Would Breakthrough Starshot be able to deflect an asteroid or comet? I have seen thoughts about using the lasers that would launch Breakthrough Starshot to deflect asteroids or comets: https://www.scientificamerican.com/article/how-to-stop-an-incoming-comet/ though I am not sure if the laser could deliver enough power at a great distance. My thought is to use the craft itself to deflect the asteroid / comet. Get the craft going a significant portion of the speed of light using the system, but aim at the asteroid (that part might be very hard to do). If you were able to hit the asteroid with the very high velocity projectile (the space sail space craft - even though it has low mass), would that be enough to significantly deflect it? Force = mass * velocity squared, so I think the velocity squared might be significant, though the mass is small.
Here is more on Breakthrough Starshot (its main goal is to explore other solar systems, but perhaps it could be used to save Earth in the future): https://en.wikipedia.org/wiki/Breakthrough_Starshot