As a trekkie this notion gets my full support and if I had the several trillion dollars it would cost, I'd offer it to them...Well not to NASA, they need a million dollars to make a cup of coffee. If we were to ever do this, it would have to be built in space, and we know how much it cost them to put nothing into orbit in the 80's in their first failed bid to make a space station. And alas untill we have created deflector shield technology a ship made to travel around the solar system is never going to look like the enterprise, if it in fact a good design for a space ship even with such technology. Needless to say having you engines poke out in such a manner isn't the best idea in the world, not when we are still at the stage where in theory the best way to slow down if flying to Jupiter will be to fly party through it's atmosphere.

But simply put, untill we have light-weight and low energy technologies to shield from radiation, space travel is out of the question. We could fly to mars and back now, but radiation wise it's just to dangerous.