Solar Motion and Lunar Eclipses in Philolaus’ Cosmological System

Appendix: Short Remarks on Solar Eclipses and the Alleged Role of the Counter-Earth in Lunar Eclipses

The error in the representation of eclipses of the Moon in the Philolaic system, described in the previous section, does not occur in the case of eclipses of the Sun. In solar eclipses, the Sun eclipses from its West side (as seen from the Earth), while the Sun’s East side is the last to be eclipsed.^[45] This is not only the case in the heliocentric and geocentric systems, but also in the Philolaic system, because in the latter system the Moon moves faster from West to East than the Sun.

A final remark on the alleged role of the Counter-Earth in causing lunar eclipses. According to Aëtius, in what is obviously an interpretation of Aristotle’s words, in the Philolaic system lunar eclipses are not only caused by the Earth’s shadow, but additionally by that of the Counter-Earth.^[46] Whether this is the right interpretation of Aristotle’s confused text will be the subject of a broader study of Philolaus’ cosmology.^[47] Dicks insists that it is impossible for the Counter-Earth to cause lunar eclipses, “since the orbit of the Moon is outside the Earth’s, while that of the Counter-Earth is inside it (i.e., nearest the Central Fire)”.^[48] I do not understand exactly what Dicks means, but he seems to assume that the Counter-Earth is always exactly between the Earth and the Central Fire, revolving counter-clockwise around the Central Fire in one day. Here it suffices to say that the only way the Counter-Earth can be supposed to cause eclipses of the moon is when it is aligned with the Moon and the Central Fire, but the Earth is not.^[49] However, even then, the shadow of the Counter-Earth would approach the Moon from the wrong side, just like the Earth’s shadow, as demonstrated in the previous section. Graham is the only one to suggest an irregular movement of the Counter-Earth: “(…) it moves independently of the Earth so that it can be wherever it needs to be to block the Sun’s light just when an (…) eclipse occurs.” Just before this quote, Graham suggests, with a question mark: “does it move opposite the Earth in direction?”, thus assuming that the Counter-Earth moves from East to West, contrary to all other celestial bodies.^[50] In that case, the Moon would be eclipsed by the shadow of the Counter-Earth from the correct side, but the Moon would have to move extremely slowly in order to be able to account for long-lasting eclipses. Moreover, if the shadow of the Earth in the Philolaic system is not able to rightly explain lunar eclipses, then the Counter-Earth remains as the only candidate left to explain all lunar eclipses correctly. This conflicts with the generally and also by Graham accepted interpretation of Aëtius’ and Aristotle’s texts, which say that the Counter-Earth additionally explains some lunar eclipses.