Radial Velocities and the Curvature of Space-time

Abstract

RETURNING to my letter on this subject published in NATURE of April 26, p. 602, I should like, in the first place, to amend an erroneous formula given in the last section of that letter. Through a bad slip of the pen, the earth's velocity component V was subtracted from v₀, the star's integration constant, instead of being deduced from the whole effect cD which, to a high degree of approximation, represents the total radial velocity of the star relatively to the sun at the moment of observation. Ultimately, the correct formula, readily obtainable by applying a local Lorentz transformation to the observer's world-line and confounding a factor I+v₀V/c² with unity, is, instead of (3), p. 603, Here D is the effect as observed from a terrestrial station. In fine, the usual formula for “the reduction to sun” is, apart from immeasurably small terms, the correct one. Thus also the equality c(D₁–D₂)=V₂–V₁ should hold not only for R = but also for any finite value of the radius, and it can be considered as sufficiently verified by numerous previous spectrograms.