According to chaos theory, even the slightest uncertainty in initial conditions can have far-reaching effects on the future state of a physical system. No matter how well we know the starting positions, the end result may be impossible to predict. The classic example is in weather forecasting, where the flap of a butterfly's wing in Brazil, it is said, can result in a storm in China. The case of the solar system would appear to be simpler: after all, the only force acting over these vast distances is gravity and, as Newton showed, the strength of that force is easily worked out for any pair of massive bodies. But when more than two bodies are involved, the picture gets messier.
To tackle what the physicists call the "many-body problem", they've turned to computers. By feeding the positions and speeds of each object into the computer, and simulating the gravitational force acting between them, they can model systems like our solar system over thousands or even millions of years. (You can think of these computer programs as the digital equivalent of the old-style brass orreries, used as educational tools in the 18th century, in which a system of gears drove a tiny model of the solar system.) At first, the forecasts of these computer programs is indeed accurate. Over millions of years, however, those predictions start to fail.
"Even a simple system can have complicated behaviour," says Norm Murray of the Canadian Institute for Theoretical Astrophysics (CITA) in Toronto. For a demonstration, Murray turns to a simple apparatus clamped to his bookshelf. A metal rod swings from a hinge; at the bottom end, a second rod is attached via another hinge - a kind of double-jointed pendulum. When he gives the rods a small push, they swing back and forth. When he gives them a bigger push, however, the interplay between the two rods takes over. The upper one still swings to and fro, but the lower rod is now wildly out of control. Sometimes it seems to stand still; a few seconds later it is spinning around like Roger Daltrey's microphone at a Who concert. This, explains Murray, is the kind of behaviour that shows up with the Sun and panets over many millions of years. "It turns out that our solar system is, in fact, chaotic," he says.
Researchers investigating the long-term motions of the planets have made some surprising discoveries. One of the first bodies they scrutinised was Mars. Like Earth, Mars has an axis of rotation that is tilted with respect to its orbit around the Sun. The rotation axis, however, is not fixed in space; instead, it slowly precedes or progresses, tracing out a cone shape over a period of about 190,000 years. That period is close to several other natural frequencies found in the outer solar system. And this matching of frequencies - what astronomers call a "resonance" - can send a body into chaotic motion.
The motion of Mars "has a coupling to the natural modes of the solar system," explains Jack Wisdom of the Massachusetts Institute of Technology. "The axis of Mars is wildly chaotic on a multi-million-year time-scale." The tilt of a planet's axis is more than just a parameter for astronomers to jot down - it's also the quantity that dictates the seasonal variation in a planet's climate. On Earth, for example, the tilt is 23 degrees; in June, the Earth's northern hemisphere is tipped towards the Sun by this amount; in December, it is tilted in the opposite direction. On Mars, once this chaotic behaviour kicks in - millions of years from now - the axis will wobble between zero and 60 degrees, in a completely unpredictable manner. When that happens, Mars will be headed for some rather severe climatic change.
Could this happen on Earth? Yes, say the researchers, but not until the Earth's precession rate - currently about 26,000 years - slows down enough to resonate with other natural motions within the solar system. Thanks to the moon's influence, the precession rate of the Earth is indeed slowing down. Still, it will be at least a billion years, astronomers say, before the chaotic axis-flipping begins.
More recently, researchers have found that our planet acts as a "big brother" to Mercury and Venus, preventing the tug of these massive outer planets from perturbing their orbits. Kim Innanen, an astrophysicist at York University in Toronto, modelled a hypothetical solar system in which the Earth and its moon were removed; he described the results in an article published in the October issue of the Astronomical Journal. In such a solar system, he writes, the influence of the outer planets "must inevitably lead to a powerful encounter between Venus and Mercury, probably leading to Mercury's eventual ejection". Indeed, even with the protection given by Earth, Mercury's membership of the solar system is by no means permanently guaranteed.
Simulations by Jacques Laskar of the Bureau des Longitudes in Paris have shown that Mercury is the most vulnerable of all the planets. Mercury, he found, has about a one-in-a-thousand chance of being tossed out of the solar system over the next five billion years.
This idea of an ejection - of a planet being flung out from the solar family, never to return - is one of the most thought-provoking in solar-system astronomy. It also raises an intriguing question: could our solar system, at one time, have harboured more than the nine planets we see today? Jack Wisdom calls it a "distinct possibility" - one that is supported by computer simulations of heavily populated solar systems: "If you put, say, 12 planets in the solar system, it's very likely that one will disappear through such an ejection."
And what of the blue-green planet we call home? Astronomers can't rule out Earth's ejection over a multi-billion-year time-scale, but for now at least, the Earth seems to have a fairly stable orbit. "I'm not too worried about any planets in the solar system being ejected any time soon," says CITA's Norm Murray. And as the astronomers remind us, we will have other things to worry about long beforehand. The Sun, for example, will balloon up as it enters its "red giant" phase about five billion years from now, completely frying Mercury, Venus and Earth. In just two or three billion years, the heat from the expanding Sun will trigger a runaway greenhouse effect on Earth, boiling off the oceans and rendering the planet uninhabitable.
The study of chaos in the solar system doesn't end with the planets. Smaller bodies like comets and asteroids also display wildly unpredictable motion over millions of years. One recent investigation looked at comets in the Kuiper belt, a ring of debris in orbit about the Sun, beyond Pluto. Were it not for the massive outer planets, these chunks of rock and ice would most probably make their plodding way around the Sun unimpeded. But thanks to periodic tugs from Neptune and its neighbour planets, some of these bodies are occasionally nudged from their orbits. Sometimes they're flung outwards, escaping from the solar system altogether. Sometimes they're thrown inwards, ending up as short-lived comets - the kind that enter the inner solar system and return every few years or decades (Halley's Comet is an example).
The most detailed study of the Kuiper belt comets was carried out by the Southwest Research Institute in Colorado and by Martin Duncan of Queen's University in Ontario. They found that the giant planets seem to act as a kind of cosmic "bucket brigade", handing these inward-bound comets from one planet to the next. While most short-period comets end up in relatively stable orbits, they can also have more dramatic encounters. Levinson and Duncan calculated that Kuiper belt comets collide with Jupiter once ever 400 years or so, and one of them strikes the Earth about once in every 13 million years. In 1994, astronomers were treated to just such a cosmic display when the comet Shoemaker-Levy 9 - very likely a former resident of the Kuiper belt - ploughed headlong into Jupiter.
While chaotic behaviour, by definition, can't be predicted exactly, the solar system is full of clues that can direct astronomers to places where chaos may be lurking. The biggest clue comes in the form of those resonances, occurring when two celestial bodies give each other a gravitational tug at regular intervals. The effect of such a resonance is not always chaotic: it could, instead, produce a "rotational lock", as in the way our moon always keeps the same face towards Earth. Although a resonance doesn't always lead to chaos, every display of chaos is thought to be triggered by a resonance. "The theme behind all of this is that resonances are now the hot area of modern solar-system dynamical research," says Kim Innanen. While these resonances - and the chaotic motion they sometimes trigger - can have dire consequences, events like comet collisions and planetary ejections are still rare. "We know that there's a great deal of chaos in the solar system," says Innanen, "but after all, we are here." !Reuse content