A calculation of perihelion precession is presented that utilizes a phase-plane analysis of the general relativistic equations of motion. The equations of motion are reviewed in addition to the phase-plane analysis required for the calculation. “Exact” phase planes for orbital dynamics in the Schwarzschild geometry are discussed, and bifurcations are identified as a dimensionless parameter involving the angular momentum is varied.
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Using x rather than for the horizontal axis pushes the singularity at to infinity. As a result, the relative locations of fixed points are more easily scaled and plotted in the phase plane.
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Also termed homoclinic orbit in the literature on nonlinear analysis.
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