The book/movie depicts Rich Purnell using some NASA/JPL supercomputers to verify his calculations.

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?