Hodographs of the Gravitational Two-Body System and Discrepancies between Newtonian Laws of Equivalent Kepler Orbits and General Relativity

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References

[1] C. P. Viazminsky and P. Vizminiska, “On the Gravitational Two-Body System and an Infinite Set of Laplace-Runge-Lenz Vectors,” Applied Mathematics, Vol. 4, No. 5, 2013, pp. 774-784.

[2] A. Alemi, “Laplace-Runge-Lenz Vector,” 2009. www.cds.Caltech.edu/Wiki/Alemicds205final.pdf

[3] E. L. Butikov, “The Velocity Hodograph for Arbitrary Keplerian Motion,” European Journal of Physics, Vol. 21, No. 4, 2000, pp. 1-6.

[4] Wikipedia, “Laplace-Runge-Lenz Vector,” 2013.

http://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector

[5] W. R. Hamilton, “The Hodograph or a New Method of Expressing in Symbolic Language the Newtonian Law of Attraction,” Proceedings of the Royal Irish Academy, Vol. 3, 1847, pp. 344-353.

[6] W. R. Hamilton, “Applications of Quaternions to Some Dynamical Questions,” Proceedings of the Royal Irish Academy, Vol. 3, Appendix III, 1847, p. xxxvi-1.

[7] S. W. Groesberg, “Advanced Mechanics,” John Wiley & Sons, Inc., Hopoken, 1998.

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[9] S. R. Spiegel, “Theoretical Mechanics,” Schaum Outline Series, McGraw Hill Book Company, New York, 1967.

[10] W. Rindler, “Essential Relativity,” Springr-Verlag, Berlin, 2006.

[11] F. D. Lawden, “Tensor Calculus and Relativity,” Chapman and Hall, London, 1975.

[12] L. D. Landau and E. M. Lifshitz, “The Classical Theory of Fields,” Pergamon International Library, Pergamon, 1980.

[13] http://en.wikipedia.org/wiki/Equivalence_principle

[14] A. Einstein, “Relativity, the Special and General Theory,” Henry Holt and Company, New York, 1920.

[15] C. Pollock. http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf

[16] L. P. Eisenhart, “Riemannian Geometry,” Princeton University Press, Princeton, 1968.