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It sounds like the Repulsor field needs to be somewhere on the board to claim the In-game Objective. You would claim the VP immediately when placing the planet. I would guess this point isn't claimable if you simply move the field from one section of the planet to another.
You mean off the board, I guess, since you confirm that in the last sentence. My guess is that it has to be on the side of the board. It's not quite an achievement just to move it from one spot to another.