Physics World has a somewhat puzzling news article about the solar system:
Physicists have known for some time that the motions of Pluto and the inner planets are chaotic. This means that a small external force on a planet could, over time, cause a major change in the position of the planet within its orbit. Although no planets are likely to collide or be ejected from the Solar System anytime soon, the chaos means that the orbits of these planets cannot be forecasted with any long-term reliability.
Whether the orbits of the gas giants are chaotic, however, is less certain — some computer simulations have found chaos while others have not. One cause of this confusion could be “numerical artefacts” — spurious errors that accumulate, for example, when a computer rounds-off the results of successive calculations.
“What’s puzzling about that?” you say. Well, that’s not the puzzling bit. The puzzling bit is here a little further down:
But according to Hayes the discrepancy is actually a result of the uncertainty in astronomers’ knowledge of the current conditions of the planets, which are used as input to the simulations. Although from observations we know the orbital positions of the gas giants to an accuracy of a few parts in 10 million, even that tiny amount of uncertainty can make the difference between regularity and chaos in a system, he says.
One of the hallmarks of chaos the phrase in the title: sensitive dependence on initial conditions. A tiny change in the initial values of a system lead to a huge change in the position some time down the road.
So, given that, doesn’t it seem like if you ask “Is this orbit chaotic?” and the answer is “I don’t know unless I know the position to better than a part in 107,” that really ought to translate to a “yes?”
(I know, I know, there’s a very formal definition of chaos, in terms of how quickly a two trajectories diverge from one another, and it’s possible to have islands of regularity within great seas of chaos on the phase diagram of a system. Still, I did a double-take when I first saw that description…)