The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge–Lenz vector. First, this method is applied to give a derivation of these General Relativity effects for the case of the spherically symmetric Schwarzschild geometry. Then the lowest order correction due to an angular momentum of the central body is considered. The results obtained are well known, but the method used is rather more efficient than that found in the standard texts, and it provides a good occasion to use the Runge–Lenz vector beyond its standard applications in Newtonian physics.
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PAPERS| April 01 1999
Light bending and perihelion precession: A unified approach
Dieter R. Brill;
Dieter R. Brill, Deepak Goel; Light bending and perihelion precession: A unified approach. Am. J. Phys. 1 April 1999; 67 (4): 316–319. https://doi.org/10.1119/1.19255
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