PLANETARY SCIENCE

From Mercury to Pluto, ChaosPervades the Solar SystemNewton didn't exactly have it wrong withhis picture of a clockwork solar system. TheNational Space and Aeronautics Adminis-tration (NASA) can still launch a probe to-wardJupiter and expect the planet to be thereas predicted when the spacecraft arrives a

few years later. But confidence that plan-etary positions could be predicted into the

distant futurehas recentlysuffered drasticerosion. Andnow comes the

clincher: In this issue ofScience (p. 56), Massachu-setts Institute of Technol-ogy (MIT) researchers Ger-ald Sussman, who buildscomputers, and Jack Wis-dom, who calculates themotions ofsolar system bod-ies with those computers,report that 100-million-year simulations of the or-

bits ofthe planets show that

says Scott Tremaine of the University ofToronto. The only way to do so was by calcu-lating all the complex gravitational interac-tions of the solar system over millions of or-

bits. By varying the initial position ofa planetby just millimeters and then looking for wildlydifferent outcomes from integration to inte-gration, the researchers could hunt for chaos.

That might sound simple, but it takes a

staggering amount of computer power. Gen-eral purpose computers are too slow to calcu-late planetary motions over long periods, so

Sussman and Wisdom relied on a speciallydesigned machine: the Super-

-ucomputer Toolkit, built byMITand Hewlett Packard Companyspecifically for calculating plan-etary motions. Just one of itseight parallel processors can

perform that task as fast as a

A chaotic quartet. The orbitalmotions of the four inner plan-ets-Mercury, Venus, Earth,and Mars-are chaotic, per-haps due to a gravitational in-teraction between Earth andMars.

all nine are chaotic. The slightest change ina planet's initial conditions of position or

velocity makes its motions millions of yearshence entirely unpredictable.

The result culminates a quest for plan-etary chaos that first hit pay dirt in 1988when Sussman and Wisdom found thatPluto's orbit is chaotic. That discovery was

broadened by Jacques Laskar of the Bureaudes Longitudes in Paris, who calculated thatthe rest of the solar system is chaotic too(Science, 14 April 1989, p. 144). But becauseLaskar used a computational shortcut thathad not been proven entirely trustworthy,there was room for doubt. No longer. Sussmanand Wisdom have dispelled any uncertaintyby calculating the motions of all nine planetswithout shortcuts. And that leaves research-ers free to move on to the next questions:What makes the solar system chaotic? Andgiven all the evidence for chaos, why haven'tthe planets plunged out of their stable orbits?

Just proving the existence of this perva-sive chaos is "a spectacular achievement,"

Cray 1 supercomputer-and a

mathematical technique devel-oped byWisdom makes the cal-culations 10 times faster still.Even so, a solid month of com-puter time was consumed byeach 100-million-year run,which is only a fraction of the5-billion-year lifetime of thesolar system but long enoughfor chaos to emerge.

Finding chaos doesn't tellyou what throws off the celes-tial clockworks, but Laskar believes that hehas identified the major source of at least theinner solar system's chaos: a complex gravi-tational interaction between Earth and Mars.Such resonances pump up planetary chaosmuch the way you pump a swing, timing in-puts of energy so that they reinforce one an-

other. The same Earth-Mars resonance high-lighted by Laskar also emerged in a 6-mil-lion-year integration of planetary motionsrun by Thomas Quinn of Oxford University,

SCIENCE * VOL. 257 * 3 JULY 1992

Tremaine, and Martin Duncan of Queen'sUniversity in Kingston, Ontario. But Wis-dom and Sussman aren't sure the dance ofEarth and Mars is to blame. "Even though weget the same numbers as Laskar, we are sayingthere are ways that his explanation could bewrong," says Wisdom.

Beyond identifying what spurs chaos, ce-

lestial mechanicians face the more subtlequestion of what holds it in check. Amongthe smaller bodies in the solar system, wherechaos has also been identified, it wreakshavoc, flinging asteroids out of the asteroidbelt and sending Satum's moon Hyperioninto a wild tumble (Science, 24 November1989, p. 998). And yet the planets' chaosseems to be constrained, not catastrophic. Inboth computer calculations and the realworld, planets may wander a bit, but they donot fly out of their orbits.A clue may lie in a simpler example re-

cently dissected by Andrea Milani and AnnaNobili of the University of Pisa, Italy. Theyshowed that although the orbit of the aster-oid Helga is chaotic because of a resonance

with Jupiter, becoming unpredictable afteronly about 7000 years, the orbit remains stablefor the full 7 million years of their calcula-tion. Milani and Nobili think that Jupiter,the source of the chaos, is also the source ofthe constraint. Two other resonances be-tween Jupiter and Helga seem to ensure

that the chaos never brings them so closethat Jupiter can fling Helga out of its orbit."We believe this is not exceptional," says

Milani, "this is just the best example." In-deed, Gerald Quinlan of the University ofToronto, studying simplified "mock solarsystems" made up of the four Jovian planetsarranged in varying orbits, has found that

constrained chaosshows up far more of-ten than the cata-strophic variety.

Further insights intothe solar system's oddmix of chaos and sta-bility might come fromwhat Tremaine calls

"the Holy Grail": an

integration ofplanetarymotions for the solarsystem's entire 5-bil-lion-year lifetime.Then again, he says, af-

ter Sussman andWisdom's giant step, "there'sa good chance there's nothing qualitativelynew"$ to be found.

-Richard A. Kerr

Additional ReadingJ. Laskar, T. Quinn, S. Tremaine, "Confirmationof Resonant Structure in the Solar System,"Icarus 95, 148 (1992).A. Milani and A. M. Nobili, "An Example ofStable Chaos in the Solar System," Nature357, 569 (1992).

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