Abstract

In spite of a rich and interesting history over the last 400 years or so, the general three-body problem in Newtonian gravity remains unsolved. The reason for this is chaos. But what is chaos, and why is it such a challenge to address in modern physics research? Ironically, it was chaos that made finding an analytic solution such a headache in the first place, and it is chaos that is presently impeding the advancement of our understanding of basic dynamics problems whenever using numerical simulations to perform the experiments. After reviewing the basic principles of a chaotic dynamical system, I will explain why this is the case using examples from the gravitational three- and four-body problems. If there is time, I will review what we know regarding binarity in galactic nuclei, and also present a project on cirbumbinary disk evolution in triple star systems and the three- and four-body problems in AGN disks.