Can you do the same for three bodies? Mathematically, it's a much more difficult problem, which is surprising. As the article says, Euler made some progress. Personally, I was unaware that any further advancements had been made. I just figured it was one of those intractable things and that was that.
And four bodies, five bodies, etc.? Fuggedaboudit.
Check out the wiki article.
Pretty exciting.
Thank you for clearing that up somewhat. I will research now that my curiosity has been peeked.
It might be more accurate to say that Newton placed a theoretical foundation under Kepler's solution. (Though Kepler thought planets orbited the sun, not the center of mass of the sun-planet system. Thanks for clearing that up, Isaac.)
It is also inaccurate to say that Newton did not solve the three (or many body) problem. The answer today is the same as it was in Newton's day, as my Gujarati Calculus professor would say, "Integrate, only." It's like Woody said about Buzz Lightyear, "That's not flying, that's falling with style." Same thing, these are not closed from solutions, they're integrating with style.