An elementary approach to simulating the perihelion of Mercury

Abstract

The relativistic correction to the precession of the perihelion of Mercury provided key evidence for the accuracy of general relativity as a theory of gravity. This example still has a large amount of potential to introduce students to the power of numerical simulations in theoretical physics, but existing approaches may be too detailed for many students and involve them beginning to learn a programming language at the same time. In this article, we take a simpler approach which uses as little coding as possible. The equation for the orbit of a planet is solved with and without relativistic corrections. It is shown that there is precession of the perihelion in the relativistic case, whereas in the Newtonian case, the orbit does not rotate about the origin. Quantitative information is extracted on the precession of the perihelion of Mercury and shown to match with observations.