Speaker: P.W. Sharp, Department of Mathematics, University of Auckland
Title: Accurate N-body simulations of the Solar System
Gravitational N-body simulations are used extensively to study the dynamics of the Solar System. Many of these simulations have five massive bodies representing the Sun, Jupiter, Saturn, Uranus and Neptune, and a large number of test particles representing asteroids and other small bodies that are assumed too small to affect the orbital motion of one another and the massive bodies. The simulations typically involve long intervals of integration and the removal of test particles through collisions with the massive bodies or ejection from the Solar System.
The numerical method used to perform such a simulation is almost always a low-order symplectic integrator with a large stepsize, or a high-order non-symplectic integrator with a sufficiently small stepsize that close to maximum accuracy is obtained. The non-interactiveness of the test particles means the simulations are easily parallelised with either type of integrator and hence a large number of test particles is readily handled if enough processors are available. However, the quest for maximum accuracy presents many challenges. I will describe these challenges and present new algorithms for achieving maximum accuracy or close to it.