Counter-Earth

[6] In Philolaus' system, the Earth and Counter-Earth revolved around the unseen Central Fire every 24 hours, while the Moon's revolution was monthly, and the Sun's yearly.

[7] 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.

[6][11][12] However, Burch believes Aristotle was having a joke "at the expense of Pythagorean number theory,"[6] and that the true purpose of the Counter-Earth was to "balance" Philolaus' cosmos—balance being needed because without a counter there would be only one dense, massive object in the system—Earth.

[6] In the 1st century AD, after the idea of a spherical Earth had gained more general acceptance, Pomponius Mela, a Latin cosmographer, developed an updated version of the idea, wherein a spherical Earth must have a more or less balanced distribution of land and water, even though all known continents were in the northern hemisphere.

Mela drew a map which postulated a continental landmass in the unknown, southern half of Earth—the antipodes—below the equator and the tropics, climes which he believed uninhabitable and impassably hot.

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.

[3] The 1968 Scientific Study of Unidentified Flying Objects headed by Edward Condon at the University of Colorado even included a "Numerical Experiment on the Possible Existence of an 'Anti-Earth'" as an appendix.

Even if the Sun blocked its view from Earth, a Counter-Earth would have gravitational influence (perturbation) upon the other planets, comets and man-made probes of the Solar System.

[16] A Counter-Earth would also eventually be visible from Earth because the gravitational forces of the other planets on it would make its own orbit unstable.

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. [ 1 ]
Diagram of modern conception of the Counter-Earth, a planet in the same orbit as the Earth, but 180° out of phase
A contour plot of the effective potential due to gravity and the centrifugal force of a two-body system in a rotating frame of reference. (In the context of this article the two bodies are the Sun—the yellow body—and Earth—the dark body between L1 and L2. The Counter-Earth would exist at L3.) The arrows indicate the gradients of the potential around the five Lagrange points —downhill toward them ( red ) or away from them ( blue ). Counterintuitively, the L 4 and L 5 points are the high points of the potential. At the points themselves these forces are balanced.