Introduction

In the last few years, the subject of dynamical planetary formation has undergone a remarkable transformation. Thus we now have an increasing database of actual observed systems which provides much material for theoretical and numerical work. It therefore seems appropriate to devote a small chapter to direct N-body simulations of planetary systems. The emphasis in the early days was on performing idealized calculations to ascertain whether the eccentricity growth due to weak perturbations could lead to significant accretion by collisions. With the increase of computing power, more realistic modelling has become feasible by direct methods, but powerful tree codes are an attractive alternative. The latter technique has proved effective for studying both planetesimal systems and planetary rings. Following the discovery of many extra-solar systems, the question of stability has become topical. Stability is often addressed using symplectic integrators which are outside the main scope of this book. In the following we distinguish between planetary formation and planetesimal dynamics. This division is somewhat arbitrary but planetesimal simulations are usually concerned with particles distributed in a thin annulus which therefore represents larger systems.

Planetary formation

Although there are early integrations of planetary dynamics relating to Bode's Law [Hills, 1970], it took another decade for the subject proper to get under way.