To needle you slightly further, though, I'd recommend you consider John Snow's investigation into cholera clusters near certain water sources in London: https://en.wikipedia.org/wiki/1854_Broad_Street_cholera_outb...
What should we make of that?
Ok, more generally...
I'm glad you're giving this some thought, because this line of inquiry (or something like it) really affected the way I think about science and knowledge. It's an incredibly rewarding line to go down, though not entirely free of frustrating dead ends.
If you find this stuff interesting, you might want to poke around a bit in 20th century philosophy. There are some (needlessly lengthy) summaries at the Stanford Encyclopedia of Philosophy, esp. under "Logical Empiricism." I hesitate to recommend that, though, it's long on history and short on significant arguments and though-provoking examples.
"Two Dogmas of Empiricism" by Quine profoundly affected the way I think about all of this. It's not an easy piece, I had to read it a few times and kept turning it over in my head for months. At first I thought it was nonsense. Then I thought it was just wrong. Then it sort of wormed its way into my head and changed a few core things I believed about knowledge. Or reorganized them. Karl Popper, Rudolf Carnap, and Wittgenstein all had profound contributions here too.
At the end of Quine's paper he says that White basically said everything important on this already in "The Analytic and the Synthetic: An Untenable Dualism." I haven't read that, but maybe it's the accessible version. One could hope.
http://www.thatmarcusfamily.org/philosophy/Course_Websites/R...
I guess the difference between astronomy and diet is that, in my conception, at least, the systems studied in astronomy tend to be less complex than the human body and, therefore, they can be modeled relatively easily. My hunch is that this has something to do the human body being a self regulating, though climate systems on earth are probably of a similar level of complexity, yet are not self regulating (or at least, not in the same way).
So, the difference in complexity between a astronomical system and the human body would be akin to the difference in complexity between a program which implements some relatively straightforward business logic vs. one that implements a system which can identify and hunt prey. You can probably prove the correctness of most programs which implement basic business logic, but I'm guessing a system which can identify and hunt prey probably cannot be proven to be formally correct. You would need to test it in the real world by tweaking inputs and measuring how it responds.