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It should gain speed until passing the mid-point, and then begin slowing until reaching the other side, and then reverse direction over and over again until the minuscule particles slow the object over time.
Speaking of accelerating objects on the surface of the moon, at a certain speed the surface of the moon would be falling away from the accelerated object faster than the low gravity keep it anchored to the surface. It would be neat to accelerate an object and provide a means of keeping it tethered to the surface, and then release it like a slingshot, allowing it to break free of the moons gravity.
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