NASA launches spacecraft to test asteroid defense concept

[caraher]

5. It doesn't "disrupt the orbital attractive force"

The impact changes the momentum of the asteroid by some small amount, affecting its subsequent trajectory.

"How would you figure out the gravitational force... at such a distance?"

That's very easy - the formula has been known for centuries thanks to Newton. Multiply the masses of two interacting objects, divide by the square of the distance between them, and multiply by a scale factor that goes by the fancy name "universal gravitational constant."

It isn't really necessary to calculate the *force* of impact at all; what matters is something called the impulse, which is the change in momentum. It's just accounting:

Momentum before: momentum of asteroid + momentum of projectile

Momentum after: new momentum of asteroid (assuming projectile basically embeds itself in the asteroid

You then calculate the new trajectory post-impact based on gravity and the new momentum