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We know from this question that an asteroid 20 km in diameter is feasible as a hollow space habitat.

There are many variables in real life, but assuming you had a spherical solid iron asteroid 20 km in diameter orbiting the Solar system in the Kuiper belt. When you start hollowing it out to form your habitat, you use a coilgun or railgun to impart thrust. Now you potentially have an interstellar ship.

Assuming you have decided to leave an outer shell 1 km thick, this gives you 18 km diameter sphere of iron as reaction mass. Assuming we could eject this mass with the velocity of 0.1 c, and the rate of ejection at 10 k tons per hour, what would be the theoretical maximum velocity such an object could reach, if we eventually want to also decelerate to zero at some distant location? Would the speed reached be sufficient to exit the Solar system and start an interstellar voyage?

Size and mass of this space vehicle's engine is negligible, and we don't care that the projectiles might hit some other object in their way.

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James Jenkins
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For simplicity's sake, let's assume a perfectly uniform sphere, as you described. The amount of volume to begin with would be about 4188 cubic km. The volume of material evacuating the sphere would be about 3053 cubic km. Thus, about 72% of the asteroid would become fuel. Let's ignore relativistic effects, because my mind isn't quite working that well yet today. First of all, how fast could you get if you don't want to stop? I'll do some handwaving calculus and say that it should go about 0.134 c, if you don't want to stop. If you do want to stop eventually, then you should accelerate to half of that speed, and then coast, using the rest of the acceleration to stop. Thus, you could go about 0.067 * c. So, how long would it take you to get somewhere?

Alpha Centauri is about 4.367 light years. Assuming a negligible acceleration/deceleration period, that's about a 65 year trip. I'll leave that to you if that's acceptable to make the trip.

PearsonArtPhoto
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  • The biggest problem may be how you get the energy to do this. Any fusion Q value will be less than 1% of the rest mass of the reactants. So there's no ordinary way to carry enough energy to expel that much propellant at that speed. – AlanSE Jul 27 '13 at 19:39
  • @AlanSE: I agree in principal, unless you can somehow get it from Solar, or you eject the hydrogen after it's excelled. But this calculation didn't include those kinds of pesky details, so... – PearsonArtPhoto Jul 27 '13 at 19:55