The New York Times Book of Mathematics by Gina Kolata

Author:Gina Kolata
Language: eng
Format: epub, mobi
Tags: ebook
Publisher: Sterling
Published: 2013-02-07T16:00:00+00:00

Tales of Chaos: Tumbling Moons and Unstable Asteroids

By JAMES GLEICK

Bad news for those who thought they could at least rely on the stable clockwork predictability of heavenly bodies: the solar system has some surprises in store.

A new picture of celestial motion suggests that the earth’s neighbors include erratically tumbling moons and unstably orbiting asteroids, a chaotic menagerie that seems to provide, among other things, a solution to the longtime mystery of where meteorites come from.

“We have a strong prejudice that the solar system is dull—perhaps pretty, but not very interesting dynamically,” Jack Wisdom of the Massachusetts Institute of Technology told an audience of physicists, mathematicians, chemists and biologists here this week. In fact, he said, the solar system’s spins and orbits are neither so simple or so regular as Newton’s descendants might expect.

New computer calculations, based on observations from the Voyager satellites and ground-based telescopes, show that just about every moon—except the earth’s—has experienced millions of years chaotic tumbling, Dr. Wisdom reported. As he showed with a computer-generated movie, “tumbling” is a kind of motion utterly unlike the familiar spin of a body around an axis.

A tumbling moon falls end over end, twists sidewise, speeds up, slows down, all the time obeying Newton’s completely deterministic laws of motion, yet defying prediction in a way that scientists used to consider impossible. One of Saturn’s moons, a 250-mile-long football-shaped body called Hyperion, appears to be tumbling now, and its unpredictability is such that even if Voyager I had measured Hyperion’s position and speed to 10-digit accuracy, God’s own computer would not have been able to calculate where it would be when Voyager II came by a year later.

Hyperion is not alone, according to Dr. Wisdom’s latest work. The moons of Mars, Phobos and Deimos, went through tumbling episodes on the order of tens of millions of years, and the propensity to tumble is the rule, not the exception.

Strangely, tumbling results from precisely the same gravitational laws and tidal forces that cause moons to lock into a stable orbital “resonance” with their planets. The earth’s moon spins once for every orbit, thus always showing the same face. Nor must the ratio be one to one. Mercury, for example, was long thought to keep the same face pointed to the sun; in fact it rotates exactly three times in every two of its “years.”

Such resonances are not permanent, because energy drains away, lost to tidal friction. And when a moon breaks out of a locked mode, tumbling can ensue. The lesson for science—and it has been a hard lesson even for physicists to grasp—is that chaotic behavior is just the flip side of a simple Newtonian coin.

“Here is a departure from everything you’ve expected,” said James Yorke, a mathematician from the University of Maryland. “You have no special perturbation or complexity. It’s just basic physics—yet it’s doing something that nobody thought about.”

This was Chaos ’87, a conference subtitled “The Physics of Chaos and Systems Far from Equilibrium” and attended by theorists and experimenters from 14 countries, including China and India.

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