Two objects following the same orbit will be exactly on opposite sides of the sun at two (symmetric) places. All the rest of the time, the straight line connecting the two orbiting objects will not go through the center of the sun also. If the line misses the center of the sun by far enough, then observers on the two objects could see each other. This is the case with Earth's orbit. The other planet would not remain hidden at all times.
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Carolyn say: Heard this one before, your dad did not invent this theory but maybe heard it online. Its along the same lines as the planet x stuff created by a nut job called Zeta, a woman who says she channels an alien to speak through her. She is complete bs. Anyway, how can your dad "believe" this theory when there is absolutely no evidence for it that he can see himself, but only a story he can hear second-hand? What you CAN see for yourself is that the earth appears to have no curvature and space is not what we at are told.
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poldi say: No, it is not possible.
None of the planets orbit the sun in perfect circles, they are all ellipses.
That means at times other planets are closer to Earth than others, and those tiny perturbations (by Venus, Mars, and Jupiter) cause the Earth's orbit to constantly change.
A planet orbiting the sun on the other side of our orbit would very quickly end up in a slightly different orbit than ours.
And that other planet would affect Venus and Mars so that we would see the effects on their orbits and could easily determine the reason.
It was an average Outer Limits episode and a bad sci-fi movie in the 70's but that's all the idea is good for.
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Donut Tim say: No, it would not be possible and yes, we have proof.
Such a configuration would be extremely unstable. The two planets would come within sight of each other in less than one year and within a couple centuries would interact violently, likely ejecting at least one of them out of the "goldilocks zone" if not out of the solar system entirely. At best, the orbit of the remaining one would be far too eccentric for life as we know it.
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