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Well if you care to research the merits and disadvantages the technique is called gravity tractor. https://en.m.wikipedia.org/wiki/Gravity_tractor#:~:text=The gravitational force of a,the vehicle nor its expelled Like every potential solution there is advantages and disadvantages. So really the choice of method depends on several factors. Asteroid mass, composition. Amount of correction needed and time to provie the correction is some of those factors. Here is a research article on the technique. https://arxiv.org/pdf/physics/0608157 This method doesn't require the asteroid composition, rotation and surface properties. It really only requires trajectory, and mass terms along with sufficient time and obviously communication with said craft for course corrections etc. Those are the main advantages the disadvantage is the communication requirement , sufficient fuel and a slow process that requires a large amount of time so early warning is a priority for the method to have sufficient time. However the method works with asteroids with rotation which negates numerous other methods. (Or complicates).

Can you summarise the key points you are making here in a paragraph, or in bullet point form?

I think that we can use rotation/spin in order to deflect the debris/parts away from a collision course. If the axis of rotation of the asteroid is more or less parallel with its path, an explosion should split the asteroid in parts going away from the axis/collision path. If the rotation is too weak, we can increase it, with well placed thrusters, prior to the carefully planned explosion. If there is no spin, or the axis is perpendicular to the asteroid path, we may use thrusters to deflect the entire asteroid. We can use as thrusters craters/wells on a side (at a pole, if it spins), where we initiate some chemical reactions or we simply heat them using large arrays of space mirrors (ultrathin reflecting sheets). The arrays of mirrors should be deployed in advance, in all directions, and used as solar power plants, before being converted into solar guns.

I forget. Do you want to discuss science or the many ways you've been wronged?

All the Earth orbit crossing asteroids in the solar system of that size are known and tracked but if one were lined up for possible collision in one century's time lt seems enough time to dismantle that asteroid and scatter the bits into not-intersecting-with-Earth orbits. Would not be easy - a massive project that probably requires more cooperation than humanity is capable of? And maybe it can be exploded into a cloud of debris too wide and diffuse to be dangerous. If that were to use up the world's stockpiles of nuclear weapons - using them for good whilst getting rid of them for good would be good. Too good I expect. Something unknown, ie from far out, won't give that much time - a few years of warning (maybe) to do things that will... take a few years to do. If I understand right if the debris isn't scattered wide enough it can be as bad as hitting as one mass. A different kind of won't be easy, with a lot more urgency I suppose.