It’s a popular science fiction trope, aliens appear in the sky and after a short while they begin to land. Perhaps like in independence day they blow up the cities first or perhaps they release a virus that exterminates most of the population, or they pretend to be human replacing people slowly. It all makes for good stories but is it actually possible that aliens could take over earth?
To answer this we need to consider the difficulties that they would face and the reasons that they would have for coming and what would happen if they did.
The first issue is naturally getting here. There are two possibilities for getting here, build ships that go less than the speed of the light, in which case it will take decades to get here from even the nearest stars or find a way to move faster than the speed of light. Each of these would take a massive amount of effort to create.
The next issue they would run into would be compatibility with the planet. There is no reason to assume aliens would be able to use our atmosphere. The same is true of climate, gravity and biology. It is likely that everything about this world would be toxic to them.
But why would they come? Even assuming that by some odd quirk of nature they have a biology similar enough to ours with our world to make it useful it what is here that is so valuable? The biosphere is the only real answer. Nothing else could make sense. For a species advanced enough to get here any chemical or mineral would be far easier to get from asteroids than a planet.
Even the biosphere makes only marginal sense. There are 100 billion stars in our galaxy and for the sake of this argument we are assuming at least two intelligent species. This would almost certainly mean a considerable number of planets with life but not intelligence and even if there weren’t terraform of a world would likely be as easy as getting to ours and they could create it to their exact needs rather than using ours. But why would a species that came here because of humans want to rule over us? Slave labor seems a possibility until you consider the machines and tools we have at a level of technology that would have to be far less than theirs. To come here they will likely have technology that would make slave labor useless. That means they would come for our minds and if they respect our minds we can only hope that they would not wish to rule over us but work with us.
Assuming though that they could get here and they wanted to rule over us what would happen? This is where the news gets very good for the aliens. Any species that had the technology to cross interstellar distances would be far more advanced than us. The energies involved in that trip would allow them to conquer us in hours.
So do we have to face the possibility that someday in the future aliens will take over and rule the earth? Perhaps but it is far more likely that if aliens do exist they will simply terraform worlds or find world that don’t have intelligent life because the truth is that the universe is vast and we just aren’t worth taking over.