I know that appreciating this sort of thing requires a big effort at suspension of disbelief, and I was prepared to ignore to ignore giant plot holes, the grad student's attempts to solve the 3-body problem using "gravimetric data" (WTF?), and the Elon Musk type inventor demanding and getting billions to develop a Newton's Third Law violating EM drive, but they managed to break me anyway.
The last straw was the arrogant and pig-headed government scientist (all the scientists here are dull, arrogant, pig-headed, and spend a lot of time saying "you're insane," mostly to the Elon Musky guy) declaring that they would crash a Jupiter probe into the asteroid fragmenting it into pieces which would mostly hit Russia and China and kill a billion people.
Now I've studied the real "Deep Impact" mission which crashed a high velocity probe into Comet Tempel 1, and I know that even a cometary pile of dust like Tempel 1 is not so easy to disrupt, so a rock-like, much bigger asteroid is not going to be any piece of cake. The gravitational binding energy of a massive object is roughly G*M^2/R (5*G*M^2/(3*R) for a uniform sphere), where G is Newton's constant, M is the mass, and R the radius. Working out the numbers for a 10 km asteroid gives about 10^18 Joules gravitational binding energy. (If the asteroid is iron or rock, the chemical binding energy for this size asteroid would be of the same order of magnitude - a few tens of kiloJoules per kg.) A heavy space probe (2000 kg) moving at 10 km/s has a kinetic energy of 10^11 Joules - much too small to do more than knock a few chips off the asteroid. How about a 10 Megaton H-bomb? It's energy release is 4.18 * 10^16 J, so it would still be too small by a factor of 50, even if you could get it to deposit all of its energy in the asteroid.