Gravitational slingshot

Having recently watched the movie "Interstellar", I got interested in understanding gravitational slingshots. Again. While the theory is quite straight forward, what I had trouble was understanding how scientists knew which points to use at what points of the trajectory. There are introductory articles here and here, there's a detailed account of how the theory behind gravitational slingshots was developed in the 60's.

As i said, my question is how scientists know which planet to use at what point in a satellite's trajectory. For example, the voyager 2 probe used Jupiter, Saturn, Uranus and Neptune to speed up. I would like to know how scientists first figured out when to launch the probe from earth and what it's approach trajectory to Jupiter should be such that after a certain period of time, it would run into Saturn, followed by Uranus and Neptune. The question is not just a problem in space but also in time because the probe takes a certain time to move from one planet to another during which the planet itself would have moved. Maybe a predictor-corrector method. Maybe it's a question best solved backwards starting from Neptune. I don't know. I need to dig a little more. I need to get better at googling. Or maybe i shouldn't be googling!

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