but exploding a string of nuclear bombs to launch this ship, with the radioactive pollution involved, might not be met with enthusiasm by the rest of the world, so thats probably out. At least there is a concrete velocity available for it: 10,000 km/s (=3.......
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One HUGE EXCEPTION: Project Orion, an ambitious plan which would use atomic bombs, exploded behind a massive pusher plate, to accelerate a large ship. All our other forms of propulsion would probably be trivial for a Project Orion ship, but exploding a string of nuclear bombs to launch this ship, with the radioactive pollution involved, might not be met with enthusiasm by the rest of the world, so that's probably out. At least there is a concrete velocity available for it: 10,000 km/s (=3.3% of the speed of light), according to Wikipedia, which is 36,000,000 km maximum per hour, or a tenth of that in a limited form 3,600,000 km/hr, which is still a good bit faster than Voyager (and yes, your numbers are off by a factor of 3,600).
So, sorry if I haven't come up with a discrete number for conventional propulsion, but those would all be overshadowed by the scary nuclear ship.
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If you read carefully, I think you'll find it's "per second".
A spaceraft accelerates for as long as it's being push by a rocket of some sort. So, theoretically the speed could be relativistic, meaning a significant fraction of light speed.
But in reality, how long acceleration can happen depends on how much fuel can be carried and what size engine burns it. As the cost of both these things is extremely weight-sensitive, both of them are not large.
Not very fast. Let's put it this way. Even if we could travel at near 20,000 miles per hour, it would take damn near a half million years to get to one of our closest star systems.
