Turns out that Star Trek is impossible.
At 99.999998% of the speed of light, the the radiation from interstellar hydrogen striking your ship will fry you like an egg:
Professor William Edelstein of the Johns Hopkins University School of Medicine explained to New Scientist that while interstellar space has just a couple of hydrogen atoms per cubic centimetre, as the crew of the Enterprise hit the gas pedal, a compression effect would greatly increase the number of atoms hitting the spacecraft.
As the spaceship reached 99.999998 per cent of the speed of light, “hydrogen atoms would seem to reach a staggering 7 teraelectron volts”, which for the crew “would be like standing in front of the Large Hadron Collider beam”.
This is a very bad thing, because humans in the path of this ray would receive a dose of ionising radiation of 10,000 sieverts, and as Bones McCoy would doubtless confirm, the lethal dose is 6 sieverts.
The result? Death in one second.
And I was so looking forward to green alien dancing girls.
Well, I guess that there is always recombinant DNA technology.