Common wisdom holds that, in order for a terrestrial planet to have life, it's helpful to have a Jupiter-like planet in the system to shield against inbound comets. How well does Jupiter do that really? Common wisdom held until recently that it would be an impossible for an icy object like Ceres to exist within the inner Solar System. From where did the ice come? Common wisdom held until recently that the Centaur asteroids and Kuiper Belt objects were dynamically distinct. Are they?
Much of our understanding of the dynamical structure of the Solar System stems from long-term computational simulations of planet and planetesimal evolution--simulations that model orbital evolution over millions, even billions, of years. We first describe a multistep scheme that achieves the theoretical lower bounds for the propagation of error over long simulations intervals, and one that integrates close encounters very accurately. We then present a summary of our investigation into three different early Solar System scenarios: whether Jupiter protected Earth from impacts in the early Solar System, the icy nature of Ceres, and the interrelation between Centaur Asteroids and the Kuiper Scattered Disk.