On Philolaus' astronomy

In Philolaus' cosmology, the earth revolves around a central fire along with the other heavenly bodies, including a planet called the counter-earth which orbits below the earth. His theory can account for most astronomical phenomena. A common criticism of his theory since ancient times is that his counter-earth does no work in the system. Yet ancient sources say the planet was supposed to account for some lunar eclipses. A reconstruction of Philolaus' cosmology shows how lunar eclipses occurring at certain times of day cannot be explained by earth blocking the sun's light. The counter-earth could explain these eclipses.