How long would it take our fastest spaceship to arrive to Proxima B?
That depends, the fastest currently in existence or the fastest we can build right now?
The fastest currently in operation would be the Voyager 1 space probe, at nearly 17 km/s, which would take roughly 75.000 years to arrive at Proxima B.
More interesting in my opinion is the fastest we can build right now.
The top speed of any new probe depends on either the exhaust velocity of the propellant or how long the probe can accelerate, which depends on various factors, like how much fuel it has or how long the propulsion system works before breaking down and how much thrust it can generate.
If the craft can’t accelerate for a long enough time to reach the exhaust velocity, then the top speed is determined by its acceleration and how long it accelerates.
The current generation of ion thrusters that will be available next year can reach a speed of 40 km/s, about 2.5 times the speed of the Voyager 1 space probe, which would get us there in roughly 30.000 years.
There are thrusters that could achieve even higher speeds, but unfortunately those require a huge amount of power, more than could be generated with solar panels or a radioisotope thermoelectric generator.
Instead it would need a nuclear reactor to power the craft, which means the craft would have to be really big, much bigger than any other unmanned probe, which means it needs a lot of fuel.
I don’t know how small we can make a nuclear reactor, which makes it hard to tell if we have the technical capability to even build such a craft, but if we could, it would get us there in roughly 22.000 years.
There is one other thing I want to mention, and that is using really tiny probes accelerated via lasers projected onto a solar sail.
This could potentially get a probe there within a century or so, but it relates to an actual space craft in the same way as a lead ball with sensors relates to a submarine, yes it can get to the bottom of the Mariana Trench much faster than a submarine can, but once there, it can’t really do much.
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