It really isn't that hard to understand. Conservation of momentum still works.
The unknowns are what happens 100-200 and more orbits from now when a close encounter now could become a direct hit then. The big uncertainty comes in that small changes in closest approach now can produce dramatic changes in future orbits.
Actually doing it is a big deal, but understanding how an impactor would work is not that hard.
Yes, big data and supercomputers doesn't equal omniscient. If we can model things inside Jupiter's orbit well 50-100 years out and do enough R&D to elevate the logically proposed solutions from theory to engineering we should be able deflect most of natures challenges and correct most of our own 'oops.' Our history in space shows the last step is necessary, beautiful theories aren't enough. Things incoming from beyond Jupiter become harder to spot, predict and this avoid. Someone needs to deduce where to position sensors to collect useful data on potential impactors that can't be acquired near Earth and send suitable probes there. Prioritize shrinking our bind spots. First nearer and riskier. Eventually further out.