Could two planets follow the same orbit and never "see" each other?

Imagine two identical planets planet A and planet B, orbiting the same star.

Is it possible that these two planets follow the exact same "route" as they orbit their sun, but are just distant enough from one another, that their star is effectively always between the two, so that a hypothetical person sitting on planet A would not be able to see planet B due to it being behind the star?

(proportions gloriously inaccurate)

I assumed, based on the limited knowledge I have on the subject, that all star systems have ellipsoidal orbits (the star being in one of the two focal points) just like our own.

If I'm wrong, though, and perhaps a stellar system with circular orbits is possible (and I assume it would make my idea more feasible) please do point it out.

If this is at all possible, what are the "requirements" to make it work?

Note that this doesn't necessarily have to last indefinitely (e.g. maybe the orbit screws itself up after, say, 1000 years)

Also, what is the approximate minimum level of technology that a civilization inhabiting planet A would need to have good chances of finding out about planet B's existence?

posted over 6 years ago

Hankrecords‭

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