NASA recently completed the experiment of colliding a
spacecraft into an asteroid. The mission’s name was DART (Double Asteroid Redirection
Test) and had the goal of determining if a small asteroid could be deflected.
Ultimately, if the experiment worked, mankind would have a possible tool to change
the trajectory of an Earth-bound asteroid, therefore avoiding a extinction event.
Remembering my high-school physics, the change in the velocity (speed and direction) could be determined by conservation of energy and conservation of momentum equations. I was going to try to re-create the needed equations, when I found that Rhett Allain (in WIRED.com) completed this exercise and explains the some of the nuances associated with calculating the change of the velocity of the impacted asteroid. Link: The Physics of Smashing a Spacecraft Into an Asteroid.
The calculations showed the target asteroid could have its velocity changed by about 1mm/sec. That doesn't seem like much, but if an incoming asteroid could be intercepted with enough time before impact, that small change could make enough of a difference to avoid impact with the Earth.
Update 10/11/2022 - NASA confirmed that they have detected a measurable difference in the asteroid's velocity: NASA confirms humans changed the motion of a celestial object for the first time (msn.com)
NASA says asteroid mission was successful, altered orbit by 32 minutes (msn.com)
Another post gives a method for calculating the probability of extinction events: Math Vacation: The Doomsday Calculation (jamesmacmath.blogspot.com)
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