thumb|250px|right|Philolaus believed there was a "Counter-Earth" (Antichthon) orbiting the "Central Fire" (not labeled) that was not visible from Earth. The upper illustration depicts Earth at night while the lower one depicts Earth in the day.
The Counter-Earth is a hypothetical body of the Solar System that orbits on the other side of the Solar System from Earth, e.g. at the L<sub>3</sub> Lagrange point of the Sun–Earth system. A Counter-Earth, or Antichthon (), was hypothesized by the pre-Socratic Greek philosopher Philolaus () to support his non-geocentric cosmology, in which all objects in the universe revolve around a "Central Fire" (unseen from Earth and distinct from the Sun which also revolves around it).
In modern times, a hypothetical planet always on the other side of the Sun from Earth has been called a "Counter-Earth", and has been a recurring theme in UFO claims, philosopher Philolaus. Philolaus' universe moved "the earth from the center of the cosmos", and provided the insight that "the apparent motion of the heavenly bodies" was (in large part) due to "the real motion of the observer"—i.e. Earth. Some (such as astronomer John Louis Emil Dreyer) have thought that Philolaus had it following an orbit such that it was always located between Earth and the Central Fire. However, Burch argues that Philolaus must have thought that it orbited on the other side of the Fire from Earth. Since "counter" means "opposite", and opposite could only be in respect to the Central Fire, it follows that the Counter-Earth must be orbiting 180 degrees from Earth.
According to Aristotle—a critic of the Pythagoreans—the function of the Counter-Earth was to explain "eclipses of the moon and their frequency", which could not be explained by Earth alone blocking the light of the Sun if Earth did not revolve around the Sun. Aristotle suggested that it was also introduced "to raise the number of heavenly bodies around the central fire from nine to ten, which the Pythagoreans regarded as the perfect number".
However, Burch believes that Aristotle was having a joke "at the expense of Pythagorean number theory",
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If there was a single Earth revolving at some distance from the center of space, then the universe's center of gravity, located in the Earth as its only dense body, would not coincide with its spatial center ... The universe, consequently, would be off center, so to speak—lopsided and asymmetric—a notion repugnant to any Greek, and doubly so to a Pythagorean.
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This could be corrected by another body with the same mass as Earth, orbiting the same central point but 180 degrees from Earth—the Counter-Earth.
Modern era
thumb|Diagram of modern conception of the Counter-Earth, a planet in the same orbit as the Earth, but 180° out of phase
Philolaus's ideas were all eventually superseded by the modern realization that a spherical Earth rotating on its own axis was one of several spherical planets following the laws of gravity and revolving around a much larger Sun. The idea of a Counter-Earth waned after the heliocentric model of the solar system became widely accepted from the 16th century. In the contemporary world, "Counter-Earth" usually refers to a hypothetical planet with an orbit as Burch described, on the other side of the "Central Fire"—i.e. the Sun. It cannot be seen from Earth, not because Earth faces away from the center,