Gauging planetary escapes and asteroid ages.

When the fragments of Comet Shoemaker-Levy 9 started plunging into Jupiter, the times and locations of the impacts came as no surprise to astronomers. Accurate measurements of the fragments' positions at various times over the last year had enabled them to calculate the orbits of these objects with extraordinary precision.

Such certainty, however, has proved elusive for planetary and asteroid orbits calculated millions of years into the future. A number of computer simulations based on equations describing the motion of bodies in the solar system indicate it's generally impossible to make precise predictions of the long-term future of planets and asteroids (SN: 2/22/92, p.120). In many cases, these motions display the extreme sensitivity to initial conditions typical of chaotic dynamics.

Now, Jacques Laskar of the Bureau des Longitudes in Paris has extended these orbital calculations, using a simplified set of equations, to cover up to 15 billion years. By looking at the effect of making slight changes in the initial orbital characteristics of the planets from one computation to another, Laskar showed that Mercury can drift into an orbit so elongated that a close encounter with Venus could cause a cataclysmic collision or send Mercury careering out of the solar system.

Laskar describes his results in the July ASTRONOMY AND ASTROPHYSICS.

According to Laskar's calculations, the motion of Jupiter and the other large planets remains very regular. In contrast, the inner planets all show varying degrees of chaotic behavior, with Mars and Mercury potentially experiencing much larger excursions from their normal orbits than Earth and Venus.

"The difference in behavior between the large planets and the inner planets is very striking," Laskar says. "One reason ... is probably that the large-planets system is not perturbed much by the inner planets."

Moreover, "if the outer planets were less regular, then the inner planets' motion would be so chaotic that ... Earth would suffer changes too large in its orbit to ensure climatic stability on its surface," he adds.

Asteroid orbits can experience large changes over even smaller time scales. The occurrence of such chaotic fluctuations may provide a way to estimate when families of asteroids formed, say Andrea Milani and Paolo Farinella of the University of Pisa in Italy.

An asteroid family is a group of objects created when a large asteroid breaks up into smaller pieces as the result of a collision. Althouth the fragments spread out rapidly in space, their orbits tend to retain certain characteristics that make them distinguishable as a group from other asteroids.

However, the orbital parameters of an individual fragment may occasionally change enough to put it outside its family. By determining the likelihood of such an escape for a given family member, researchers can obtain a rough estimate of the family's age. Astronomers have identified more than 20 asteroid families.

Milani and Farinella applied their technique to the Veritas asteroid family, a particularly dense cluster close to Jupiter's orbit. They calculated how the orbital characteristics of two family members (including the largest, 490 Veritas) would change over millions of years.

Reported in the July 7 NATURE, the calculations show that these two members would wander outside the family borders within approximately 50 million years. The results suggest that the Veritas asteroid family can be no more than 50 million years old, the researchers conclude.