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> New Horizons nearly did.

New Horizons didn't nearly overtake Voyager. It's currently traveling about 4 km/s slower, and as it's still closer to the Sun, it's also decelerating more.

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Yes, I wrote that short for brevity. If you must have the full thing spelled out: New Horizons nearly got enough velocity at Jupiter to eventually overtake Voyager. 4 km/s is "nearly" in astronomical terms. New Horizons wasn't really trying to optimize for speed at Jupiter (its closest approach was over 10m km), and a spacecraft that did could easily overtake Voyager using Jupiter alone and not need an alignment with Saturn or anything else.

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