I think it's clear that science gets us truth, but that the mechanism for that complex social activity can't be reduced to a few axioms or principles; Feyerabend gives a detailed description [1] of how bad a scientist Galileo was (as judged by modern theories of what science is), yet he was right, and he advanced truth.
Heliocentrism isn't truth, it's opinion [that's my opinion, lol!!]. Einstein's relativity makes heliocentrism false in demanding that there is no aether and so no special points in space.
Science provides our understanding of a best current description of reality - the whole point of scientific endeavour is to demonstrate we were wrong and that our understanding/description was flawed.
Moreover it relies on maths, which is provably unable to verify it's own consistency and completeness.
Furthermore it's an axiomatic system that produces a probabilistic framework that gives us little to hang our conception of reality on [what I'm saying is our perception is not particularly informed by physical reality, we have to subdue our instinctive perceptions to work with what amounts to our best, most consistent, physics view of reality].
Science gives us as much truth as we can see in a well lit test-tube.
Actually GR makes both geocentrism and heliocentrism "true". One is free to pick whatever coordinate system is most convenient to solve a given problem.
What is your view on science, do you think it can create - and verify - a true result? Whither axiomatic underpinning in such a view?