There are a few ways I can see it going down depending on the technology of the invading species of extraterrestrial. If they have the technology to get here, I would assume they also have the technology to take over. The extent of their technology no doubt determining how much or little of a mess there is.
Here are a few ways I see it happening:
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Level 1 Invaders – Aliens from a dead world.
After having used up all the resources of their home world, and almost destroyed the planet with polution a high population and other problems, they seek out a new world. They are not experienced in taking over worlds, this is the first time they will do so, and will do so out of desperation. They are not in the habbit of traveling to distant worlds, but do have the technological capability to move most of their population to another planet should the continuation of their species depend on it.
They probably don’t have an intention to take over, they are just looking for shelter and colaboration, but after a while of trying to get allong, two similarly dumb species go to war with each other. As the fight is over the planet, no one is prepared to use nukes or ace weapons, and a bloody and drawn out war takes place. Human/Alien commercial trade insures humans have enough alien technology to put up a good fight, but the aliens end up winning due to a few trump card moves.
They have about 150 – 250 years of technological advantage over us.
Level 2 Invaders – Low end clear cutters.
This will be the 17th world they take over, on a few worlds they have taken over within days as the highest life form on the planet was not much smarter than a earth cat, on others they have fought hard but guaranteed battles with primitive cultures.
They will start by taking out our satelite systems and military bases from space, perhaps 4 or 5 times further away than the moon. Once 4 or 5 billion humans have been killed, advanced foot soldiers are deployed to the surface. We do manage to get a few shots off, we even take down a few of their bigger ships, but they end the day calling it an efficient conquest. The whole process takes 2 to 3 days in total.
They have about 300 – 500 years of technological advantage over us.
Level 3 Invaders – Experienced pest control.
As part of galactic legislation, our solar system is going to become a new kind of super motel. The invading party does not value our existence any more than we value the life of an ant, but rather than kill us they will just relocate us.
The entire thing is done automatically with the use of machines, no actual aliens are on the mission as all they have to do is beam us up in to the transport ship, ready to be transported to our new home/zoo. The entire process takes about 2 or 3 hours.
They have about 500 to 1500 years technological advantage on us.
Level 4 Invaders – This is my jurisdiction… Not anymore it’s not.
An intergalactic civilization recognizes the strategical value of our solar system in their war against another alien race. A battle ship is deployed to set up a base. A cloud of nanobots the size of jupiter intercepts all the planets in the solar system, instantly reconfiguring them for the battle ship that is seconds behind. We are gone before they get here.
Should they not be in a war and were just setting up a small base, maybe they would just come down and set up without even being bothered by our presence and attempts.
These guys are about 10.000 to 50.000 years more technologically advanced than us.
Level 5 Invaders – The new summer home.
These guys make the borg look sloppy, we are simply just gone. They did not need to use weapons as our existence was canceled out, a kind of machine that uses time travel paradoxes was used to delete us.
They have 50.000 to 100’s of millions of years technological advantage.