I’m not sure how large the Vogon constructor fleet was, but if it wasn’t too numerous, I’m pretty sure a single Vogon Constructor Ship could do very significant damage and as said above, the chances of us being able to fight back against any interstellar space craft is pretty much zero.
Other ships from the HHG series that might work:
Billion Year Bunker - should have more than enough weaponry aboard, most of them too dangerous to use.
Bistromath - for pretty much the same reasons as the Heart of Gold.
It’s only unpredictable if you’re not specifying the expected outcome. IIRC, it can do basically whatever the hell it wants as long as the computer can calculate the probability of the outcome. With, I admit, some side effects while it’s doing its thing.
So the axiom of choice is not only true in the Star Trek universe, but can be applied to physical situations? Must be how they developed all that advanced technology. Perhaps once we have have specified a well-ordering of the real numbers, warp-drive technology will pop right out on us.
I also have to wonder how often Steve MB has used that joke, and how many people he’d think would understand it.
For those saying you’d need a big-ass ship with room for lots of ground soldiers: Cortez conquered the Aztec Empire with less than a thousand men (and he had already scuttled his starship-equivalents back on the coast, to keep his men from having second thoughts and maybe bugging out). Pizarro conquered the Inca Empire with fewer than 200 men.
Clearly, if a.) the aliens wish to conquer Earth (as opposed to just sterilizing it) and b.) they don’t have millions of warrior bugs or clones or battledroids on hand, then the trick for the aliens is to be sneaky and underhanded and not just engage in a frontal assault. As already noted, play divide-and-conquer; find some disaffected groups who don’t like the dominant groups and arm them (though maybe not with your very best weapons tech). If you can persuade a substantial chunk of the population that you’re the Messiah or the Chosen Ones or something, all the better. Be prepared to co-opt local elites into running the place for you (and coercing the native population into mining the dilithium crystals or ginger or whatever it is you’re here for). You may also want to look into finding some “warrior-like” ethnic groups and hiring them as mercenaries–think Somalis or American rednecks with death rays (Its Galactic Majesty’s First Terran Raygunners).
(On the off chance the aliens have already figured out how to tap into the Internet and are reading this: Of course, what would really crush our will to resist and deliver our planet into your hands is sending Sexy Nymphomaniac Humanoid Space Babes and, uh, dark chocolate! Yeah, that’s the ticket. And kittens.)
Conquering would require a bit more finess, but nearly every ship capable of interstellar travel could destroy humanity easily. Even an alien fratboy party could do it. You don’t even need to get inside Earth’s atmosphere. Just nudge a few decently sized asteroids or comets in the right direction, and you have genocide coming some years in the future. Right now there’s nothing we could really do to prevent it, and we might not even notice it coming.
I think the Venture Star from Avatar could do the job. It’s fuel was tons of antimatter. Since one ounce of antimatter is equal to 1.22 megatons, all you need is a small containment capsule to hold the antimatter during reentry.
You hire the Chinese for occupation troops for a percentage of the take and a bonus of not blowing the crap out of Beijing.
They didn’t do it in Avatar, since they couldn’t blow up the Navi with an Antimatter bomb without also destroying the Unobtainium and besides Colonel Quaritch wasn’t exactly a rocket scientist and probably didn’t know much about how the Venture Star worked.