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Planetary perturbation equations based on relativistic Keplerian motion

Published online by Cambridge University Press:  04 August 2017

Neil Ashby
Neil Ashby*
Affiliation:
Department of Physics, Campus Box 390, University of Colorado Boulder, Colorado, USA 80309

Abstract

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Solutions of the geodesic equations for bound test particle motion in a Schwarzschild field are expressed using Jacobian elliptic functions. Keplerian orbital elements are identified and related to a set of canonical constants. Relativistic Lagrange planetary perturbation equations are derived.

Type
Dynamical Effects in General Relativity
Information
Symposium - International Astronomical Union , Volume 114: Relativity in Celestial Mechanics and Astrometry , 1986 , pp. 41 - 52
Copyright
Copyright © Reidel 1986 

References

1. Fitzpatrick, P.M., Principles of Celestial Mechanics, Academic Press (New York, 1970), p. 174.Google Scholar
2. Hagihara, , Jap. Jour. Astr. and Geophys. 8, 67 (1931).Google Scholar
3. Sudarshan, E. C. G. and Mukunda, N., Classical Dynamics: A Modern Perspective, Wiley-Interscience, (New York, 1974), Ch. 8.Google Scholar
4. Weber, J., General Relativity and Gravitational Waves, Interscience, (New York, 1961).Google Scholar
5. Fock, V., The Theory of Space, Time, and Gravitation, Second Revised Edition, Pergamon Press, (Oxford, 1966).Google Scholar
6. Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, U. S. Govt. Printing Office, Washington, D.C., 20402, (1964), Ch. 17.Google Scholar
7. Cayley, A., An Elementary Treatise on Elliptic Functions, (1876), reprinted by Dover Publications, (New York, 1961).Google Scholar
8. Ashby, N., “Relativistic Kepler Problem and Construction of a Local Inertial Frame,” Contract Report NB80RAA02404, Time and Frequency Division, National Bureau of Standards, (Sept. 1980).Google Scholar