The real value of Mercury's perihelion advance

Abstract

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones of general relativity. After the effects of the gravitational perturbations of the other planets have been accounted for, the remaining advance fits accurately to predictions according to the theory of general relativity, that is, 43 arc s per 100 yr. In fact, radar determinations of Mercury's motion since the mid-1960s have produced agreement with general relativity at the level of 0.5%, or to ±0.2arcs per 100 yr. We have recently been puzzled by an apparent uncertainty in the value of the theoretical prediction for the advance within general relativity, as cited in various sources. The origin of this discrepancy is a 1947 article by Clemence1, who used unconventional values for the astronomical unit (A) and the speed of light (c) in his calculation of the predicted advance. Since that time, virtually everyone has followed suit. Although the current value of the prediction, using the best accepted values for the astronomical constants and for the orbital elements of Mercury, is 42.98 arc s per 100 yr, there is a preponderance of citations over the past 25 years of Clemence's value 43.03 arc s per 100 yr. Here we derive the accurate value and uncover the source of Clemence's value.