Are long-term N-body simulations reliable?
Abstract: Astrophysicists rely on solution for the N-body problem for a myriad of dynamics problems, from those in dark matter dynamics to those in planetary dynamics. Over 50 years ago, Miller found that errors in our simulations of the N-body problem grow exponentially in time. So why should one trust any such simulation over long times? In this talk, I explore a three-body planetary system. The motion over long times can be compared to recent results from Hadden & Lithwich (2018). I find conventional integration methods are as accurate as more sophisticated symplectic methods. In fact, a higher order symplectic method gave unreliable statistics in one test.