Let's revisit Comins' "Dopple World". Last May, astronomers lost patience trying to find any.
Many factors keep Dopple from forming in practice. Moving Jovians early in the system's formation might perturb one but not the other. For Earth, resonance with Venus would have done for a Dopple before it started. (Theia was never a Dopple; our own Moving Jovian brought it in from on up.)
Although Lagrange doesn't care if Dopple World exists, the worlds care. When a large mass comes in and out of focus, it raises tides. The planets we've found tend Neptunian so are presumed squishy. Laplace found that tides can stabilise orbits, as around Jupiter - and beyond. But that's when there are three or more orbiters around... Jupiter, or a sun. Absent a family of stabilisers, one or the other Dopple World will do a not!Theia or just get yeeted.
Lagrange's minimum is 24.96 times the subplanet; I don't know that our observations suffice to find, say, 0.0123 times the main planet (like our own Moon) in a Libration halo. Especially if the larger planet is not tidal, or perhaps negligibly tidal.
Sean Raymond envisioned creating a full Dopple system. I allow these could counteract one anothers' tides. This can only work with a LOT of space in between the mutual Lagrange points, such that the tides are Lunar-level. And Raymond's system is a megastructure - if we find one, we must assume Larry Niven has been there.
JANUS 5/16/23: Raymond has abandoned his Dopple notion but now asks after horseshoe orbits, like Cruithne I guess. They might be stable if of similar mass. I still don't know about tides however.
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