EARTH MAY BE ON COLLISION COURSE WITH ASTEROID IN A MILLION YEARS.

Byline: Malcolm W. Browne The New York Times

Some bad news from European mathematicians: There seems to be a significant chance that within the next 1.14 million years an asteroid named 433 Eros could hit Earth, with dire results for the human race and most other species.

Little 433 Eros is not on most lists of potential planetary catastrophes. Although it sometimes comes close to Earth's orbit, the 14-mile-diameter asteroid is not one of the approximately 150 known planetoids more than one-half mile in diameter whose orbits actually cross that of Earth. The present track of 433 Eros intersects the orbit of Mars.

But the complex and constantly changing gravitational interactions of the major planets with small solar-system objects like 433 Eros make their orbits unstable and easily disturbed.

In a paper published Thursday in the journal Nature, mathematicians at the University of Pisa in Italy and the Observatory of the Cote d'Azur in France report that within a million or so years, there is a 50 percent chance that 433 Eros will be nudged into an Earth-crossing orbit. If that should happen, the asteroid might eventually hit Earth.

A consolation, the mathematicians say, is that there is practically no chance of this happening in the next 100,000 years, ``so we have some time to prepare,'' one said. But only 10 percent or so of the potential Earth-hitting asteroids have been detected, astronomers believe, and without a systematic early warning system, Earth could be taken by surprise.

Planetary experts have a special interest in 433 Eros because it is larger than most other asteroids; it is the second-largest known asteroid in a near-Earth orbit. (The largest is 1036 Ganymed, 20 miles in diameter. It should not be confused with Ganymede, one of Jupiter's moons.)

A hit by any asteroid 0.6 mile or larger in diameter would have devastating effects on terrestrial and marine life as well as human civilization, say Pietro Farinella of the University of Pisa and his Italian and French colleagues.

Andrea Milani, a member of the Pisa group, said in a telephone interview that an impact by 433 Eros would have about 10 times the destructive effect of the asteroid that is believed to have created the Chicxulub crater in the Yucatan Peninsula some 65 million years ago.

That impact has been implicated by scientists as one of several possible causes of the mass extinctions that occurred at the end of the Cretaceous period, which included the demise of the dinosaurs and many other animals and plants.

The calculations that led to Thursday's Nature report are based on an array of approximate solutions to a notoriously difficult physics challenge known as the ``N-body problem.''

When the gravitational fields of only two objects interact it is easy to calculate the results exactly. But when there are three or more interacting objects, precise calculations are impossible, and space scientists must settle for good approximations.

These approximations are adequate for calculating the trajectories of spacecraft or predicting the orbits of major planets, but when the calculations are extended to the behavior of asteroids millions of years hence, they break down chaotically and unpredictably.

The calculations applied to 433 Eros, Farinella said, were based on integrations of approximate numerical solutions to the N-body gravitational problem developed by Roland Zdanek Bulirsch of the University of Munich and Jossef Stoer of the University of Wuerzburg.

The orbit of 433 Eros becomes less and less certain as one projects it into the far future. To improve their estimates, the mathematicians took the gravitational fields of all the planets except little Pluto into account, and calculated their possible combined effects on various possible orbits of 433 Eros in the distant future.

They found that a ``resonance'' could develop between Mars and the asteroid, which under certain circumstances could push 433 Eros into an Earth-crossing orbit.

When eight mathematically plausible orbits of the asteroid were computed over a period spanning 2 million years, three orbits began to intersect with Earth's orbit, and one actually produced a collision with Earth 1.14 million years from now.

Initial reactions by astronomers to the 433 Eros calculations ranged from mild interest to dismay.

``It's quite interesting but not really surprising,'' said Brian Marsden of the Smithsonian Astrophysical Laboratory in Cambridge, Mass. ``But I don't think we need hold a special place in our catalog of fears for 433 Eros. Comet Swift-Tuttle is just as big, and that might hit the Earth too. In fact there are probably about 3,000 objects one kilometer or more in size that could hit the Earth.''