Why would aliens intend to visit earth?
These are my speculations,
Studying human colony system. We humans are researching on ant colony algorithms, Swarm optimization, bird flocking etc. So like wise they could be researching about us, how we are evolving towards a type-1 civilization.
How a civilization is getting dominance over life forms. We can observe the fact that humans are dominant species in earth and they are using all natural/earthly resources and thereby depleting the conventional forms of energy. They could be studying how a life form could bring destruction to an entire planet.
Inner conflict in a civilization . In order to visit the earth, the aliens species should be type-2 or advanced civilization. They could have resolved their inner conflicts before evolving into type-2. They will be an united civilization (no religious and racist boundaries). So they could study humans about their religious conflicts , racism, earthly boundaries, war, terrorism, democracy etc.
Trying to save earth. They may be trying to warn us about other potential danger, or could be trying to save earthlings from getting extinct.
Getting humans into a galactic alliance . Their will be other advanced aliens , so this aliens want to join their team to build up a galactic alliance, may be for a peace treaty or for building an army against other species.
Invading Earth . Invasion will be a walk in the park for aliens. But still there is a chance for study/research, how we are capable of building a strong resistance against them, our armory, weaponry, will power so and so.
- Conquest. For the purposes of discussion, let's assume that there are no intelligent space-faring species within a radius of several light years from Earth (this seems, at least superficially, to be the case as far as we now can tell). If a space-faring species from a home world many light years distant from us has the capability to travel so far as to casually visit our planet, I think it's plausible to assume that they would not have much to gain from the conquest of Earth for any of the usual reasons, like procuring resources. They would already have plenty of raw materials at their disposal. But what if such a space-faring species were nomadic in nature, galactic hunter-gatherers moving through space over the course of thousands or even millions of years in much the same way hungry after-church diners move through a lunch buffet? The Earth might make a juicy morsel indeed; such a species might wish to subjugate our planet for its own sustenance, particularly if its natural habitat and biological needs were rather akin to ours. In much the same way that humans consume meat because it is a ready-made, rich source of nutrition, the trappings of a human civilization might be much more appetizing to such an alien race than the prospect of scavenging asteroids and desert planets for generations on end. Alternatively, they might wish to settle here for a while, a prospect which they would likely find easier to achieve without the interference of humankind.
- Establishing friendly relations. On the other hand, a nomadic super-intelligence might, after evaluating our planet and its inhabitants, decide that making friends with Earth would be more to its long-term advantage than a ransacking. Perhaps they would seek the prospect of free passage to and from our planet during their extensive travels, making a sort of wilderness way-station out of our solar system. They might even be willing to trade with us for the privilege, and in doing so, would undoubtedly create a kind of second Renaissance on Earth as our people became exposed to new ideas, new technologies, new perspectives and customs.
- Research. Perhaps a quite advanced alien race has visited us already, or even visits regularly, without our being aware of it. Maybe we are under investigation. For reasons of economy and security, these aliens may seek to carry out this research via unmanned probes, much as we currently study planets other than our own. What information they would be seeking is certainly open to speculation: having detected our presence through some means - our radio transmissions, perhaps -they might be scouting as a prelude to either of the aforementioned purposes, or 'just because.' As an extreme hypothesis (but, in my view, a rather more plausible one than we might be ready to admit), perhaps our entire biosphere is actually an experiment undertaken by extraterrestrials, something vaguely analogous to an ant farm or aquarium. They'd certainly want to check in on events from time to time at least, or maybe it could be that we are continuously monitored, totally unaware, by alien eyes and minds.
My "gut feeling," for whatever it's worth, is that even if our galactic neighborhood contains as many as a few hundred species with cultures and technologies roughly comparable to our own, it is likely that very few if any of them will ever encounter one another. I think this for two reasons: first, an advanced civilization seems about as likely to destroy itself unintentionally, or to succumb to natural catastrophes, as it is to persevere perpetually (in other words, civilization may not, as a rule, last very long at all on cosmic timescales); and second, even for a very advanced civilization, regular interstellar travel-and-return is not likely to be a sustainable enterprise in terms of return on investment. The distances are just too vast spatially and temporally, which is why I suspect that if we are ever confronted by an alien race or happen upon one ourselves, it will be via a nomadic space-faring existence, not one based on planet-dwelling.
There may be a lot of reasons. In fact I guess that any reason you my think of is valid given the fact that we not yet know any alien intelligence. My guesses of most common reasons are:
Advanced space faring civilization must have scientific knowledge to do so. One of ingredients of scientific progress is curiosity. Therefore aliens might be driven be sheer curiosity to learn about us. We humans will certainly do it if we will discover any alien intelligence that would be within our range to visit.
