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If such a planet actually existed in our current scientific cosmology, as a spherical world that revolved around the sun, it would be permanently hidden behind the sun but nevertheless 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.
Since Earth has an elliptical orbit and 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. Further, 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.