Why did all the ancient philosophers seem so fascinated by astronomy? Their interest in math and "physics" is understandable, as math can be seen as very similar to certain branches of philosophy in that it is not the study of a particular existence, but, rather, the study of "existence," and physics is the study of the seemingly occult laws that govern everything, which is also very similar to philosophy in a sense, but astronomy is just the extrapolation of those two fields on "arbitrarily chosen" pieces of mass. Math, and even physics to a large extent, are "implicit" (for lack of better term) to existence, while astronomy is wholly explicit.

You are completely right to notice the early absorption with astronomy. I have heard people say “Greek philosophy began on May 28, 585 BC, at 6:13 in the evening” – because of astronomy. Thales, who is often called the first Greek philosopher, predicted a solar eclipse that we now know to have taken place on that date. Not only did Thales thereby establish the credentials of philosophers as “ones who know” by being able to predict a coming natural event; he also thereby proved a point about the natural world that encapsulates early philosophy’s turn away from religion. If astonishing events like solar eclipses are not the capricious actions of mysterious gods but rather quite regular events in the natural world, then the world can be adequately studied through rational methods and without dependence on old stories handed down about divine action. Mind you, this is only one way to understand the earliest philosophers. My point is that interest in astronomy is part of this picture and even one of the...