"A wobble in the precise clockwork of the solar system could see the Earth collide with Mercury, Mars or Venus, scientists have predicted.
But they say reassuringly that such a mishap is unlikely to occur for billions of years.
The orbits of the planets are not completely stable because of the gravitational interplay between them. Over time, the system can become increasingly disordered - like a poorly balanced tyre that eventually tears itself off the axle of a moving car.
In a similar way, planets can end up being flung out into space, diving into their parent star, or smashing into each other.
Two French scientists have now calculated the chances of our solar system falling apart within the Sun's remaining lifespan of about five billion years. They found that while the "gas giants" - Jupiter, Saturn, Uranus and Neptune - are pretty stable, smaller rocky planets - including the Earth - are on a far less solid footing.
Computer simulations of 2,501 scenarios uncovered around 25, or 1%, which led to a disruption of Mercury's orbit and potential interplanetary collisions. In one case, all the terrestrial planets were destabilised, raising the possibility of Mercury, Mars or Venus smashing into the Earth. Another scenario saw Mars and the Earth approaching to within just 794 kilometres of each other.
"Such a close approach would be disastrous for life on the Earth, with a possible tidal disruption of Mars and subsequent multiple impacts on earth," Dr Jacques Laskar and Mickael Gastineau, from the Paris Observatory, wrote in the journal Nature.
Slight adjustments of the Mars near-miss produced five outcomes with Mars being ejected from the solar system and another 196 which included a collision. In 48 of these, the Earth ends up crashing into Mars or Venus.
In an accompanying News & Views article, Dr Gregory Laughlin, from the University of California at Santa Cruz, said there were implications for planet populations around stars other than the Sun.
He wrote: "With 99% certainty, we can rely on the clockwork of the celestial rhythm - but with the remaining 1% we are afforded a vicarious thrill of danger. What now remains is to understand the extent to which the hand of dynamical chaos that so lightly touches our solar system has moulded the galactic planetary census."
Alec
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