Pacific Institute for the Mathematical Sciences - PIMS

Is the Outer Solar System Chaotic?

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I will also show lots of pretty (but as yet unpublished) pictures at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.

2:30pm, Rm. 8500, TASC II