Vol.:(0123456789) 1 3 Rendiconti Lincei. Scienze Fisiche e Naturali https://doi.org/10.1007/s12210-022-01061-0 RESEARCH PAPER Philolaus’mysterious astronomical system Lucio Russo 1 Received: 17 December 2021 / Accepted: 10 February 2022 © The Author(s), under exclusive licence to Accademia Nazionale dei Lincei 2022 Abstract It is argued that the mysterious astronomical system traditionally attributed to Philolaus is in fact the result of a misunderstanding. Keywords Ancient astronomy · Philolaus · Pythagorean school 1 The astronomical system attributed to Philolaus Philolaus, contemporary of Socrates and teacher of Archy- tas, is one of the main exponents of the Pythagorean school. Today few remember him, but the early modern age scien- tists had in great consideration his contribution to astron- omy. Copernicus, in the dedicating letter of De revolutioni- bus orbium caelestium, cites Philolaus among the ancient scientists who suggested him to attribute motions to the Earth. Both Galileo and Newton quote him (erroneously) as an assertor of heliocentrism. 1 The inverse square law, play- ing an essential role in Newton’s theory of universal gravita- tion, appears for the frst time in the Astronomia Philolaica: the work in which Ismaël Boulliau believed to have recon- structed the astronomical theory of Philolaus. 2 According to the astronomical theory traditionally attributed to Philolaus (see, for example, Hufman 1993, pp. 231–288, Hufman 2008, 2013) at the center of the uni- verse there is a fre (having nothing to do with the Sun, just one of the bodies revolving around this center). The Earth generates the alternation of day and night through a circu- lar motion around the central fre. In its motion, the Earth always turns the same face, opposite to the inhabited one, towards the fre, which is therefore always invisible to us. Around the same fre move in a circle not only the Moon, the planets and the Sun, but also (on an orbit of a smaller radius of that of the Earth) the Counter-Earth (Ἀντίχθων), that is a body similar to the Earth but always on the opposite side of it with respect to the central fre, and hence being always invisible. This theory has always appeared strange because almost completely unrelated to observable phenomena. The motion of the Earth, like the actual motion of the Moon around the Earth, consists of a rotation and a revolution with exactly the same period (of one day). To explain the alternation of night and day, however, only the rotation is sufcient and the revolution is therefore completely unmotivated. Burch, who thinks that Philolaus believed in the Earth fatness, associates the useless motion of revolution to this fatness (Burch 1954, p. 276), but does not explain why, whence this association appears unjustifed. The central fre not only is not directly visible but does not generate any observable efect; it is strange, in particular, that the phases of the Moon, already explained by Parme- nides through the light coming from the Sun, are in any way not infuenced by the light necessarily coming from the central fre. 3 Its introduction seems to be motivated only by aprioristic considerations, metaphysical or religious, which may suggest the idea of associating to the center of the uni- verse, as the noblest place, the noblest element, namely fre. 4 The invisible Counter-Earth has no observable efects as the central fre and we do not even understand the aprior- istic reasons that could have led Philolaus to introduce it. Burch assumed that the Counter-Earth had the purpose of * Lucio Russo russo@mat.uniroma2.it 1 Dipartimento di Matematica, Università Tor Vergata di Roma, Rome, Italy 1 G. Galilei, lettera a Cristina di Lorena; I. Newton, De mundi syste- mate liber, 1. 2 I. Boulliau, Astronomia Philolaica, Piget, Parisis, 1645. 3 The absence of lighting efects by the central fre was noted by Gra- ham. 4 This argument is referred to by Aristotle in the passage given below as testimony H.