What is the anti-Earth? Counter-Earth? Does it really exist?

  The Pythagorean philosopher Philolaus taught in the second half of the 5th Century before Christ, it's a "central fire" admit that forms the center of gravity and the universe. All things would be attracted to this center and all heavenly bodies revolved around it. At the innermost orbit around the central fire revolves the supposed counter-earth. This is followed by (from inside to outside) Earth, Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn, and quite outside the sphere of fixed stars. In its orbit around the central fire which (as a flat imaginary) earth rotation has a bound, so they turn to the central fire always the same page. The central fire is for the people to always "down" and invisible, as the inhabited side of the planet is always facing away from the central fire. The counter-earth was introduced by Philolaus from balancing reasons as a counterweight to the earth. This had the following background: the Greek philosophers imagined the planet as "light, ethereal" objects before. The earth, however consisted of earth and water and was undoubtedly a "heavier" body.  If the Earth orbited the only major celestial bodies, the central fire, so the focus of the universe would no longer central. Since this is the point, however, to whom everything revolves, required Philolaus' model, a second body of this earth caused by the imbalance balanced: the counter-earth.