Using Rockets to save The Earth from Asteroids

All of these asteroids are orbiting the sun with a period of several years perhaps as long as ten years. But if you can get to an asteroid on the previous orbit say a decade before it otherwise hit Earth You might only have to change the velocity of the asteroid by a very small amount so that when it passes where Earth would be Earth wouldn't be there. We can detect these asteroids that are large enough to really affect Earth well enough that we could know decades in advance. So then what you have to do is get up to the asteroid and do something that would change its velocity slightly. Some of them are very solid pieces of rock others are loose conglomerations of rubble and so if you push on them they might just fall apart. So you've got to be careful as to what kind of asteroid you're dealing with as to how you deal with it.