Lets see who wins the race to destroy the Earth, us or the stars!

look up the definition of deflection then come back.

You mean like the one where they shoot rockets at the MOUNT EVEREST SIZED ASTEROID to push it away?

Think bigger. It's all about degrees in space. A laser can heat up the asteroid enough to cause gas to evaporate off the surface. That tiny amount of thrust can change the trajectory of that asteroid by maybe a few inches when the laser hits. That few inches turns into thousands of miles after the asteroid continues on that slightly new trajectory for a few weeks or months. Done early enough, it could set the asteroid far beyond it's original path so that it doesn't hit the earth at all.

Think of how a bullet is deflected by wind over large distances. Ever scoped in a rifle by changing the scope or sight left or right, or up or down? That is compensating for the effects of the wind on the bullet during that day. If the wind is moving 5mph from right to left, it's not pushing the bullet much, but it's changing the trajectory by a lot over a larger distance.