From Science:
T. S. Eliot got it wrong. The world could indeed end with a bang, not a whimper, as the poet prophesied. New supercomputer simulations predict that, in 3 billion to 4 billion years, there is a slight chance that Venus or Mars will slam into our planet thanks to the subtle gravitational interactions between Jupiter and Mercury. Although the solar system seems placid and stable, catastrophic collisions and other violent events helped shape it. Scientists think our moon condensed from the debris of a Mars-sized world that smacked into the very young Earth. Uranus rotates on its side, probably because of a planetary collision. And Jupiter's great mass ensures that only asteroids occupy the orbit between it and Mars; anything larger gets ejected from the area by the gas giant's gravity.
Jupiter's gravitational reach also has a slight chance of destroying Earth someday, say astronomers Jacques Laskar and Mickael Gastineau of the Institut de Mecanique Celeste et de Calcul des Ephemerides in Paris. The researchers ran more than 2500 simulations based on a model they developed that projected the precise orbits and interactions of the entire solar system over the next 5 billion years. In tomorrow's issue of Nature, the team reports that in 99% of the simulations, the solar system continued to operate smoothly for this length of time. But in 1% of the cases, things got messy. The culprit was Mercury's orbit. If its trajectory is altered by as little as 0.38 millimeters over the course of the next 140 million years, explains Laskar, that incredibly tiny difference would be magnified steadily by repeated encounters with Jupiter's gravity, growing by a factor of 10 about every 10 million years. By about 1.7 billion years from now, Laskar says, “Mercury's [orbital] eccentricity increases to large values,” and by 3.34 billion years, there could be “a complete destabilization of the inner planets.” As a result, Mars or Venus might ram into Earth. On the bright side, Laskar says, “one is ensured that nothing will happen [in the next] 100 million years.”
More here.