I think the inertia question would affect the velocity of the ghost relative to the rest of the planet. But unless the ghost has the necessary movement powers to maintain their position, I have to think the earth’s path versus the ghost’s straight line through space would diverge pretty quickly.

Interesting to think about, especially in light of the other reply discussing the hypothetical of ghosts being able to choose & switch frames of reference.

Honestly though, since just about everything is affected by the way gravity bends spacetime, including light, I bet they’d stay with the earth. Maybe just have to hover above the surface in order to not fall down to the core of the planet.