On the asteroid to the stars

On Day 55 anniversary of manned space flight, of course all thinks about way to stars.

And in general, for a long time I had twisted the idea that the current level of technology the most feasible interstellar transport is the asteroids.
That is, we take a small asteroid - 2-3 km, to hang it of nuclear engines and in a very real settlements.
We get:
1. The huge supply of the working fluid for nuclear engines - will allow a small but constant thrust to accelerate the asteroid considerable speed, maybe even to the percent of light.
2. protected from outer space to the space of 1 km3, which is located quite comfortable accommodation for dozens of people, farms, greenhouses, etc., down to parks and cultural centers). Even plants with 3D printers, of course. «Smile»
3. Due to the constant thrust will be constant gravity, which is also nice and helpful to health ... Also we need a magnetic protection against cosmic radiation on the basis of the Earth's magnetosphere
This allows fast enough (for decades) to reach the nearest stars with planetary systems.