2009 PIMS-CSC Seminar - 07

The stability of our Solar System has been debated since Newton devised the laws of gravitation to explain planetary motion. Newton himself doubted the long-term stability of the Solar System, and the question has remained unanswered despite centuries of intense study by generations of illustrious names such as Laplace, Langrange, Gauss, and Poincare. Finally, in the 1990s, with the advent of computers fast enough to accurately integrate the equations of motion of the planets for billions of years, the question has finally been settled: for the next 5 billion years, and barring interlopers, the shapes of the planetary orbits will remain roughly as they are now. This is called "practical stability": none of the known planets will collide with each other, fall into the Sun, or be ejected from the Solar System, for the next 5 billion years. Although the Solar System is now known to be practically stable, it may still be "chaotic". This means that we might---or might not---be able to precisely predict positions of the planets within their orbits, for the next 5 billion years. The precise positions of the planets can effect the tilt of each planet's axis, and so can have a measurable effect on the climate. For the past 15 years, there has been some debate about whether the Solar System exhibits chaos or not: when performing accurate integrations of the planetary motions, some astronomers observe chaos, and some do not. This is particularly disturbing because it is known that inaccurate integration can inject chaos into a numerical solution that would otherwise be stable. In this talk I will demonstrate how I closed that 15-year debate on chaos in the solar system by performing the most carefully justified high precision integrations of the orbits of the outer planets that has ever been done. The answer surprised even the astronomical community, and was published in _Nature Physics_. I will also show lots of pretty (but as yet unpublished) pictures at the end, demonstrating the fractal nature of the boundary between chaos and regularity in the Outer Solar System.