There's no “two body problem” here, the solar system is an n-body problem.
And the “three-body problem” is overblown in pop culture: even n-body problems are fairly predictable in the short-ish term, it's just that you cannot predict things over a long period because measurement imprecisions have a snowball effect, but it's not particularly unintuitive (I'd say it's more intuitive than the idea that we could predict things with perfect precision over billions of years).
And the “three-body problem” is overblown in pop culture: even n-body problems are fairly predictable in the short-ish term, it's just that you cannot predict things over a long period because measurement imprecisions have a snowball effect, but it's not particularly unintuitive (I'd say it's more intuitive than the idea that we could predict things with perfect precision over billions of years).