I don't see this in other comment responses, but it seemed obvious to me: A better grasp of and getting closer to understanding fundamental physics?

Possibly also a better ability to read messages sent from the Heavens? Comparisons between the motions of celestial versus earthly bodies? Perhaps even insights as to how to imbue earthly objects with some celestial motion properties, so as to gain better control on the motion of objects in various other domains (e.g. ballistics, architecture, navigation)? If what moves the celestial objects can be harnessed, perhaps a new type of vessel that could travel through the land, air or aethers?

All of these are things that, if I put myself in the frame of mind of a 17th-cent' philosopher / scholar, would be very pertinent and seem like intuitively obvious possibilities as to what might come from studying the properties and regularities of Celestial Things. And I didn't even have to think about it for more than five minutes. They were fiddling with no actual answers and no high school astrophysics for lifetimes, or large parts thereof.