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It would be most likely a whole solar system. Consider that new horizons only had hours during its flyby to collect all the telemetry that it did. Imagine having 600 pixels of resolution for an exo planet for up to 15 years. Plus all the other telemetry you'll be collecting about the galactic space near us.
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With a Jupiter/solar oberth boost we can at best do around 20 AU per year, so best case scenario it would take atleast 25 years to get there, which honestly isn’t bad at all. For comparison voyager does around 3.6 AU/year.
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A series of permanent stations near the vicinity of the oberth burns at Jupiter and the sun could add a lot of Delta V by firing a laser at the probe and the probe could fire one back. Even more so if it was a series of laser boosters strategically placed around the solar system. The numbers start to get really crazy.
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