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NASA Is Going To Crash a Satellite Into an Asteroid (fortune.com)
The National Aeronautics and Space Administration (NASA) is moving ahead with plans to try out deflection techniques on a passing asteroid to prepare for future, threatening space matter. From a report: The space agency has entered the preliminary design phase for its Double Asteroid Redirection Test (DART). This represents the first trial of what's called the "kinetic impactor technique" of asteroid deflection. Put another way, NASA hopes that by hurling a refrigerator-sized spacecraft at one of the space rocks at a speed roughly nine times that of a bullet, it can knock the asteroid off course and save the Earth. The plan is to launch the first DART satellite at a binary asteroid called Didymos ("Twins"); the twin asteroids are scheduled to pass by earth in 2022 and 2024. (Neither pass poses any threat, according to NASA.) By striking one of the two asteroids, scientists will be able to measure the impact of the collision.
Actually no, it's not a straightforward calculation. That's why they want to conduct the test.
It's not a simple collision like we learned about in physics class, with the change in the asteroid's momentum coming entirely from the impactor. The impactor will hit at extremely high velocity (by earth standards), meaning that it will carry a lot of kinetic energy (one half mass times velocity squared) in a small volume. This kinetic energy will vaporize and blow off part of the asteroid, which because of the asteroid's small size, will completely escape.
The mass of the ejecta will greatly exceed the mass of the impactor, so even though it may move much more slowly than the impactor it will carry away considerably more momentum (mass times velocity). The momentum of this ejecta will have most of the effect on the asteroid's trajectory.
But it's unknown exactly how much momentum will be carried away by the ejecta as this depends on the makeup of the asteroid, its density, porosity, how quickly the impactor stops and releases its energy, etc. So that's why they want to try it.
A similar effect was at play in the JFK assassination that helped cause the counter-intuitive "back and to the right" motion of his head that had so many people incorrectly thinking there was a second shooter.