Could there be another planet in Earth's exact orbit, but behind the Sun?

The Ancient Greeks proposed just such a 'counter-Earth' , but there is no such object.

We know how gravity works in the solar system. There is no way that a counter-Earth would remain exactly behind the Sun while being constantly perturbed by the other planets. Eventually it would end up on a slightly different orbit by a few miles, and the synchrony would vanish. It would slowly slide out from behind the Sun and would have been observed over the millennia as a new planet.

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