Thank you for your detailed explanation. And I'm sorry for arguing, maybe I'm still misunderstanding something.
I think we can both agree on this: "Every body in the universe attracts the other body with a force that is proportional to product of their masses and inversely proportional to square of distance between them."
It seems that we only disagree on how to interpret that. But I feel as though I need to ask: What do you believe would happen if you chose to move the Sun in a direction that would bring it closer to the Earth? If gravity attracts objects, then how would it repel the Earth away from the Sun's advance?
But either way, I think once the human race gets out there into space then we won't really need our home star for survival anymore. Maybe another question is how will we escape the Universe when time slows down in the big freeze?