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Voyager 1 loses contact with NASA, turns on retro transmitter not used since 1981
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It's a bit more complicated than that. New Horizons actually went way faster than the Voyager probes, getting to Pluto in only 9.5 years. It took Voyager 2 just slightly longer than 12 years to reach Neptune for comparison. The planetary alignment you are thinking about was due to relative proximity. Obviously you can't use Saturn to slingshot you to Uranus if they are on opposite sides of the solar system. All the outer planets were going to be on the same side of the solar system, allowing the Voyager probes to visit them all in succession.