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Jupiter and the Sun orbit a point located outside of the Sun. Using your definition would this make Jupiter a double planet with the Sun? A double star, and thus not a planet?

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Since the Sun isn't a planet, it shouldn't change anything for those.

For a more apt example: In a billion years when the moon's orbit has expanded an additional ~118,000 km it would suddenly stop being a moon?

The problem with barycenter is it is equally changed by distance as it is mass ratio.

I don't disagree with your point but it's an issue that plagues definitions in general. If something is "near" and slowly backs away, at some point it becomes "far," but there's no clear dividing point. On the other hand, according to law and custom, someone does suddenly stop being a minor when they become a legal adult. In that case we choose a clear arbitrary cutoff for simplicity's sake. A third type of definitional change is one where there is a clear non-arbitrary cutoff, e.g. a star turning into a black hole, or an irregularly shaped asteroid accreting enough matter through collisions to turn into a dwarf planet. Arguably, the barycenter moving from within one planet to outside of it would constitute this third type of change. So I think if two former planet/moon objects evolve to orbiting around an external barycenter, it's not arbitrary to state that the less massive no longer a moon of the other, even if, at some point in the past it was, and in the case of our Moon, will likely be again.

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