Sommerfeld's and Einstein's Precession of Perihelia

The problem of explaining the precession of the perihelion for planet Mercury has not been solved by any theory, Sommerfeld’s, Newton’s, or Einstein’s. Sommerfeld’s analysis of atomic orbits, so successful in explaining atomic orbits, fails when applied to planetary orbits. Nevertheless, if application of Sommerfeld’s analysis to explaining planetary orbits is correct, one must conclude that planetary orbits do precess by significant amounts which must be accounted for. The orbital speed causes precession of perihelia by an amount not incorporated in Newtonian and Einstein analysis. This page sets forth the issues and insights raised by applying Sommerfeld’s method to the precession of perihelia in the Solar system, and the orbital speed and barycentric effects. Einstein’s method depends on a simplified version of his theory of general relativity, the application of Sommerfeld’s method, depends on parameters of a precessing ellipse, The computed difference between Sommerfeld’s and Einstein’s methods, and the incorporation of orbital speed for explaining the precession of perihelia, is determinative of the validity of Newton’s and Einstein’s theories. A planet’s first barycenter distance is determined more accurately by the Sun-planet 2-body system and a second barycenter distance is determined least accurately by the n-body Solar system. Neither system has any effect on a planet’s, orbit speed and precession.