Maybe compute the energy of a system, run it for a few years, and see if the delta energy is "within acceptable parameters"? First off is to remember that you want to unit-test, as well as integration test. That means test the integrator with a mock forcing function with closed-form known solution, as well as testing the forcing function against known-good output. Also, for a whole-system test, one common way is to start with a simple system with a known solution. In this case, I'd recommend simulating some two-body problems (including ones with highly elliptical orbits so you get a "slingshot" behavior).