How did science make it possible for us to learn these facts about Earth?For most of human history, scholars assumed Earth was the...

Science made the knowledge that you describe possible in
two ways.

First and foremost, science is a way of
thinking.  It is based on observation rather than on theories.  It is based on looking
at the evidence and trying to create theories that fit that evidence.  This is in
contrast to older ways in which theories were held to be true and evidence to the
contrary was ignored or explained away (as in the attempts of ancient thinkers to
explain the fact that the movement of the planets did not fit with the idea that they
orbited the Earth).  When people started to think scientifically, they started paying
more attention to what they observed and that eventually led to them realizing that the
Earth orbited the Sun.

Second, science is about technology
that allows measurement and observation.  Technology allowed the heliocentric theory to
be confirmed.  This is because Galileo's creation of a good telescope allowed him to
accurately observe and track the movements of various heavenly
bodies.

So science allowed us to learn these things because
it created the tools and (just as importantly) the way of thinking that allowed for
these discoveries.