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Don’t panic, but an asteroid has a 1.9% chance of hitting Earth in 2032
(arstechnica.com)
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If we are able to nudge an asteroid, would an asteroid of this size nudge the earth?
Technically the solar system is a multi-body system, and everything nudges everything else, but the mass of the earth is far greater than the mass of the asteroid, to the point that it doesn't matter.