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The closest they can ever be is on the order of 1,200,000,000 km; on average it's about 20% more than that.

Note that it's not a simple matter of "point your spaceship in the right direction and just keep going straight", because that's not how celestial mechanics works. Voyager 1 passed by Saturn (and Enceladus as well) about 3 years after launch; Voyager 2 (which was actually launced first) took 4 years to get there, because it was launched along a different trajectory.

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