Trading resources with Earth is rather not economical after all asteroids are much better source for advanced civilization. However we have immaterial goods to trade. We humans consume lot of "data" in form of movies, pictures, texts, game essentially anything that is result of creativity. Aliens might be the same and it that department we have lot to offer. Of course that will need both sides to understand each other but assuming that it is possible trade relations might be established.
We don't have any real evidence extraterrestrials exist, much less any they have ever visited Earth. We have hundreds of stories, anecdotes, photographs, films, but no solid evidence.
Anyone who claims to have encountered a 30-foot (9-meter) long winged fire-breathing dragon, however sincere their beliefs that it really occurred, must provide evidence greater than a photograph and their sworn statement. However well-meaning and honest the reporter, there is not enough evidence that'll dragons ever existed. In contrast, while it is reasonably scarce there is sufficient evidence that the equally large and remarkable dinosaurs existed from 200 to 65-million years ago.
How or even why extraterrestrials would cross a minimum of 27,000,000,000,000 miles (40,000,000,000,000 km) just to visit is an important question you might want to consider.
With all due respect, I am suggesting that if extraterrestrials actually existed we would all know about it, they'd be routinely written up in science textbooks, and most importantly, scientists would be actively studying them.
Extraterrestrials, like dinosaurs, and winged, fire breathing dragons, are definitely a part of our culture, found in YouTube videos, televising programs, movies, cartoons, comic books and coloring books. Dragons were once wholly believed to exist. Today they are studied by people interested in art, folklore, and mythology. Not by scientists.
Assuming they are intelligent beings just like human but with more advanced civilization, then we could reflect to ourselves upon guessing what would be their motives:
- Seeking discovery and scientific knowledge. NASA mentioned this as one of their reason to explore space, typically done by scientific minded nations or civilization. Based on the general reluctance of Aliens in making contact with human civilization, their elusive behavior, the sightings of probe-like behaviors from the UFO, or even the act of abducting human and animals for laboratory tests, hence in my opinion this is the most plausible hypothesis at the moment.
- Seeking relationship, as a mutual relationship between strong civilizations would increase the likelihood of individual civilizations to survive or even thrive. Think of NATO (North Atlantic Treaty Organization), or OPEC (Organization of the Petroleum Exporting Countries). It's the motive of Space Brothers alliance as proposed by George Adamski and other contactee . It's also a popular theme for intelligent sci-fi series as well, like Star Trek.
- Patronage, like the act of modern human in creating humanity NGO, or creating sanctuary for endangered animals. A popular hypothesis among Ancient Astronauts studies popularized by Von Daniken, where the legend of Gods from old civilizations are perceived more as interaction from a superior intelligent civilizations transferring some of their advanced knowledge and science, instead of a metaphysical events.
- Warding (or The Zoo hypothesis), it's somewhat similar with Patronage, but with emphasis on not to contaminate or interfere with human civilization, and let it achieve advancement on its own before making the First Contact. This is the idea that visualized in many Star Trek episodes and movie adaption upon encountered less advanced civilizations.
- Seeking fame & glory, like Christopher Colombus did when setting sail to reach for far East and established a shorter route for spice trading, or all of the races to get to a specific point first, e.g.: Race to the South Pole, Race to the Moon, first ascent to Mount Everest, etc.
- Seeking resources, like Marco Polo did hundreds of years ago to establish a trade route between European and Asian countries. It is also the hypothesis put forward by Zecharia Sitchin study on Anunnaki and planet Nibiru, which he claimed based on translation of Mesopotamian iconography and symbolism. Also a theme behind sci-fi movies like Avatar and Aliens, where human plays the Alien role.
- Colonization, which is the expansion of authorities over people or territories, like what the old kingdoms did in the past. A major hypothesis on the lores of warring alien races on pre-historic Earth, i.e.: Draconians vs Greys vs Nordics. Also a popular sci-fi plot for Aliens visiting earth, e.g.: "Independence Day","Battleship","Mars Attack","V", or "Invasion of a Body Snatcher". Prominent scientist Stephen Hawking also warn against the possibilities of hostile Alien civilizations out there, and discouraged us from initiating contact for fear of being colonized or even destroyed. He had a change of mind though, when in 2015 announced his involvement in Breakthrough Listen initiative.
There is also a less popular hypothesis which suggests that there are some Alien life forms that visiting Earth for reproduction purpose, more like Salmon migration to rivers during mating period. However it hasn't gained much popularity in term of studies, and it involves presumably unintelligent alien life forms.
If an alien species with the capability of traveling great distances was to come to Earth, you are looking at one of two possibilities. Possibility one they are here for our natural resources and they will remove the pestand they will remove the pests ie. humans. Possibility two is they are looking for labor and enslave the human population. I personally hope for a hopeful third option which is just to explore new worlds.