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Perhaps worth stating that although proxima centauri is the closest star to us at 4.25 LYr, Centauri A is the closest solar-type star to the Sun and isn't exactly far behind at 4.34 LYr.

Bring on the ion thruster visitor spacecraft!

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https://www.projecthyperion.org

chemical launch, on starship in full expenditure mode(500000lbs+payload],ion thrust, solar sail, "accelerator module" that sacrifices itself in an aero braking manouver to then release an in system observation ship

If you can also make the probe survive a close flyby by the star (that should ideally require just a good sun shield & robust orientation control) you could the so called solar Oberth manuever - basically this[0] but to slow down an incoming interstellar probe, not to launch one. A simple storable high thrust solid rocket motor would be ideal for this.

[0] https://www.centauri-dreams.org/2021/10/06/assessing-the-obe...

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