The advance of Mercury's perihelion

A very famous ``test'' of the General Theory of Relativity (GTR) is the advance of Mercury's perihelion (and of other planets too). To be more precise, this is not a prediction of General Relativity, since the anomaly was known in the XIXth century, but no consistent explanation had been found yet at the time GTR was elaborated. Einstein came up with a solution to the problem in 1914. In the case of Mercury, the closest planet to the Sun, the effect is more pronounced than for other planets, and observed from Earth; there is an advance of the perihelion of Mercury of about 5550~arc seconds per century (as/cy). Among these, about $5000$ are due to the equinox precession (the precise value is {$5025.645$}~as/cy) and about $500$ ({$531.54$}) to the influence of the external planets. The remaining, about $50$~as/cy ({$42.56$}), are not understood within Newtonian mechanics. Here, we revisit the problem in some detail for a presentation at the undergraduate level.