A simple exact series representation for relativistic perihelion advance

TL;DR

This paper introduces a simple, rapidly converging series formula for calculating the relativistic perihelion advance of Mercury, providing a more elegant and efficient method to verify predictions of General Relativity.

Contribution

It presents a novel, straightforward series representation for relativistic perihelion precession, improving computational simplicity and convergence speed over previous methods.

Findings

Derived a new series for perihelion precession

Series converges very quickly, enhancing computational efficiency

Validates Einstein's predictions with a simple analytical approach

Abstract

The small discrepancy between the observed orbit of Mercury and the orbit predicted by Newtonian gravity was a key test of Einstein's theory, and a dramatic verification of the correctness of General Relativity. This `anomalous precession' of the perihelion is here calculated using a particularly simple method and resulting in a new and elegant series for the precession which converges very quickly.