| MadSci Network: Engineering |
I discussed the factors which limit the speed of a rocket in a previous answer. Please refer to the links in it for definitions and explanations of the concepts I'm using here.
While Deep Space 1's ion engine is a very high-tech propulsion system, for the purposes of computing top speed, it's the same as any other rocket. The "rocket equation" relates the final speed of a rocket to the amount of fuel it carries and its "specific impulse". When we're talking about traveling at a large fraction of the speed of light, we must use the "relativistic rocket equation", which includes the effects of Einstein's special theory of relativity. However, the basic concept is the same as the regular rocket equation.
If you solve the equation, you find that to reach 90% of light speed, Deep Space 1 would have to carry a fuel load greater than all the mass in the known universe. That means that DS1 cannot possibly go that fast.
We can use the (non-relativistic) rocket equation to compute the top speed for a spacecraft powered by an ion engine like the one used by DS1. If we assume that 90% of the spacecraft's launch mass is fuel, and that the engine has an exhaust velocity of 30 km/sec, the spacecraft's final speed is 70 km/sec. Travelling at this speed, the spacecraft would take about 10,000 years to reach the nearest star. You could probably double this speed, and halve the time, by using a multiple-stage rocket and performing gravitational "slingshots" around the planets.
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