle J, Cuntz M, Musielak ZE (2008) The instability trasition for the restricted 3-body problem - I. Theoretical approach, Astronomy & Astrophysics, Vol. 489 No.3
Herrick S (1972) Astrodynamics, vol II. Van Nostrand Reinhold, London
Kaula WM (1966) 2001) Theory of satellite geodesy. Blaisdell Publishing Company, Dover Publications, New York
Kudryavtsev SM (2007) Long-term harmonic development of lunar ephemeris, Astronomy & Astrophysics, vol 472 No.2King RW, Masters EG, Rizos C, Stolz A, Collins J (1987) Surveying with Global Positioning System. Dümmler-Verlag, Bonn
Licandro J, Alvarenz-Candal A, Leon Jde, Pinilla-Aloso N, Lazzaro D, Hampins H, 2008, Spectral properties of asteroids in cometary orbits, Astronomy & Astrophysics, Vol. 481 No.3
Lynden-Bell D, 2009, Analytical orbits in any central potential, MNRAS Vol. 402 Issue 3 (p1937-1941)Li H, Xu G, Xue H, Zhao H, Chen J,Wang G (1999) Design of GPS application program. Science Press, Peking, 337pp. ISBN 7-03-007204-9/TP.1049 (in Chinese and in C)
Meeus J (1992) Astronomische Algorithmen. Johann Ambrosius Barth
Montenbruck O, Gill E (2000) Satellite Orbits: Models. Methods and Applications, Springer-Heidelberg
Mysen E, 2009, On the predictability of unstable satellite motion around elongated elestial bodies, Astronomy & Astrophysics, Vol. 506 No.2
Pal A, 2009, An analytical solution for Kepler’s problem, MNRAS Vol. 396 Issue 3 (p1737-1742)
Schneider M, Cui CF (2005) Theoreme über Bewegungsintegrale und ihre Anwendung in Bahntheorien, Bayerischen Akad Wiss, Reihe A, Heft Nr. 121, 132pp, München
Seeber G (2003) Satellite Geodesy: Foundations, Methods, and Applications. Walter de Gruyter, Berlin, 589pp
Torge W (1991) Geodesy. Walter de Gruyter, Berlin
Vallado David A, 2007, Fundamentals of Astrodynamics and Applications (3rd Ed), Microcosm Press & Springer
Van Kamp PD (1967) Principles of Astronomy. W.H. Freemann and Company, San Francisco, CA/London
Wang LX, Fang ZD, Zhang MY, Lin GB, Gu LK, Zhong TD, Yang XA, She DP, Luo ZH, Xiao BQ, Chai H, Lin DX (1979) Mathematic handbook. Educational Press, Peking, ISBN 13012–0165
Xu, G. (2008): Orbits, Springer Heidelberg, ISBN 978-3-540-78521-7, 230 pages, in English
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Xu, G., Xu, J. (2013). Solutions of Geopotential Perturbations. In: Orbits. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32793-3_6
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DOI: https://doi.org/10.1007/978-3-642-32793-3_6
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