If one were to arbitrarily put multiple planets in orbit around a star, one might find the system to be dynamically unstable: the orbits would deviate exponentially from their original paths on time scales of a few orbital periods. Real planetary systems, which have survived for at least millions of orbits, are not dynamically unstable. On these long time scales, a planet behaves as if its mass were spread around its orbit, like an elliptical ring around the star. These rings pull on each other gravitationally, causing slow changes in their shapes and orientations, which may lead to so-called secular instability or secular chaos. The Principal Investigator and collaborators on this project plan to develop a complete theory of secular instability, using analytic techniques as well as computer simulations of interacting elliptical rings and direct N-body simulations. Their goal is to determine whether secular instability and secular chaos can quantitatively explain and predict (1) the long-term orbital evolution of the Inner Planets, (2) the distribution of orbital properties and masses of "hot Jupiter" exoplanets, and (3) the properties of exoplanet systems in general. In particular, they aim to determine whether secular chaos is a viable alternative to disk-driven migration for the formation of hot Jupiters which may be able also to account for the wide distribution of orbital inclinations with respect to the stellar equator. They will make quantitative predictions for the eccentricities and spacings of extrasolar planets, and build an understanding of how observations of exoplanet systems can be used to constrain planet formation physics. The project will support and train one postdoctoral researcher and two undergraduate summer students, and the Principal Investigator will give public presentations on the results of the work.