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Do we know enough about the number of space rocks and comets out there to be able to say with confidence there is X% chance of, say, a 1km diameter asteroid hitting us in the next 100 years? How is X calculated?

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I think the core is issue is the level of uncertainty due to the complex gravitational influences.

Its pretty easy to model just say the planets affect on an asteroids object, but there are other sufficiently large bits of mass floating around, that over the course of a multi year orbit have enough affect to matter.

I think as computing power gets better, more data is collected on bits of mass floating around out there, the accuracy of the predictions will increase.

But I suspect tracking down, and monitoring the orbits of all that mass will be a bigger problem than computing power. (I.e. A cluster of 1024 CPU's (Say 128 1U 2 socket, 4 core servers, like the original SO runs on) these days is actually dirt cheap, compared to what that kind of power used to cost.

More directly to your question, I suspect X% chance on something 100 years out is little more than a wild guess. If there were no other influences in the solar system, than we currently know about, then it might start to work. But in 100 years, the little perturbations add up, to make any real estimate little more than guess work (In my mind, at least).

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Another way that asteroid impact probability is calculated is using the Torino Scale: its a scale that categorizes impact hazards of Near Earth Objects. Astronomers use it to assess the seriousness of collisions. Wiki: http://en.wikipedia.org/wiki/Torino_Scale

Another way that astronomers calculate the impact hazard would be the Palermo Technical Impact Impact Hazard Scale: its a logarithmic equation that is slightly more complex than the torino scale. Wiki: http://en.wikipedia.org/wiki/Palermo_Technical_Impact_Hazard_Scale

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