|MadSci Network: Astronomy|
I suppose the correct answer to this question is that the shuttle could never get to Alpha Centauri, because it only has enough propellant to reach low earth orbit.
However, the NASA Shuttle Reference website tells us that the shuttle orbits at 27 875 km per hour. So let's assume that somehow the shuttle could boost itself out of orbit and coast in the direction of Alpha Centauri at about this speed.
Alpha Centauri is about 4.35 light years from the sun. Light travels at about 300 000 km per second. So 4.35 light years is:
60 seconds per minute * 60 minutes per hour * 24 hours per day * 365 days per year * 4.35 years * 300 000Space, as Douglas Adams wrote, is big. Really big.
= 41 200 000 000 000 km
Coasting along at 27 875 km per hour, our shuttle would take about 1 500 000 000 hours to get there, which is about 169 000 years.
Try the links in the MadSci Library for more information on Astronomy.