Sounds like a good fit for probabilistic programming, much like Stuart Russell did here https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be&t=16m40s ht

Sounds like a good fit for probabilistic programming, much like Stuart Russell did here https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be&t=16m40s https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be.... His method could find locations of nuclear tests better than the existing UN system at the time by a lot. His model uses bayesian inference in a stochastic/symbolic/simplified/statistic model of physics (how shockwaves propagate on the surface of the earth). You could do the same here: assuming the relevant laws (kepler? newton law of gravity?), and a prior distribution on the location/mass of your 9th planet, given what we observe for the other planets, what's the posterior distribution on the mass/location of the 9th planet. The statistical model is likely to be small (the Russell statistical model for Nukes fits on one slide). The issue is how to do inference efficiently. Fortunately, probabilistic systems have come a long way and can do these kind of inferences.