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I find it amazing that they believe they can calculate . . .

It is amazing, and what makes it work is the use of digital computing. One of my grad school problems was to calculate a trajectory to the moon for a given delta-V in Earth orbit. Obviously the delta-V has to be large enough to get out of Earth orbit in the first place, but the problem was one of trading off time in travel versus original delta-V.

That requires numerical integration, and that requires computer speed of calculation. Nowadays that sort of calculation can be done in seconds for any given trajectory, and a matter of minutes for an optimal trajectory. But I remember hanging around the computer lab for hours at night waiting for my computer program to be run.

There is a point of diminishing returns on accuracy. You can include the primary effects of the major bodies (for lunar insertion it's Earth, Luna, and Sol). But there are effects for secondary bodies - which become major as you get away from the Earth (like Jupiter). And then there are the minor bodies like other asteroids. The key to optimizing the computer problem is to recognize when uncertainty in the original conditions (the observational data) overwhelms errors caused by neglecting secondary bodies and you might as well just print out some results (now, of course, "printed" to a screen).

What is more interesting to me is sensitivity analysis where you assume your analyzed orbit comes 50 miles closer to the Earth or Luna than your nominal trajectory. From that you can get 10,000 miles difference in the orbit on next closest approach, or even more. On the other hand, your uncertainty in the measurements makes that 50 mile error less and less likely as you get data over a longer period.

So, I "believe they can calculate the asteroid's orbit" to incredible precision - but recognize that minor errors can have major impacts. It will be interesting to watch. And 2032 is only 7 years from now, so I hope to be able to see it happen.