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Would it be possible for a planet to have a geometry that allows relatively stable orbits beneath the surface? I understand an artificial object could achieve this just fine, given the technology, but could a naturally formed planet either have the structure to allow for this or be carved out in such a way that it remains stable while allowing this?
By "relatively stable orbit" I don't mean a circular one nor one that doesn't require periodic corrections, simply one that could count as stable enough that a modern satellite could use its thrusters to correct it for its operational lifetime (10-20 years).
Obviously this would require the planet to lack an atmosphere. However, I'm wondering if specifically, an atmosphere-less planet with a vast subterranean cave that spans its underground would allow for this. Would it require rocky columns? If there was no physical connection between the underground and surface would it hold together?