Abstract
A modification to the Lindstedt-Poincaré method of strained parameters is applied to the differential equation of the orbit of a test particle in the Schwarzschild exterior metric. A new perturbation solution for the equation of the bound orbit, which is completely free of secular terms in the angular coordinate, is derived. The precession of the orbit per revolution is calculated using this solution and it is found to give a more accurate result than existing perturbation solutions. The method should be applicable to similar orbital problems in general relativity.
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Mason, D.P., Wright, C.J. An improved singular perturbation solution for bound geodesic orbits in the Schwarzschild metric. Gen Relat Gravit 16, 149–159 (1984). https://doi.org/10.1007/BF00762444
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DOI: https://doi.org/10.1007/BF00762444