In November 1915, Einstein completed a calculation whose result so agitated him that he worried that he might be having a heart attack. He later wrote to a friend that “for several days I was beside myself in joyous excitement.” What Einstein calculated was the contribution to the advance of the perihelion of Mercury from the first post-Newtonian corrections to Newtonian gravity provided by his newly completed theory of general relativity. This had been a notorious and unsolved problem in astronomy, ever since Le Verrier pointed out in 1859 that there was a discrepancy of approximately 43 arcseconds per century in the rate of advance between what was observed and what could be accounted for in Newtonian theory from planetary perturbations (refer to Secs. 3.1 and 3.4). Many earlier attempts to devise relativistic theories of gravity, including Einstein's own “Entwurf” (outline) theory of 1913 with Marcel Grossmann, had failed to give the correct answer. Now armed with the correct field equations, Einstein found an approximate vacuum solution that could be applied to the geodesic motion of Mercury around the Sun. He found that the orbit was almost Keplerian, but with a perihelion that advances at a rate that matched Le Verrier's observations.

For Einstein, this success with Mercury was the first concrete evidence that his theory, over which he had struggled so mightily for the past four years, might actually be correct.