The correct answer is D) stay in the same position. When a vessel rolls to the starboard side with no movable or moving weights onboard, the center of gravity will remain in the same position. This is because the center of gravity is a fixed point determined by the distribution of the vessel's mass, and it does not change unless the weight distribution changes. Without any shifting weights, the center of gravity will not move to port, starboard, or down, but will stay in its original position. The other options are incorrect because the center of gravity does not shift in response to the vessel's rolling motion alone, as long as the weight distribution remains constant.