Earlier quoted context omitted.
Empirically? One suspects a different adverb would have been more correct in that sentence.
Do you contend that human beings have not empirically measured the spherical, or roughly spherical shape of the Earth?
When you build a runway for a plane or a long bridge, you do.
A model is not necessarily useful in all contexts. People still use the flat earth model in useful ways because it's simpler to assume the earth is flat in some situations. Of course, once you go beyond the capabilities of the flat earth model your numbers will wildly diverge into the realm of useless while the round or spherical models provide useful numbers for longer.