Great comment! I've been trying to understand it more and was hoping to find more people discussing the result, or the implications of the result, and this was the missing piece for me after watching a few videos.

Here's the paper about the blowup for the gravitating bodies: https://www.jstor.org/stable/2946572?origin=crossref

There's a Wiki article about it: https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture