Orbital equations are straightforward and deterministic, I am wondering why an AI would be needed for this? You could solve explicitly.
The reason planet nine is suspected to exist is due to the commonalities in the orbits of trans-neptunian objects. That is, there appears to be a large gravitational influence on TNOs that causes the distribution of their orbits to exhibit irregularities that don't make sense with only two factors influencing their orbits.
If you went to college when I did, first of all, you're eligible to join the AARP, and second, the problems that you studied were overwhelmingly solved in closed form. This was true in math as well, both in college and at the K-12 level.
Now, are ML algorithms worth adding to our tool belt of numerical methods? Oh, probably. When the fad is over, some useful applications will remain. We already use regression a lot, and that's a primitive form of ML.