Magazine article Natural History

Chaos in the Solar System

Magazine article Natural History

Chaos in the Solar System

Article excerpt

The ability to predict future events with precision is what distinguishes science from almost all other human endeavors. Daily newspapers often give dates for upcoming phases of the moon or the time of tomorrow's sunrise. But they do not report news items of the future such as next Monday's plane crash or next Tuesday's closing prices on the New York Stock Exchange. The general public knows intuitively, if not explicitly, that science makes predictions, but it may surprise people to learn that science can also predict that something cannot be predicted. Unpredictability is the basis of chaos. And unpredictability characterizes the future evolution of the solar system.

A chaotic solar system would no doubt have upset the German astronomer Johannes Kepler, who is generally credited with the first predictive laws of physics, published in 1609 and 1619. Using a formula that he derived from planetary positions on the sky, he predicted the average distance between any planet and the sun by knowing the duration of the planet's year. In 1687, Isaac Newton published the Principia, which contains the law of universal gravitation from which Kepler's laws can be mathematically derived.

In spite of the immediate success of his new laws of gravity, Isaac Newton remained concerned that the solar system might one day fall into disarray. With characteristic prescience, Newton noted: "The Planets move one and the same way in Orbs concentric, some inconsiderable Irregularities excepted, which may have arisen from the mutual actions of...Planets upon one another, and which will be apt to increase, till the system wants a Reformation." Newton implied that God might occasionally be needed to step in and fix things. The celebrated French mathematician and dynamicist Pierre-Simon Laplace had the opposite view of the world. In his 1799 four-volume treatise Mecanique celeste, he declared that the universe was stable and fully predictable. Laplace later wrote, "[with] all the forces by which nature is animated ... nothing [is] uncertain, and the future as the past would be present to [one's] eyes." When queried by Napoleon Bonaparte on the absence of any reference to God in his treatise, Laplace replied, "Sire, I have no need of that hypothesis."

The solar system does, indeed, look stable if all you have at your disposal is a pencil and paper--with or without God. But in the age of supercomputers, where millions of computations per second are routine, solar system models can be followed for hundreds of millions of years. What thanks do we get for our deeper understanding of the universe? Chaos--which reveals itself through the application of our well-tested physical laws in computer models of the solar system's future evolution. Today's leading solar system modelers include Scott Tremaine and his colleagues at the Canadian Institute of Theoretical Astrophysics and Jack Wisdom and his colleagues at the Massachusetts Institute of Technology.

Chaos has also reared its head in other disciplines, such as meteorology, predator-prey ecology, and in most other places where there are complex interacting systems. To understand chaos as it applies o the solar system, one must first recognize that the difference in location between two objects--their distance--is just one of many differences that can be calculated. Two objects can also differ in energy, orbit size, orbit shape, and orbit inclination. It is therefore useful to broaden the concept of distance to include the separation of objects in these other variables as well. For example, two objects that are (at the moment) near each other in space may have very different orbit shapes. Our modified measure of distance would tell us that the two objects are widely separated.

A common test for solar system chaos begins with two computer models that are identical except for a small detail. For example, in one of the models, Earth might recoil slightly in its orbit as a result of being hit by a small meteor. …

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