Abstract
Kaula's satellite linear perturbation theory has been extended for the case of highly eccentric orbits by using elliptic function expansions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brumberg E.V.: 1992, ‘Perturbed Two-Body Motion with Elliptic Functions’, in H. Kinoshita and N. Nakai (eds.), Proc. 25th Symposium on Celestial Mechanics, National Astronomical Observatory, Tokyo, 139–155.
Brumberg, E.: 1994, ‘Analytical Perturbation Technique for Highly Eccentric Orbits Based on Elliptic Function Theory’, in K. Kurzyńska, F. Barlier, P.K. Seidelmann, and I. Wytrzyszczak (eds.), Proc. Conf on Dynamics and Astrometry of Natural and Artificial Celestial Bodies, Astronomical Observatory of A. Mickiewicz University, Poznań, Poland, 167–174.
Brumberg, E. and Fukushima, T.: 1994, ‘Expansions of Elliptic Motion Based on Elliptic Function Theory’, Celes. Mech. 60, 69–89.
Brumberg, V.A.: 1967, ‘Development of the Perturbative Function in Satellite Problems’, Bull, ITA 11, 73–83, in Russian.
Brumberg, V. A., Evdokimova, L.S. and Kochina, N.G.: 1971, ‘Analytical Methods for the Orbits of Artificial Satellites of the Moon’, Celes. Mech. 3, 197–221.
Byrd, P.F. and Friedman, M.D.: 1971, Handbook of Elliptic Integrals for Engineers and Scientists, Springer-Verlag, Berlin-Heidelberg-New York.
Deprit, A.: 1979, ‘Note on Lagrange's Inversion Formula’, Celes. Mech. 20, 325–327.
Kaula, W.M.: 1961, ‘Analysis of Gravitational and Geometric Aspects of Geodetic Utilization of Satellites’, Geophys. J. 5, 104–133
Klioner, S.A.: 1992, ‘Some Typical Algorithms of the Perturbation Theory within Mathematica and Their Analysis’, in H. Kinoshita and N. Nakai (eds.), Proc. 25th Symposium on Celestial Mechanics, National Astronomical Observatory, Tokyo, 172–182.
Krasinsky, G.A.: 1973, ‘Method for Calculating the Perturbations of Close Satellites Caused by the Asphericity of the Earth’, Astron. Zh. 50, 1076–1084, in Russian, (English translation: 1974, Sov. Astronomy 17, 680–685).
Sokolsky, A.G., Vakhidov, A.A. and Vasiliev, N.N.: 1995, ‘Computation of Elliptic Hansen Coefficients and Their Derivatives’, Celes. Mech., submitted.
Author information
Authors and Affiliations
Additional information
On leave from Institute of Applied Astronomy, St.-Petersburg
Rights and permissions
About this article
Cite this article
Brumberg, E., Brumberg, V.A., Konrad, T. et al. Analytical linear perturbation theory for highly eccentric satellite orbits. Celestial Mech Dyn Astr 61, 369–387 (1995). https://doi.org/10.1007/BF00049516
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00049516