Although science is based on the premise such a truth exist in regard to reality. Aka what we call realism in ontology. So i think we can see science as a subset of philosophy in that sens.

However i don't think science is just about facts, it's also about understanding them to a point we can predict them. That's what we call theory or model. Hence the distinction between experimental and theoretical science.

So what i really meant by truth is what we think is the true theories to explain phenomenons.

That's why i said we adapt our beliefs to proof. We don't know if a model is correct or not, and we say we believe it's true if there is enough evidence.

However, what allows us to change our mind is the fact that we can't never be 100% sure if something is true. Leaving always a possibility to correct our belief if new proof is found.

(This idea to use probability for our beliefs is based on Bayesian epistemology.)

...

For your exemple, Greeks already had pretty good geometrical knowledge, Ptolemy created this idea of epicyclic trajectories to explain geocentrism. Which is what the model of Copernicus would have resulted in earth's frame of reference.

(Of course Greek's models were not as good as Copernicus, mostly because of their obsession with finding mathematics in the universe.)

What made Galileo say his observations proved heliocentrism, and so Copernicus, is the movement of other stars around Jupiter.

But dispite being close, Copernicus model didn't actually worked, and so neither did Ptolemy's idea of epicycle, because they had circular trajectories.

It was Kepler, based on the observations of Tycho Brahe, who created a model that actually worked using elliptical trajectories, later formalize by Newton.

(Einstein later explained how frames of reference are all physically equal. Making geocentric frame of reference not technically wrong.)

Just to end on your last point, what i mix up isn't science with philosophy but rather scientists. Scientists are the one that needs philosophy, they are the one concerned by moral decisions, not science itself. That's an important distinction in most context...