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Bill say: It would be possible EXCEPT for the Fact that NASA has Satellites in orbit around the SUN that have looked at the opposite side of Earth's orbit and there is nothing there.
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Guru Hank say: No of course it bloody doesn't. (the orbits would end up chaotic)
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Morningfox say: We have proof. (1) Any planet like that would have a gravity effect on Venus and Mars (and other planets). We don't see any effect like that, so this counter-Earth doesn't exist.
(2) the effect of the gravity of Venus and Mars on this counter-Earth would make the counter-Earth orbit unstable, so that it would not be exactly opposite to Earth after a year or two. So then we would be able to see it.
(3) We have sent space probes, namely the two STEREO coronograph spacecraft, around the sun in 2006. They would have noticed any counter-Earth, but they didn't see anything there.
(4) Even when the counter-Earth was behind the sun, radio astronomers could detect the magnetic field around it. But they don't find it.
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CarolOklaNola say: Yes, the theory does make sense, but there is NO counter earth, and we would KNOW if there Was a counter earth because Earth's orbit is slitghtly elliptical , NOT circular, The MASS of counter Earth would change how the Sun moves and the center of of mass of the ENTIRE Solar System moves. AND the lagrange point 2 is gravitationally unstable./ There is NO counter Earth, We have LOOKED there with satellites and probes MORE than 30 YEARS ago. There i NO counter Earth on the other side of the Sun. Show your father this answer.
BTW, that theory is THOUSANDS of years old. It is NOT original with your father or you.