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The celestial mechanics problems that have been completely solved are very limited and don't represent the system as a whole. Lately computer modelling is giving some pictures of entire systems of good complexity. They throw in everything they can think of, but are they getting all the parameters?. It's similar to the problem of trying to model earth's and other planets' and stars' climates. You can get some results and maybe some inspiration, but really the technology of computer modelling is just in its infancy. How do planetary orbits circularize? Where do galactic spiral arms come from and how do they move? I don't know if there is an employed, working scientist who will say it is definitely this or that. We don't even know if spiral arms move clockwise or CCW. We don't even know they aren't a total artifact of stellar evolution rather than orbital mechanics. Of course, we haven't left our front porch yet, either, so we can't be expected to actually know anything.

Yeah, we know enough to get Voyager to go past Neptune, but that may be the basics. Do rotating bodies affect time and space around them differently than non-rotating bodies? I think studies of our satellites a few years ago proved that earth's rotation did have some kind of effect on space that Einstein predicted.