Ole Rømer, the speed of light, the apparent period of Io, the Doppler effect, and the dynamics of Earth and Jupiter
Ole Rømer's (1676) method of using variations in the apparent period of Jupiter's moon, Io, to demonstrate that the speed of light is finite made use of what we would today call a ``Doppler'' method. He did this 166 years before Christian Doppler described what we now call the Doppler effect and the mechanism in 1842. Although the method Rømer conceived is unquestionably valid, his original and only paper on the subject left out much of the detail necessary to determine whether his measurements were adequate to the task of demonstrating the effect he claimed to have observed. Unfortunately, the timekeeping available to Rømer and his colleagues Picard and Cassini, each of whom made some of the observations involved, was, at best, not quite up to the task of measuring the necessary times with sufficient accuracy. Mathematical analysis of the dynamics of the Earth/Jupiter synodic system allows a more thorough analysis of Rømer's work than has previously been made. Rømer's case was built on four ``observations,'' one of which clearly failed, one of which was successful, and two of which were quite questionable.