I was reading this recent article in Forbes about the fact that relativistic problems can't be solved exactly. In it the author makes the argument "the two body problem has an exact solution, so all Newtonian mechanics are easy".
That immediately got me thinking about the three body problem, which then led me to wonder:
- Is the orbital mechanics of three isolated bodies in Newtonian mechanics always chaotic? Have we proved that it either is always chaotic, or that there are definitely non-chaotic cases?
- Even if chaotic, are there cases that are bounded-output stable in the sense that if I had god-like powers I could set up a system with a sun, planet, and moon that would continue orbiting in that relationship forever without ever suffering from a collision or rearranging the relationship (i.e., the planet and moon would continue to orbit one another, even if never quite the same way twice).
- Once I've searched on "orbital mechanics", what additional keywords would I use to research the above topics myself?