By "Is the sun anchored" I am referring to its place relative to the planets. I am pretty sure the answer is yes, as the planets also exert a gravitational force upon the sun (Newton's third law). This would cause the sun to "move" somewhat, no matter how small the force exerted. Then again, I may be completely wrong. I think my general statement is right because I performed a few experiments online with a similar solar-system like structure. All feedback appreciated, Thanks!