On the Determination of Planetary Distances in the Copernican System

On the Determination of Planetary Distances in the Ptolemaic System

“…It is difficult to acknowledge that such well-informed scholars ignored Goldstein's translation of Planetary Hypotheses. It is true that van Helden's book (1985), which devoted an entire chapter to Ptolemy's methods, was published almost at the end of the debate and later than the majority of the contribution-except that of Petroni and Scolamiero (1986) and the last reply of Hutchinson (1990); but Otto Neugebauer (1975, 917-922) developed the topic (in the very work that was quoted by Hutchison as his source for the non-triangulation method), 2 as did also Olaf Pedersen (1974,(391)(392)(393)(394)(395)(396)(397), not to mention Kuhn's brief reference in The Copernican Revolution, already noted. Maybe, therefore, one could argue that Ptolemy's nested sphere model was neglected in the 1980s debate, not because it was unknown but because it was judged to be irrelevant: the core issue was whether the relative distances of the planets from the centre (either of the earth, for Ptolemy, or of the sun, for Copernicus) could be calculated with astronomical observations using only the intrinsic geometrical structure of the theories in question.…”