Precession of the Orbit of Mercury

Abstract

The influence of the planets of the Solar System on the precession of the orbit of Mercury is investigated in the framework of classical mechanics. The influence of each planet on the motion of Mercury is calculated in the context of a restricted problem of three bodies: the Sun, the planet in question, and Mercury. It is demonstrated that the average shift of the perihelion of the orbit of Mercury determined in the context of a planar circular restricted three-body problem is 556.5″ per century and agrees with the observed shift (570″) with a relative accuracy of 2.5%. It is also demonstrated that the observed perihelion shift of Mercury features oscillatory components with a total amplitude up to 20″ and periods from several years to several decades. Owing to the presence of these components, the perihelion shift rate calculated based on observations conducted for several tens or even hundreds of years may differ considerably from the true average rate. This is likely the reason why the calculated average perihelion shift rate is not completely consistent with observational data.