Suppose that, for whatever reason, neither Copernicus nor anyone else had discovered the heliocentric model, and cosmology remained stuck in the geocentric model. ("For whatever reason" could mean that the Church violently and successfully suppressed this line of research; funding for astronomy dried up; scientists just lost interest & worked on other fields; etc.).
However, suppose that all other fields of science, technology, engineering, and invention proceeded apace.
Which technologies/inventions of our modern world could exist even if people still thought the Sun revolved around the Earth, and which couldn't?
I'm assuming, for example, that space probes sent to other planets wouldn't exist; you couldn't properly calculate the trajectory based on a fundamental misunderstanding of cosmology. But could you have artificial satellites in Earth orbit? Travel to the Moon?
And what about non-obviously-space-related inventions? Do you need heliocentric cosmology to invent/design the steam engine? The cotton gin? The automobile? The airplane? Antibiotics? Skyscrapers? The nuclear bomb? The IBM PC? The Internet? The iPhone? Or could most/all of these exist even if everyone mistakenly believed the Earth was the center of the universe?
What I'm really asking about, I think, is about path-dependence. My instinct is that most if not all modern terrestrial technologies could have been invented with the wrong cosmology, but maybe I'm wrong...?