A method of obtaining the rate of perihelion precession in a system of two charged masses

It is shown in this paper that the angular rate of perihelion precession of a spinless charged body, boson or planet, moving around a massive charged source can be described by the Klein-Gordon equation with gravitational and electromagnetic fields, and further that this general relativistic motion can be solved fairly simply in a system of coordinates rotating at certain angular velocities of perihelion precession characteristic of the state of the system. At these rates of rotation, the problem is reduced to that of solving a Schroedinger equation with potential inversely proportional to the radius, and another equation which determines the characteristic rate of perihelion precession. Applied to the case of a pair of rotating charged bosons of zero spin, the resulting fine structure agrees with the known fine-structure levels of this problem. Applied to the motion of Mercury around the Sun, the first-order calculation gives a rate of perihelion precession of 42.98 sec arc/century. The effect of possible electrical charges of Mercury and the Sun on the perihelion precession are considered from which it is concluded that these effects need not be considered in the test of general relativity based on Mercury's perihelion precession. (u.K.)