NASA's Dart Mission Changed Orbit of Asteroid Didymos Around Sun
nasa.govFor reference, if Didymos were on a collision course with earth, we'd need to our interceptor to hit it about 16,000 years prior to impact to get it to miss Earth, or more realistically a substantially larger kinetic impactor/ swarm of impactors.
What about a nuclear bomb?
Explosions don't work that way in space. Very little energy goes into moving the object. Almost all of it either dissipates into space or is spent breaking a large rock into many small rocks that still hit your planet.
You need to impart kinetic energy and quite literally push the rock away. The only reasonable way to do that is throwing inert kinetic projectiles.
Think about starting a Newton's Cradle by lighting a firecracker under it instead of dropping one of the balls. Technically the firecracker has an order of magnitude more energy, but basically none of it is translated into 'useful' kinetic motion.
Detonating a nuke close enough to the surface of a comet or asteroid will cause a lot of it to boil away which produces a lot of thrust. And you could always use more than one!
https://www.universetoday.com/articles/nuclear-detonations-c...
Dart's results can't be directly translated for nuclear weapons
What about a solar sail?
Would take thousands of years, and only if the trajectory was favorable.
Dart's results can't be directly translated for solar sails