Knowing nothing (or less than nothing if thats possible) about Celestial Mechanics, considering that the technique (gravitational assist/slinghsot maneauver???) was used in space probes as early as the 1970s, how much computing power would be needed to do these calculations?
I guess the faster the computing resources, the earlier you would get your solutions. But are these calculations that could be done on more run of the mill computing hardware?
In his interview with Adam Savage the author described how he wound up writing his own custom code to calculate the trajectories of their spacecraft. One could imagine that NASA would need to consider a lot more "real-world" variables than a sci-fi author, so it is somewhat reasonable to think time on a supercomputer could have come in handy.
Also, the computer in the movie was Pleiades at NASA Ames.