Any number of sources put the peg the Sun at approximately 99.8% of the total Solar System mass.
If one were to consider any interaction of the Sun with a body exhibiting gravity perhaps several orders of magnitude higher, could the Solar System be assumed to be concentrated in the Sun?
In other words, how much would planetary movement in orbit around Sol be relevant to any interaction of Sol, and another body where the other body is (potentially) several orders more massive than Sol?
p.s. The context for the other body being more massive is available in the original question on Space SE (in case it is relevant/required for an answer here)