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Is there a way to calculate if an impact from a given asteroid (say 5 miles in diameter, solid rock to which we know the mass) would start an impact winter? If yes, I would like to see a real example of an existing asteroid, if possible some calculations, and the conclusion that an impact winter would be imminent.

I'm not sure if I'm not forcing the boundaries of available knowledge, but I would like to be able to understand and deduce if a given asteroid impact would start an impact winter. I know what that is, and I've read the Wikipedia article Impact winter. I'm interested in a specific example, if possible.

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I'd heard about a really detailed simulation of an India-Pakistan nuclear war, and found an oblique reference to it on Wikipedia. The money quote is "Five million tons of soot would be released, which would produce a cooling of several degrees over large areas of North America and Eurasia, including most of the grain-growing regions. The cooling would last for years, and according to the research could be 'catastrophic.'"

Hence, it sounds like five million tons is a maximum limit to the minimum size of an impacting body to create a global catastrophe. In fact, that is probably really optimistic, because a high speed astronomical impact could probably kick up much more soot than its own mass.

Andrew
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Many of the mass extinctions on Earth are hypothesized to have been caused by either flood basalt events and VEI 8 supervolcanic eruptions that could create a volcanic winter or an asteroid impact that could create an impact winter.

The Chicxulub impact was probably casued by a 10-12 kilometer asteroid that delivered up to 100,000,000 MT of TNT. Some say that a similar mechanism could occur by a 3 kilometer asteroid.