Speaker: Wayne Hayes
Computer Science Department
University of California at Irvine
Title: The Interplay of Chaos Between the Inner and Outer Solar System
Abstract: We report on some simple experiments on the nature of chaos in our Solar System. We make the following interesting observations. First, we look at the system of Sun + 4 Jovian planets as an isolated 5-body system interacting only via Newtonian gravity. We find that if we measure the Lyapunov time of this system across thousands of initial conditions all within observational uncertainty, then the value of the Lyapunov time seems relatively smooth across some regions of initial condition space, while in other regions it fluctuates wildly on scales as small as we can reliably measure using numerical methods. This probably indicates a fractal structure of Lyapunov exponents measured across initial condition space. Then, we add the 4 inner terrestrial planets and several post-Newtonian corrections such as General Relativity into the model. In this more realistic Sun + 8-planet system, we find that the above structure of chaos for the outer planets becomes uniformly chaotic for almost all planets and almost all initial conditions, with a Lyapunov timescale of about 5--20 million years. This seems to indicate that the addition of the inner planets adds more chaos to the system. Finally, we show that if we instead remove the outer planets and look at the isolated 5-body system of the Sun + 4 terrestrial planets, then the terrestrial planets alone show no evidence of chaos at all, over a large range of initial conditions inside the observational error volume. We thus conclude that the uniformity of chaos in the outer planets comes not from the inner planets themselves, but from the interplay between the outer and inner ones. Interestingly, however, there exist rare and isolated initial conditions for which one individual outer planetary orbit may appear integrable over a 200 million year timescale, while all the other planets simultaneously appear chaotic.
Bio: Wayne Hayes received his undergraduate degree in Computer Science and Astrophysics and his M.Sc. and Ph.D. degrees from the Department of Computer Science, all at the University of Toronto. As an undergraduate working with Mart Molle he designed and published an improvement to the Ethernet network protocol that attracted the interest of Cisco Systems, Inc. He spent a year with the IBM optimizing compiler group, a year programming financial risk analysis software at Algorithmics, Inc., and a year at Altera Corporation programming heuristics to solve NP-hard optimization problems in FPGA design and fitting. He was a post-doctoral fellow at the Fields Institute for Research in Mathematical Sciences, and spent a summer studying protein folding at the Samuel Lunenfeld Research Institute. He was a Research Associate at the Institute for Physical Science and Technology at the University of Maryland, College Park, where he worked under Japan Prize winner James Yorke and collaborated with members of The Institute for Genome Research (TIGR) and The Baylor College of Medicine to advance the art of genome sequence assembly. He is currently an Assistant Professor of Computer Science at the University of California at Irvine.