Einstein and the Perihelion Motion of Mercury

TL;DR

This paper discusses Einstein's historical efforts to explain Mercury's perihelion motion, highlighting the development of general relativity and its success in accounting for the observed anomaly.

Contribution

It provides a detailed analysis of Einstein's early calculations and the evolution of his theory leading to the complete explanation of Mercury's perihelion precession.

Findings

Einstein's 1913 theory explained 18 of 43 arcseconds per century.

In 1915, Einstein's new theory accounted for all 43 arcseconds.

The paper includes annotated transcriptions of key historical manuscripts.

Abstract

On November 23, 2021, the Einstein-Besso manuscript on the perihelion motion of Mercury will be auctioned at Christie's. Expected to fetch around $3M, it promises to be the most expensive scientific manuscript ever sold at auction. In this preprint, we present the parts of our forthcoming book, How Einstein Found His Field Equations. Sources and Interpretation (Springer, 2021) dealing with Einstein's attempts, in 1913 and in 1915, to account for the anomalous advance of Mercury's perihelion. In 1913, as documented in the Einstein-Besso manuscript, Einstein and his friend Michele Besso found that the Einstein-Grossmann or Entwurf (= outline or draft) theory, a preliminary version of general relativity, could only account for 18 of the 43 seconds-of-arc-per-century discrepancy between Newtonian theory and observation. In November 1915, however, putting the techniques developed in his collaboration with Besso to good use, Einstein showed that his new general theory of relativity could account for all missing 43 seconds of arc. After a brief introduction, we provide an annotated transcription of the key pages of the Einstein-Besso manuscript and an annotated new translation of the November 1915 perihelion paper.