A very simple derivation of the periastron advance to all post-Newtonian orders of perturbation in Schwarzschild geometry

We present an extremely simple derivation of the general relativistic periastron advance for Schwarzschild geometry. The method lends itself to iteration, and so in principle may achieve an arbitrary level of accuracy with relative ease. Our technique involves no analysis of differential equations beyond that of a simple harmonic oscillator. The practical utility of the calculation is limited by its neglect of frame-dragging rotational effects.