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So, assume that at one point in the distant future, humanity has a docking facility/military observation post in orbit around the star of Alpha Centauri B for.....well, military purposes, which could range from protecting trade trajectories from criminals, to being a secret testing site to basically anything military-related.

Assume you have a supply craft that just finished resupplying this facility in orbit around Alpha Centauri B(which unfortunately has no worlds anywhere, along with the rest of the system and basically is reserved for the armed forces of some political entity either back on Earth or in some distant rogue colony, which in this case, I will assume it belongs to a nation back on Earth), and it needs to return to the Solar System to get the next round of supplies.

So, assuming a multi-stage antimatter beam core engine-propelled craft (which contains four stages used to reach a speed of 0.75 c, two of them have already been used and the supplies got to them via an orbital transfer vehicle or OTV docked with the main craft, which is in a no-fly zone), what would the escape velocity need to be for our spacecraft to leave the Alpha Centauri system (specifically Alpha Centauri B) and return to Earth?

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closed as off-topic by PearsonArtPhoto Jul 5 '16 at 13:07

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  • $\begingroup$ Initial (departure) orbit radius? Also, escape velocity means really low speed on the outside of the sol's Hall Sphere. So, the trip to Earth would take millennia. $\endgroup$ – SF. Jul 5 '16 at 12:47