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Counter-Earth is a non-existent Earth-like hypothetical planet on Earth's orbit but on the other side of the Sun.
It was hypothesized by the Pythagorean school and used by John Norman as the setting for his Gor novels, as well as appearing in multiple Marvel Comics.
A similar concept was used in Gerry Anderson's 1969 movie Journey to the Far Side of the Sun, (also known as Doppelganger), in which the Counter-Earth is identical to Earth in every respect except that left and right are reversed. (But if that were so, then surely the planet would also orbit the sun in the opposite direction and collide with the Earth....)
If such a planet actually existed, it would be permanently hidden behind the sun, but would nevertheless be detectable from Earth because of its gravitational influence upon the other planets of the Solar System. No such influence has been detected, and indeed space probes sent to Venus, Mars and other places could not have successfully flown by or landed on their targets if a Counter-Earth existed, as it was not accounted for in navigational calculation. Furthermore, since Earth has an elliptical orbit its orbital velocity varies slightly; a counter-Earth would have to be in a very precisely tuned orbit to remain behind the Sun at all times.
A counter-Earth's orbit would be unstable on a relatively short geological timescale, and would soon drift away from being exactly opposite Earth's location. This would eventually result in the two planets either colliding or experiencing a near-miss that would eject both of them from their current orbit.
A counter-Earth would not be in the L3 Lagrange point, since Lagrange points require that one of the three masses involved be negligible compared to the other two.
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